BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Yan Soibelman (Kansas State University)
DTSTART:20200416T203000Z
DTEND:20200416T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/1
DESCRIPTION:Title: Holomorphic Floer theory and deformation quantization\nby Yan
Soibelman (Kansas State University) as part of M-seminar\n\n\nAbstract\nI
n his 21st problem Hilbert asked about reconstruction of Fuchsian differen
tial equation from its monodromy. This Riemann-Hilbert problem has a long
history of solutions and counterexamples. During last decades it was gener
alized in two different directions. Most well-known is the generalization
to higher dimensions and D-modules\, with possibly irregular singularities
. The monodromy data are replaced by constructble sheaves. Another\, less
known\, generalization deals with not necessarily differential equations\
, e.g. with difference of q-difference ones.\n\nIn 2014 together with Maxi
m Kontsevich we started a project on what we called Holomorphic Floer theo
ry. The word "holomorphic" refers to the fact that we consider Floer theo
ry (e.g. Fukaya categories) for comlex symplectic manifolds. Aim of my tal
k is to explain some parts of the project which lead to a general formula
tion of the Riemann-Hilbert correspondence as a relation between Floer the
ory and deformation quantization.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Cheltsov (University of Edinburgh)
DTSTART:20200430T193000Z
DTEND:20200430T203000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/2
DESCRIPTION:Title: K-stability of Fano 3-folds\nby Ivan Cheltsov (University of
Edinburgh) as part of M-seminar\n\n\nAbstract\nA smooth Fano manifold admi
ts a Kahler-Einstein metric if and only if it is K-polystable (K-stable if
the automorphism group is finite). In this talk\, I will explain how to p
rove and disprove K-polystability and K-stability using basic tools of bir
ational geometry. The talk will will be focused on smooth Fano threefolds.
This is a joint group project with Carolina Araujo\, Ana-Maria Castravet\
, Kento Fujita\, Anne-Sophie Kaloghiros\, Jesus Martinez-Garcia\, Constant
in Shramov\, Hendrick S\\"u\\ss\, and Nivedita Viswanathan.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peng Zhou (UC Berkeley)
DTSTART:20200423T203000Z
DTEND:20200423T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/3
DESCRIPTION:Title: Variation of toric GIT quotient and variation of Lagrangian skele
ton\nby Peng Zhou (UC Berkeley) as part of M-seminar\n\n\nAbstract\nIt
is well-known that the GIT quotient depends on a choice of an equivariant
ample line bundle. Various different quotients are related by birational
transformations\, and their B-models (D^bCoh) are related by semi-orthogon
al decompositions\, or derived equivalences. If we apply mirror symmetry\,
it is natural to ask how the A-models of the mirror of various quotients
are related. We give a description in the case of toric variety\, where th
e A-side is described using constructible sheaves and Lagrangian skeleton.
\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Kerr (Kansas State University)
DTSTART:20200507T203000Z
DTEND:20200507T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/4
DESCRIPTION:Title: Phase tropical hypersurfaces\nby Gabriel Kerr (Kansas State U
niversity) as part of M-seminar\n\n\nAbstract\nIn this talk\, I will give
the definition of the phase tropical hypersurface arising from a polytope
with a coherent triangulation. This is a topological version of a singular
integrable system. I will discuss aspects of a joint work with I. Zharko
v which proved that there is a homeomorphism between the phase tropical hy
persurface and a complex hypersurface (this is known as Viro's Conjecture)
. With this\, Mikhalkin's pair of pants decomposition of a complex hypersu
rface becomes a polyhedral decomposition and several Lagrangians arising i
n mirror symmetry have conjectural accompanying decompositions which are w
ell controlled topologically. I will discuss these subcomplexes and eviden
ce of their mirrors in matrix factorizations. This is joint work with I. Z
harkov.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuel Diaconescu (Rutgers University)
DTSTART:20200514T160000Z
DTEND:20200514T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/5
DESCRIPTION:Title: Mckay correspondence and cohomological Hall algebras\nby Eman
uel Diaconescu (Rutgers University) as part of M-seminar\n\n\nAbstract\nIt
is shown that derived McKay correspondence for type A Kleinian singularit
ies induces an isomorphism of cohomological Hall algebras associated to se
mistable objects of fixed slope. Moreover\, these algebras are explicitely
determined in terms of Yangians associated to finite type A Dynkin quiver
s. This is joint work with Mauro Porta and Francesco Sala.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Neitzke (Yale University)
DTSTART:20200521T203000Z
DTEND:20200521T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/6
DESCRIPTION:Title: Abelianization of flat connections\, and its q-deformation\nb
y Andrew Neitzke (Yale University) as part of M-seminar\n\n\nAbstract\nAbe
lianization of flat connections is a construction motivated by supersymmet
ric quantum field theory\, which has turned out to be connected to various
bits of geometry -- in particular\, to Donaldson-Thomas theory\, cluster
algebra\, the exact WKB method for analysis of ODEs\, and hyperkahler geom
etry. In some of these subjects it is known that there exists a natural q-
deformation which takes us from the commutative to the noncommutative worl
d. This suggests that there ought to exist a q-deformation of abelianizati
on as well. I will explain joint work in progress with Fei Yan on construc
ting this q-deformation in a geometric way using spectral networks. This c
onstruction is inspired by related work by various authors\, especially Bo
nahon-Wong\, Gabella\, Gaiotto-Witten. One byproduct is a new scheme for c
omputing known polynomial invariants of links in R^3\, which generalizes t
he usual "vertex models".\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umut Varolgunes (Stanford University)
DTSTART:20200528T203000Z
DTEND:20200528T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/7
DESCRIPTION:Title: Non-archimedean mirrors of symplectic cluster manifolds in real d
imension four\nby Umut Varolgunes (Stanford University) as part of M-s
eminar\n\n\nAbstract\nI will start by explaining what I mean by a symplect
ic cluster manifold focusing on how to represent them by certain combinato
rial data called an eigenray diagram (4d only!). These symplectic manifold
s admit a Lagrangian fibration over the real plane with only focus-focus s
ingularities. They do not need to have convex boundary or exact symplectic
form\, but they are open and geometrically bounded. Eigenray diagrams are
related to toric models and the relation will be briefly mentioned. Then\
, using relative symplectic cohomology and a locality statement that relie
s on monotonicity techniques\, I will describe conjectural mirrors of symp
lectic cluster manifolds as certain deformed (over the Novikov field) clus
ter varieties. This is joint work with Yoel Groman.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Negut (MIT)
DTSTART:20200604T190000Z
DTEND:20200604T200000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/8
DESCRIPTION:Title: A brief survey of 2D K-HAs\nby Andrei Negut (MIT) as part of
M-seminar\n\n\nAbstract\nI will give an introduction into the study of an
interesting class of algebraic structures\, namely K-theoretic Hall algebr
as of quivers and surfaces. The emphasis will be on computational tools\,
such as shuffle algebras and intersection theory\, and how to use them in
order to obtain concrete applications to problems from geometry\, represen
tation theory and mathematical physics.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Pantev (University of Pennsylvania)
DTSTART:20200611T160000Z
DTEND:20200611T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/9
DESCRIPTION:Title: Enhanced moduli of D-branes and superpotentials\nby Tony Pant
ev (University of Pennsylvania) as part of M-seminar\n\n\nAbstract\nModuli
of D-branes on to Calabi-Yau manifolds are naturally equipped with enhanc
ed geometric structures which play important role in classical field theor
y and are an essential input for the quantization problem. I will explain
how one can recognize when such enhanced structures arise from a local or
global superpotential. I will discuss applications to higher dimensional C
hern-Simons functionals\, to non-abelian Hodge theory\, to the moduli spac
es of framed sheaves on log Calabi-Yau geometries\, and to the moduli of m
onopoles. This is based on joint works with Calaque\, Katzarkov\, Toen\, V
aquie\, and Vezzosi.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mina Aganagic (UC Berkeley)
DTSTART:20200618T203000Z
DTEND:20200618T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/10
DESCRIPTION:Title: Knot categorification and mirror symmetry\nby Mina Aganagic
(UC Berkeley) as part of M-seminar\n\n\nAbstract\nI will describe some asp
ects of two geometric approaches to the knot categorification problem\, wh
ich follow from string theory. They provide new examples of homological mi
rror symmetry and its equivariant generalization\, with deep relation to r
epresentation theory.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dima Arinkin (University of Wisconsin-Madison)
DTSTART:20200625T180000Z
DTEND:20200625T190000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/11
DESCRIPTION:Title: Singular support of categories\nby Dima Arinkin (University
of Wisconsin-Madison) as part of M-seminar\n\n\nAbstract\nIn many situatio
ns\, geometric objects on a space have some kind of singular support\, whi
ch refines the usual support. For instance\, for smooth X\, the singular s
upport of a D-module (or a perverse sheaf) on X is as a conical subset of
the cotangent bundle\; there is also a version of this notion for coherent
sheaves on local complete intersections. I would like to describe a highe
r categorical version of this notion. Let X be a smooth variety\, and let
Z be a closed conical isotropic subset of the cotangent bundle of X. I wil
l define a 2-category associated with Z\; its objects may be viewed as `ca
tegories over X with singular support in Z'. In particular\, if Z is the z
ero section\, this gives the notion of categories over Z in the usual sens
e.The project is motivated by the local geometric Langlands correspondence
\; time permitting\, I plan to sketch the relation with the Langlands corr
espondence at the end of the talk.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Smirnov (University of North Carolina)
DTSTART:20200709T183000Z
DTEND:20200709T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/12
DESCRIPTION:Title: Elliptic stable envelopes and symplectic duality\nby Andrey
Smirnov (University of North Carolina) as part of M-seminar\n\n\nAbstract\
nIn this talk I'll explain the following idea: "the elliptic stable envelo
pes of symplectic dual varieties coincide." I'll describe a simplest examp
le of $T^*P^1$ in details and discuss other cases in which the statement i
s proven.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech)
DTSTART:20200716T203000Z
DTEND:20200716T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/13
DESCRIPTION:Title: Rozansky-Witten geometry of Coulomb branches\nby Sergei Guko
v (Caltech) as part of M-seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kontsevich (IHES)
DTSTART:20200702T183000Z
DTEND:20200702T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/14
DESCRIPTION:Title: On higher critical points in calculus of variations\nby Maxi
m Kontsevich (IHES) as part of M-seminar\n\n\nAbstract\nIn classical mecha
nics\, the variational principle implies the existence of a canonical clos
ed 2-form on the space of solutions of the Euler-Lagrange equation. I will
explain an origin of this 2-form via coarse geometry\, and relation with
the 1st cohomology with compact support of the space-time. Then I'll intro
duce a generalization to higher critical points. The basic example is high
er Chern-Simons theory on 5-dimensional manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Dimofte (UC Davis)
DTSTART:20200723T203000Z
DTEND:20200723T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/15
DESCRIPTION:Title: 3D Mirror Symmetry and HOMFLY-PT Homology\nby Tudor Dimofte
(UC Davis) as part of M-seminar\n\n\nAbstract\nA recent construction of HO
MFLY-PT knot homology by Oblomkov-Rozansky has its physical origin in “B
-twisted” 3D N=4 gauge theory\, with adjoint and fundamental matter. Mat
hematically\, the construction uses certain categories of matrix factoriza
tion. We apply 3D Mirror Symmetry to identify an A-twisted mirror of this
construction. In the case of algebraic knots\, we find that knot homology
on the A side gets expressed as cohomology of affine Springer fibers (rela
ted but not identical to work if Gorsky-Oblomkov-Rasmussen-Shende). More g
enerally\, we propose a Fukaya-Seidel category mirror to the Oblomkov-Roza
nsky matrix factorization.\nJoint work with N Garner\, J Hilburn\, A Oblom
kov\, and L Rozansky.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Zaslow (Northwestern University)
DTSTART:20200730T203000Z
DTEND:20200730T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/16
DESCRIPTION:Title: A Diagrammatic Calculus for Legendrian Surfaces\nby Eric Zas
low (Northwestern University) as part of M-seminar\n\n\nAbstract\nI will d
escribe work with Roger Casals. We show how planar diagrams called N-grap
hs encode Legendrian surfaces which cover the plane N-to-1. These N-graph
s can be used to express Reidemeister moves\, surgeries\, and connect sums
\; to describe a Markov move a` la braids\; to construct large classes of
examples of any genus\; to define moduli spaces which can be used to disti
nguish surfaces up to Legendrian isotopy\; to discuss cluster charts and m
utations\; to construct exact Lagrangian fillings\; and to define a planar
algebra.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Ekholm (Uppsala University)
DTSTART:20200806T180000Z
DTEND:20200806T190000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/17
DESCRIPTION:Title: Holomorphic curves on knot conormals\nby Tobias Ekholm (Upps
ala University) as part of M-seminar\n\n\nAbstract\nWe give an overview of
results from the last few years. We first describe the "skeins on branes
” approach (joint with Shende) to open Gromov-Witten invariants and show
how this leads to a direct geometric interpretation of the quantization o
f the augmentation variety of a Legendrian knot conormal\, as a quantum cu
rve. We then describe a partially conjectural quiver picture (joint with K
ucharski and Longhi) for the holomorphic curve counts on a Lagrangian knot
conormal\, where all curves stems from a finite set of basic holomorphic
disks. Via more refined disk counts\, this quiver picture leads to a desc
ription of HOMFLY homology. Finally\, we apply similar reasoning to the kn
ot complement Lagrangian we find that a count of holomorphic annuli\, aft
er SFT stretching\, can be viewed as the semi-classical limit of an instan
ce of Gukov-Pei-Putrov-Vafa Z-hat theory. This leads to a direct geometric
interpretation of the Z-hat invariant (joint with Guen\, Gukov\, Kucharsk
i\, Park\, and Sulkowski).\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael McBreen (CUHK)
DTSTART:20200813T203000Z
DTEND:20200813T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/18
DESCRIPTION:Title: Symplectic duality and twisted quasimaps\nby Michael McBreen
(CUHK) as part of M-seminar\n\n\nAbstract\nHypertoric varieties are a hyp
erkahler analogue of toric varieties which arise frequently in geometric r
epresentation theory. I will explain how the virtual count of twisted quas
imaps to a hypertoric variety can be reformulated as a kind of trace on a
periodized symplectically dual hypertoric. Joint work with Artan Sheshmani
and Shing-Tung Yau.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiraku Nakajima (IPMU)
DTSTART:20200820T230000Z
DTEND:20200821T000000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/19
DESCRIPTION:Title: Bow varieties and representations of affine Lie algebras\nby
Hiraku Nakajima (IPMU) as part of M-seminar\n\n\nAbstract\nCherkis bow va
rieties of affine type A are common generalization of quiver varieties and
Coulomb branches of affine type A. We construct commuting representations
of affine $sl_l$ and $sl_n$ on the direct sum of their homology groups (m
ore precisely homology groups of attracting sets)\, as common generalizati
on of corresponding results for quiver varieties and geometric Satake for
affine $sl_n$. This is a part of a joint work in progress with Dinakar Mut
hiah.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pyongwon Suh (Northwestern University)
DTSTART:20200827T203000Z
DTEND:20200827T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/20
DESCRIPTION:Title: The coherent-constructible correspondence for toric projective b
undles\nby Pyongwon Suh (Northwestern University) as part of M-seminar
\n\n\nAbstract\nThis talk is about the coherent-constructible corresponden
ce (CCC). CCC is a version of homological mirror symmetry for toric variet
ies. It equates the derived category of coherent sheaves on a toric variet
y and the category of constructible sheaves on a torus that satisfy some c
ondition on singular support. Recently\, Harder-Katzarkov conjectured that
there should be a version of CCC for toric fiber bundles and they proved
their conjecture for $\\mathbb{P}^1$-bundles. I will explain how we can pr
ove (half of) their conjecture for $\\mathbb{P}^n$-bundles. If time permit
s\, I will give a more precise version of the conjecture for arbitrary tor
ic fiber bundles.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Goncharov (Yale University)
DTSTART:20200903T203000Z
DTEND:20200903T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/21
DESCRIPTION:Title: The second universal motivic Chern class and cluster structure o
f moduli spaces of G-local systems\nby Alexander Goncharov (Yale Unive
rsity) as part of M-seminar\n\n\nAbstract\nThe second motivic Chern class
is the generator of the degree 4\, weight 2 motivic cohomology of BG\, whe
re G is a split simple algebraic group over Q. I will construct a collecti
on of explicit cocycles for the second motivic Chern class. It has a numbe
r of applications\, such as local combinatorial formulas for the usual sec
ond Chern class of a G-bundle over a manifold\, or explicit constructions
of the determinant bundle on Bun(G)\, the extension of G by K_2 etc. The c
onstruction is closely related to the cluster structure of the moduli spac
e of decorated G-local systems on a surface S with boundary.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (University of Toronto)
DTSTART:20200910T203000Z
DTEND:20200910T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/22
DESCRIPTION:Title: Categorical g-actions for modules over truncated shifted Yangian
s\nby Joel Kamnitzer (University of Toronto) as part of M-seminar\n\n\
nAbstract\nGiven a representation V of a reductive group G\, Braverman-Fin
kelberg-Nakajima defined a Poisson variety called the Coulomb branch\, usi
ng a convolution algebra construction. This variety comes with a natural
deformation quantization\, called a Coulomb branch algebra. Important cas
es of these Coulomb branches are (generalized) affine Grassmannian slices\
, and their quantizations are truncated shifted Yangians.\nMotivated by th
e geometric Satake correspondence and the theory of symplectic duality/3d
mirror symmetry\, we expect a categorical g-action on modules for these tr
uncated shifted Yangians. I will explain three results in this direction.
First\, we have an indirect realization of this action\, using equivalen
ces with KLRW-modules. Second\, we have a geometric relation between these
generalized slices by Hamiltonian reduction. Finally\, we have an algebr
aic version of this Hamiltonian reduction which we are able to relate to t
he first realization.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Mellit (University of Vienna)
DTSTART:20200917T183000Z
DTEND:20200917T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/23
DESCRIPTION:Title: The curious hard Lefschetz property for character varieties\
nby Anton Mellit (University of Vienna) as part of M-seminar\n\n\nAbstract
\nI will talk about a way to decompose various character varieties into ce
lls where each cell looks like a product of an affine space and a symplect
ic torus. This can be thought of as abelianization. As an application\, we
deduce the curious hard Lefschetz property conjectured by Hausel\, Letell
ier and Rodriguez-Villegas\, which claims that the operator of cup product
with the class of the holomorphic symplectic form is an isomorphism betwe
en complementary degrees of the associated graded with respect to the weig
ht filtration of the cohomology.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junxiao Wang (Northwestern University)
DTSTART:20200924T203000Z
DTEND:20200924T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/24
DESCRIPTION:Title: The Gamma Conjecture for the tropical 1-cycles in local mirror s
ymmetry\nby Junxiao Wang (Northwestern University) as part of M-semina
r\n\n\nAbstract\nThe Gamma Conjecture in mirror symmetry relates central c
harges of dual objects. Mathematically\, periods of a Lagrangian submanifo
ld are related to characteristic classes of the mirror coherent sheaf. In
this talk\, I will test the Gamma Conjecture in the setting of local mirro
r symmetry. For a given coherent sheaf on the canonical bundle of a smooth
toric surface\, I will identify a 3-cycle in the mirror using tropical ge
ometry by comparing its period with the central charge of the coherent she
af through the Gamma Conjecture. If time permits\, I will also discuss abo
ut the higher dimensional case. This work is based on Ruddat and Siebert's
work on the period computation and is inspired by Abouzaid\, Ganatra\, Ir
itani and Sheridan's work on the Gamma Conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Okounkov (Columbia University)
DTSTART:20201001T203000Z
DTEND:20201001T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/25
DESCRIPTION:Title: Monodromy: yesterday\, today\, and tomorrow\nby Andrei Okoun
kov (Columbia University) as part of M-seminar\n\n\nAbstract\nMonodromy of
solutions of differential equations is very much a recurring theme in mat
hematics\, from XIX century to the present day. For instance\, the Kohno-D
rinfeld theorem from 30+ years ago\, which describes the monodromy of the
Knizhnik-Zamolodchikov equations of the Conformal Field Theory in term of
braiding for the associated quantum group\, as a striking example of how r
epresentation-theoretic ideas may shed light on this problem. In this talk
\, I will talk about some more recent advances that include ideas from enu
merative geometry and representation theory over a field of prime characte
ristic.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Cherkis (University of Arizona)
DTSTART:20201008T203000Z
DTEND:20201008T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/26
DESCRIPTION:Title: Doubly Periodic Monopoles and Exploded Geometry\nby Sergey C
herkis (University of Arizona) as part of M-seminar\n\n\nAbstract\nClassic
al monopole dynamics captures both the geometry of the moduli spaces of qu
antum supersymmetric gauge theories and the dynamics of certain brane conf
igurations. It is also a good source of self-dual gravitational instanton
s -- hyperkahler manifolds in real dimension four.\n\nAfter an overview of
these relations for various monopoles\, we shall focus on doubly periodic
monopoles and their moduli spaces. In particular\, the natural compactif
ication of these moduli spaces is formulated in terms of exploded geometry
of Brett Parker.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ron Donagi (University of Pennsylvania)
DTSTART:20201015T203000Z
DTEND:20201015T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/27
DESCRIPTION:Title: Families of Hitchin systems and N=2 theories\nby Ron Donagi
(University of Pennsylvania) as part of M-seminar\n\n\nAbstract\nMotivated
by the connection to 4d N=2 theories\, we study the global behavior of fa
milies of tamely-ramified $SL_N$ Hitchin integrable systems as the underly
ing curve varies over the Deligne-Mumford moduli space of stable pointed c
urves. In particular\, we describe a flat degeneration of the Hitchin syst
em to a nodal base curve and show that the behaviour of the integrable sys
tem at the node is partially encoded in a pair (O\,H) where O is a nilpote
nt orbit and H is a simple Lie subgroup of FO\, the flavour symmetry group
associated to O. The family of Hitchin systems is nontrivially-fibered ov
er the Deligne-Mumford moduli space. We prove a non-obvious result that th
e Hitchin bases fit together to form a vector bundle over the compactified
moduli space. For the particular case of $M_{0\,4}$\, we compute this vec
tor bundle explicitly. Finally\, we give a classification of the allowed p
airs (O\,H) that can arise for any given N. (This is joint work with Aswin
Balasubramanian and Jacques Distler)\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zack Sylvan (Columbia University)
DTSTART:20201022T203000Z
DTEND:20201022T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/28
DESCRIPTION:Title: Homological mirror symmetry near SYZ singularities\nby Zack
Sylvan (Columbia University) as part of M-seminar\n\n\nAbstract\nI'll disc
uss homological mirror symmetry for the spaces $\\prod x_i=1+\\sum y_j$\,
which appear as neighborhoods of SYZ singularities. I'll start by discussi
ng wrapped HMS\, and then I'll explain how to cook up a torus-like closed
Lagrangian brane for every point of the mirror. This is work in progress w
ith M. Abouzaid and in part with A. Perry.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Yue Yu (Université Paris-Sud)
DTSTART:20201026T160000Z
DTEND:20201026T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/29
DESCRIPTION:Title: Frobenius structure conjecture and application to cluster algebr
as\nby Tony Yue Yu (Université Paris-Sud) as part of M-seminar\n\n\nA
bstract\nI will explain the Frobenius structure conjecture of Gross-Hackin
g-Keel in mirror symmetry\, and an application towards cluster algebras. I
will show that the naive counts of rational curves in an affine log Calab
i-Yau variety U\, containing an open algebraic torus\, determine in a simp
le way\, a mirror family of log Calabi-Yau varieties\, as the spectrum of
a commutative associative algebra equipped with a multilinear form. The st
ructure constants of the algebra are constructed via counting non-archimed
ean analytic disks in the analytification of U. I will explain various pro
perties of the counting\, notably deformation invariance\, symmetry\, glui
ng formula and convexity. In the special case when U is a Fock-Goncharov s
kew-symmetric X-cluster variety\, our algebra generalizes\, and in particu
lar gives a direct geometric construction of\, the mirror algebra of Gross
-Hacking-Keel-Kontsevich. The comparison is proved via a canonical scatter
ing diagram defined by counting infinitesimal non-archimedean analytic cyl
inders\, without using the Kontsevich-Soibelman algorithm. Several combina
torial conjectures of GHKK follow readily from the geometric description.
This is joint work with S. Keel\, arXiv:1908.09861. If time permits\, I wi
ll mention another application towards the moduli space of KSBA stable pai
rs\, joint with P. Hacking and S. Keel\, arXiv: 2008.02299.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dennis Gaitsgory (Harvard University)
DTSTART:20201105T213000Z
DTEND:20201105T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/30
DESCRIPTION:Title: The moduli space of l-adic local systems and application to geom
etric and classical Langlands theory\nby Dennis Gaitsgory (Harvard Uni
versity) as part of M-seminar\n\n\nAbstract\nIn the talk we will define a
new geometric object\, the stack of local systems with restricted variatio
n. We will discuss the appropriately modified version of the geometric Lan
glands conjecture and its relationship with the classical Langlands conjec
ture via the operation of categorical trace of Frobenius.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoosik Kim (Brandeis University)
DTSTART:20201112T213000Z
DTEND:20201112T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/31
DESCRIPTION:Title: Disc potential functions of Quadrics\nby Yoosik Kim (Brandei
s University) as part of M-seminar\n\n\nAbstract\nA disc potential functio
n introduced by Fukaya—Oh—Ohta—Ono plays an important role in studyi
ng Lagrangian submanifolds and the ambient symplectic manifold. In this ta
lk\, I will explain how to compute the disc potential function of quadrics
. The potential function provides the Landau-Ginzburg mirror\, which agree
s with Przyjalkowski’s mirror and a cluster chart of Pech—Rietsch—Wi
lliams’ mirror.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vivek Shende (UC Berkeley)
DTSTART:20201119T193000Z
DTEND:20201119T203000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/32
DESCRIPTION:Title: Sheaf quantization in Weinstein symplectic manifolds\nby Viv
ek Shende (UC Berkeley) as part of M-seminar\n\n\nAbstract\nI will explain
how\, using only the microlocal sheaf theory (i.e. no holomorphic curves)
\, one can produce a category associated to a Weinstein symplectic manifol
d. Exact Lagrangians will give objects of this category. This is work wi
th David Nadler. (A posteriori\, it is possible to show that this categor
y is equivalent to the Fukaya category\, but that is a long and different
story).\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Nekrasov (Simons Center for Geometry and Physics)
DTSTART:20201203T213000Z
DTEND:20201203T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/33
DESCRIPTION:Title: Towards Lefschetz thimbles in field theory\nby Nikita Nekras
ov (Simons Center for Geometry and Physics) as part of M-seminar\n\n\nAbst
ract\nI will review the quantization procedure viewed from a higher dimens
ional perspective: old-fashioned path integrals\, Kontsevich Poisson sigma
model\, cc branes of Kapustin-Orlov\, and\, finally\, four dimensional O
mega-deformed N=2 gauge theories. By rephrasing the computation of quantum
model partition function in four dimensional language we arrive at the mo
tivation to search for critical points of analytically continued (complexi
fied) action functional. I will then report on the recent progress (in a j
oint work with I.Krichever) in this problem in the case of two dimensional
sigma models\, notably with the target spaces being the spheres and compl
ex projective spaces.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Addington (University of Oregon)
DTSTART:20210128T213000Z
DTEND:20210128T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/34
DESCRIPTION:Title: Derived autoequivalences of moduli spaces of sheaves on K3 surfa
ces\nby Nicolas Addington (University of Oregon) as part of M-seminar\
n\n\nAbstract\nSome years ago I constructed a new autoequivalence of the d
erived category\nof the Hilbert scheme of n points on a K3 surface using "
P-functors."\nLater Donovan\, Meachan\, and I extended the construction to
some moduli\nspaces of torsion sheaves\, and illuminated the geometric me
aning of the\nstory. Now my student Andrew Wray and I can extend it to mo
duli spaces of\nsheaves of any rank\, powered by a new proof of the standa
rd results about\nthose moduli spaces. We deform to a Hilbert scheme in o
ne step\, using\ntwistor lines.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Gaiotto (Perimeter Institute for Theoretical Physics)
DTSTART:20210204T213000Z
DTEND:20210204T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/35
DESCRIPTION:Title: Brane quantization\nby Davide Gaiotto (Perimeter Institute f
or Theoretical Physics) as part of M-seminar\n\n\nAbstract\nI will review
the A-model Gukov-Witten setup for the quantization of a phase space and i
ts relation to the analytic version of the Langlands correspondence recent
ly proposed by Etingof\, Frenkel and Kazhdan.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominic Joyce (University of Oxford)
DTSTART:20210211T170000Z
DTEND:20210211T180000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/36
DESCRIPTION:Title: Enumerative invariants in Algebraic Geometry and wall crossing f
ormulae\nby Dominic Joyce (University of Oxford) as part of M-seminar\
n\n\nAbstract\nIn Gross-Joyce-Tanaka arXiv:2005.05637\, we described a uni
versal conjectural picture for enumerative invariants counting semistable
objects in abelian categories/gauge theories\, which claimed that under so
me assumptions:\n (i) one can construct invariants\, as virtual classes in
the rational homology of the “projective linear” moduli stack\, for a
ll topological invariants (fixed Chern classes etc)\, including classes wi
th strictly semistables\;\n (ii) these invariants satisfy a wall-crossing
formula under change of stability condition\, written in terms of a Lie br
acket on the homology of the moduli stack\, which came out of my project o
n vertex algebra structures on homology of moduli stacks.\nWe proved the c
onjecture for representations of acyclic quivers.\n In work in progress\
, I have now proved/am proving versions of the conjectures for a broad fam
ily of settings in Algebraic Geometry\, in which invariants are formed usi
ng Behrend-Fantechi virtual classes. These include suitable quivers with r
elations\, coherent sheaves on curves\, surfaces and some 3-folds\, and al
gebraic Seiberg-Witten invariants and Donaldson invariants of projective c
omplex surfaces. The SW/Donaldson theory picture includes wall-crossing fo
rmulae\, related to those of Mochizuki\, which implicitly determine algebr
aic U(n) and SU(n) Donaldson invariants\, of any rank\, in terms of rank 1
Seiberg-Witten type invariants and invariants of Hilbert schemes of point
s\, for any projective complex surface\, without restriction on $b^1$\, or
$b^2_+$\, or a simple type assumption.\n The talk will give an overview o
f this programme.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Efimov (Steklov Institute for Mathematics)
DTSTART:20210218T170000Z
DTEND:20210218T183000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/37
DESCRIPTION:Title: Nuclear modules over proper DG algebras\nby Alexander Efimov
(Steklov Institute for Mathematics) as part of M-seminar\n\n\nAbstract\nI
will explain a certain general natural construction of a dualizable prese
ntable DG category Nuc(A) associated with a proper DG algebra (or a proper
DG category) A over a commutative ring k. As a special case\, it gives (a
n "unbounded" version of) the category of nuclear modules on a formal sche
me\, which was defined recently by Clausen and Scholze.\n The compact obj
ects of Nuc(A) are given by (the usual) pseudo-perfect A-modules PsPerf(A)
(i.e. those A-modules which are perfect over k). However\, unlike PsPerf(
A)\, the category Nuc(A) has very nice properties: it satisfies Zariski de
scent over Spec(k)\, and so does its continuous K-theory. Moreover\, its c
ontinuous K-theory and Hochschild homology are expected to have a very con
crete description in terms of A.\n I will also explain that Nuc(A) is a s
pecial case of an even more general notion/construction\, which (surprisin
gly) was not considered before: internal Hom in the symmetric monoidal cat
egory\, whose objects are dualizable presentable DG categories\, and the m
orphisms are given by strongly continuous functors (i.e. the functors whos
e right adjoint commutes with infinite direct sums).\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Nadler (UC Berkeley)
DTSTART:20210225T213000Z
DTEND:20210225T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/38
DESCRIPTION:Title: Verlinde formulas in Betti Geometric Langlands\nby David Nad
ler (UC Berkeley) as part of M-seminar\n\n\nAbstract\nI'll review the Bett
i variant of Geometric Langlands then describe progress towards expressing
automorphic categories of smooth curves in terms of such categories for m
arked genus zero curves. Time permitting I'll discuss specific application
s in low genus. Joint work with Zhiwei Yun.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Weekes (University of British Columbia)
DTSTART:20210304T213000Z
DTEND:20210304T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/39
DESCRIPTION:Title: Coulomb branches for quiver gauge theories with symmetrizers
\nby Alex Weekes (University of British Columbia) as part of M-seminar\n\n
\nAbstract\nBraverman-Finkelberg-Nakajima have recently given a mathematic
al construction of the Coulomb branches for 3d N=4 theories. From a repres
entation-theoretic perspective\, one reason that their work is especially
appealing is that affine Grassmannian slices of ADE types arise this way\,
associated to quiver gauge theories. By allowing general quivers\, Coulom
b branches also provide a candidate definition for affine Grassmannian sli
ces in all symmetric Kac-Moody types. In this talk I will discuss joint wo
rk with Nakajima\, where we generalize the BFN construction of the Coulomb
branch to incorporate "symmetrizers". In this way we recover affine Grass
mannian slices in BCFG type\, and a candidate definition for symmetrizable
Kac-Moody types.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Caldararu (University of Wisconsin-Madison)
DTSTART:20210311T213000Z
DTEND:20210311T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/40
DESCRIPTION:Title: A survey of categorical enumerative invariants\nby Andrei Ca
ldararu (University of Wisconsin-Madison) as part of M-seminar\n\n\nAbstra
ct\nI will survey recent progress in defining and computing categorical en
umerative invariants\, analogues of Gromov-Witten invariants defined direc
tly from a cyclic $A_\\infty$-category and a choice of splitting of the Ho
dge filtration on its periodic cyclic homology. A proposed definition of s
uch invariants appeared in 2005 in work of Costello\, but the original app
roach had technical problems that made computations impossible. New result
s allow us to give an alternate definition of Costello's invariants\, wher
e explicit computation is possible -- and indeed we apply our results to B
-model calculations for elliptic curves and categories of matrix factoriza
tions. My talk is based on joint work with Junwu Tu and Kevin Costello.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Soibelman (IHES)
DTSTART:20210318T183000Z
DTEND:20210318T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/41
DESCRIPTION:Title: Motivic invariants for moduli of parabolic Higgs bundles and par
abolic connections on a curve\nby Alexander Soibelman (IHES) as part o
f M-seminar\n\n\nAbstract\nMotivic classes can realize certain algebro-geo
metric invariants using elements of the Grothendieck ring of varieties or\
, more generally\, of stacks. I will introduce motivic classes through rat
ional point counting over a finite field\, then discuss motivic class comp
utations for moduli spaces and moduli stacks of semistable Higgs bundles (
as well as vector bundles with connections on a curve)\, and finish by add
ressing the parabolic case.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Polishchuk (University of Oregon)
DTSTART:20210325T203000Z
DTEND:20210325T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/42
DESCRIPTION:Title: Supermeasure on moduli of supercurves\nby Alexander Polishch
uk (University of Oregon) as part of M-seminar\n\n\nAbstract\nThis is a re
port on joint work with Giovanni Felder and David Kazhdan. I will discuss
the moduli space of supercurves and its compactification\, the moduli of s
table supercurves. As in the classical case\, the analog of Mumford’s is
omorphism gives an expression of the canonical bundle on this moduli space
in terms of the Berezinian of the Hodge bundle. We consider the correspon
ding supermeasure obtained from this isomorphism together with the natural
hermitian metric on the Hodge bundle. Our main results concern its polar
behaviour at infinity and on the null-theta divisor.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Rimanyi (University of North Carolina)
DTSTART:20210401T203000Z
DTEND:20210401T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/43
DESCRIPTION:Title: 3d mirror symmetry for characteristic classes of bow varieties\nby Richard Rimanyi (University of North Carolina) as part of M-seminar
\n\n\nAbstract\nOne of the predictions of N=4 d=3 mirror symmetry concerns
characteristic classes\, namely so-called stable envelopes of singulariti
es. We will explore the notion of stable envelopes\, their role in enumera
tive geometry and representation theory. Then we will discuss Cherkis bow
varieties that come in pairs (3d mirror pairs) such that the elliptic stab
le envelopes on two spaces in a pair conjecturally "coincide" (after tran
sposition\, switching equivariant and dynamical variables\, and inverting
ℏ).\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Webster (Perimeter Institute for Theoretical Physics)
DTSTART:20210408T203000Z
DTEND:20210408T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/44
DESCRIPTION:Title: Knot homology and coherent sheaves on Coulomb branches\nby B
en Webster (Perimeter Institute for Theoretical Physics) as part of M-semi
nar\n\n\nAbstract\nRecent work of Aganagic proposes the construction of a
homological knot invariant categorifying the Reshetikhin-Turaev invariants
of miniscule representations of type ADE Lie algebras\, using the geometr
y and physics of coherent sheaves on a space which one can alternately des
cribe as a resolved slice in the affine Grassmannian\, a space of G-monopo
les with specified singularities\, or as the Coulomb branch of the corresp
onding 3d quiver gauge theories. We give a mathematically rigorous constru
ction of this invariant\, and in fact extend it to an invariant of annular
knots\, using the theory of line operators in the quiver gauge theory and
their relationship to non-commutative resolutions of these varieties (gen
eralizing Bezrukavnikov's non-commutative Springer resolution).\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohammed Abouzaid (Columbia University)
DTSTART:20210415T193000Z
DTEND:20210415T203000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/45
DESCRIPTION:Title: Arnol'd Conjecture and Morava K-theory\nby Mohammed Abouzaid
(Columbia University) as part of M-seminar\n\n\nAbstract\nThe Arnol'd con
jecture on the minimal number of fixed points of a Hamiltonian diffeomorph
ism has motivated a large number of developments in symplectic topology ov
er the last few decades. I will explain a proof\, joint with Blumberg\, th
at the number of such fixed points is larger than the rank of the homology
with coefficients in any field. The proof will involve developing tools a
nd methods of Floer homotopy theory.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Seidel (MIT)
DTSTART:20210422T203000Z
DTEND:20210422T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/46
DESCRIPTION:Title: Fukaya categories of Calabi-Yau hypersurfaces\nby Paul Seide
l (MIT) as part of M-seminar\n\n\nAbstract\nWe will discuss some structura
l properties of the Fukaya categories of Calabi-Yau hypersurfaces\, concer
ning their dependence on the Kaehler (Novikov) parameter\, that can be pro
ved without relying on homological mirror symmetry.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Simpson (University of Nice)
DTSTART:20210429T203000Z
DTEND:20210429T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/47
DESCRIPTION:Title: On some Fukaya categories of singular Lagrangians with coefficie
nts\nby Carlos Simpson (University of Nice) as part of M-seminar\n\n\n
Abstract\nThis is about work in progress with Fabian Haiden and Ludmil Kat
zarkov. We consider the folkloric construction of Fukaya categories over
the Novikov ring\, for objects that are graphs in a surface (the complex p
lane) together with sections of a fiber dg-category patched together with
A_n-objects at (n+1)-fold vertices of the graph. We discuss aspects of the
question of defining these categories\, and then look at the case of 6 en
dpoints on a regular hexagon with A_2 coefficient category. Mirror symmetr
y already gives a stability condition\, and we show that the semistable ob
jects are represented by spectral networks that can be pictured in an expl
icit way.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Mirković (University of Massachusetts (Amherst))
DTSTART:20210506T203000Z
DTEND:20210506T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/48
DESCRIPTION:Title: Loop Grassmannians of lattices\nby Ivan Mirković (Universit
y of Massachusetts (Amherst)) as part of M-seminar\n\n\nAbstract\nTo each
choice of a based lattice L\, a cohomology theory A and a poset\nP one can
associate a space Gr(L\,A\,P). This generalizes the loop Grassmannians of
\nsemisimple groups which is the case of the coroot lattice\, classical co
homology and\nthe point poset.\nThis is an attempt to replace reductive gr
oups (in some aspects) by “coliding particles”.\nOne could also view i
t as an approach to loop Grassmannians through homology rather\nthan cohom
ology\, motivated by the Contou-Carrere symbol.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denis Auroux (Harvard University)
DTSTART:20210916T210000Z
DTEND:20210916T220000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/49
DESCRIPTION:Title: Lagrangian Floer theory for trivalent graphs and HMS for curves<
/a>\nby Denis Auroux (Harvard University) as part of M-seminar\n\n\nAbstra
ct\nThe mirror of a genus g curve can be viewed as a trivalent\nconfigurat
ion of 3g−3 rational curves meeting in 2g−2 triple points\;\nmore prec
isely\, this singular configuration arises as the critical locus\nof the s
uperpotential in a 3-dimensional Landau-Ginzburg mirror. In\njoint work wi
th Alexander Efimov and Ludmil Katzarkov\, we introduce a\nnotion of Fukay
a category for such a configuration of rational curves\,\nwhere objects ar
e embedded graphs with trivalent vertices at the triple\npoints\, and morp
hisms are linear combinations of intersection points as\nin usual Floer th
eory. We will describe the construction of the\nstructure maps of these Fu
kaya categories\, attempt to provide some\nmotivation\, and outline exampl
es of calculations that can be carried out\nto verify homological mirror s
ymmetry in this setting.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greg Moore (Rutgers University)
DTSTART:20210922T203000Z
DTEND:20210922T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/50
DESCRIPTION:Title: 2d Categorical Wall-Crossing With Twisted Masses\nby Greg Mo
ore (Rutgers University) as part of M-seminar\n\n\nAbstract\nWe review how
supersymmetric quantum mechanics naturally leads to several standard cons
tructions in homological algebra. We apply these ideas to 2d Landau-Ginzbu
rg models with (2\,2) supersymmetry to discuss wall-crossing. Some aspects
of the web formalism are reviewed and applied to the categorification of
the Cecotti-Vafa wall-crossing formula for BPS invariants. We then sketch
the generalization to include twisted masses. In the final part of the tal
k we sketch how some of these ideas give a natural framework for understan
ding a recent conjecture of Garoufalidis\, Gu\, and Marino and lead to pot
entially new knot invariants. The talk is based on work done with Ahsan Kh
an and the final part is the result of discussions with Ahsan Khan\, David
e Gaiotto\, and Fei Yan.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Braverman (University of Toronto and Perimeter Institute
)
DTSTART:20210930T203000Z
DTEND:20210930T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/51
DESCRIPTION:Title: Universal Coulomb branch and theta-sheaves\nby Alexander Bra
verman (University of Toronto and Perimeter Institute) as part of M-semina
r\n\n\nAbstract\nIn the first half of the talk I shall recall basic defini
tions related to derived geometric Satake equivalence and its relation to
construction of Coulomb branches of 3d N=4 gauge theories (no physics back
ground is assumed). In the 2nd half I will describe certain "universal Cou
lomb object" on the affine Grassmannian of the group Sp(2n) (following sug
gestions by Drinfeld and Raskin) and discuss its relation with the so call
ed theta-sheaf studied by Lafforgue and Lysenko.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamas Hausel (IST Austria)
DTSTART:20211007T180000Z
DTEND:20211007T190000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/52
DESCRIPTION:Title: Explicit Hitchin System on Lagrangians\nby Tamas Hausel (IST
Austria) as part of M-seminar\n\n\nAbstract\nI will report on joint proje
ct with Hitchin where we compute some examples of the multiplicity algebra
of the Hitchin system on upward flows as jet schemes of cohomology rings
of Grassmannians.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vivek Shende (University of Southern Denmark)
DTSTART:20211014T183000Z
DTEND:20211014T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/53
DESCRIPTION:Title: Localization of Fukaya categories and quantizing the Hitchin sys
tem\nby Vivek Shende (University of Southern Denmark) as part of M-sem
inar\n\n\nAbstract\nFor a complex curve C and reductive group G\, the spac
e of G-bundles on C has been of much interest to many mathematicians. For
the purposes of the geometric Langlands correspondence\, one wishes to co
nstruct certain `Hecke eigensheaves' over this space. It has long been ex
pected (and in some cases known) that these should arise from quantization
of fibers of Hitchin's integrable system\, this being the map h: T*Bun(C\
, G) --> A which\, for G = GL(n)\, records the spectral curve of a Higgs b
undle. Historically this means that one tries to associate a D-module on
Bun(C\, G) to each fiber of h.\n\nMore recently\, the fact that Langlands
dual groups give rise to dual Hitchin fibrations has led to the expectatio
n that geometric Langlands duality should be some sort of homological mirr
or symmetry. In this talk we will take a step towards making this precise
: recent results on the localization of wrapped Fukaya categories allow us
to use Floer theory to associate a constructible sheaf on Bun(C\, G) to a
fiber of the Hitchin fibration. (More precisely\, we may do for smooth f
ibers\, in components of Bun(C\, G) where there are no strictly semistable
Higgs bundles\, and should assume G connected center). We don't yet know
how to check that we have eigensheaves\, but can check some expected prop
erties: our sheaves have the expected endomorphisms\, rank\, microstalks o
n certain components\, and sheaves from different fibers are orthogonal.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Odesskii (Brock University)
DTSTART:20211021T180000Z
DTEND:20211021T190000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/54
DESCRIPTION:Title: Multiplication kernels\nby Alexander Odesskii (Brock Univers
ity) as part of M-seminar\n\n\nAbstract\nCommutative associative multiplic
ations on a space of functions can be defined in terms of multiplication k
ernels which are an infinite-dimensional analog of structure constants of
multiplication in finite-dimensional case. Associativity constrain gives a
n integral equation for multiplication kernel. I will explain various ways
of dealing with this integral equation in purely algebraic terms. In part
icular\, connections with integrable systems will be discussed and a lot o
f examples will be constructed. The talk is based on the paper M. Kontsevi
ch\, A. Odesski Multiplication kernels\, arXiv:2105.04238\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Davison (University of Edinburgh)
DTSTART:20211025T183000Z
DTEND:20211025T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/55
DESCRIPTION:Title: Cohomological DT theory and nonabelian Hodge theory for stacks -
1\nby Ben Davison (University of Edinburgh) as part of M-seminar\n\n\
nAbstract\n(this talk is a part of a three-lectures minicourse)\n\nThe non
abelian Hodge correspondence provides a diffeomorphism between certain coa
rse moduli spaces of semistable Higgs bundles on a smooth projective curve
C (the Dolbeault side) and coarse moduli spaces of representations of the
fundamental group of C (the Betti side). In the case of coprime rank and
degree\, these spaces are smooth\, and the famous P=W conjecture states t
hat the isomorphism in cohomology provided by the above diffeomorphism tak
es the weight filtration on the Betti side to the perverse filtration on t
he Dolbeault side. The purpose of these talks is to use recent advances i
n cohomological Donaldson-Thomas theory to extend this story to moduli sta
cks.\nFor coprime rank and degree\, two key features in the study of class
ical nonabelian Hodge theory are the perverse filtration with respect to t
he Hitchin base\, and the purity of the cohomology of the Dolbeault moduli
space. I will present an extension of the BBDG decomposition theorem to
moduli stacks of objects in 2CY categories\, which enables us to reproduce
both of the above features for stacks in nonabelian Hodge theory.\nThese
results\, along with cohomological Hall algebras\, allow us to connect the
intersection cohomology of coarse moduli spaces with the Borel-Moore homo
logy of the above stacks\, providing the connection between three versions
of the P=W conjecture: the original conjecture for smooth moduli spaces\,
the version for intersection cohomology of singular moduli spaces\, and a
new version for stacks.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Davison (University of Edinburgh)
DTSTART:20211027T183000Z
DTEND:20211027T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/56
DESCRIPTION:Title: Cohomological DT theory and nonabelian Hodge theory for stacks -
2\nby Ben Davison (University of Edinburgh) as part of M-seminar\n\n\
nAbstract\n(this talk is a part of a three-lectures minicourse)\n\nThe non
abelian Hodge correspondence provides a diffeomorphism between certain coa
rse moduli spaces of semistable Higgs bundles on a smooth projective curve
C (the Dolbeault side) and coarse moduli spaces of representations of the
fundamental group of C (the Betti side). In the case of coprime rank and
degree\, these spaces are smooth\, and the famous P=W conjecture states t
hat the isomorphism in cohomology provided by the above diffeomorphism tak
es the weight filtration on the Betti side to the perverse filtration on t
he Dolbeault side. The purpose of these talks is to use recent advances i
n cohomological Donaldson-Thomas theory to extend this story to moduli sta
cks.\nFor coprime rank and degree\, two key features in the study of class
ical nonabelian Hodge theory are the perverse filtration with respect to t
he Hitchin base\, and the purity of the cohomology of the Dolbeault moduli
space. I will present an extension of the BBDG decomposition theorem to
moduli stacks of objects in 2CY categories\, which enables us to reproduce
both of the above features for stacks in nonabelian Hodge theory.\nThese
results\, along with cohomological Hall algebras\, allow us to connect the
intersection cohomology of coarse moduli spaces with the Borel-Moore homo
logy of the above stacks\, providing the connection between three versions
of the P=W conjecture: the original conjecture for smooth moduli spaces\,
the version for intersection cohomology of singular moduli spaces\, and a
new version for stacks.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Davison (University of Edinburgh)
DTSTART:20211028T183000Z
DTEND:20211028T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/57
DESCRIPTION:Title: Cohomological DT theory and nonabelian Hodge theory for stacks -
3\nby Ben Davison (University of Edinburgh) as part of M-seminar\n\n\
nAbstract\n(this talk is a part of a three-lectures minicourse)\n\nThe non
abelian Hodge correspondence provides a diffeomorphism between certain coa
rse moduli spaces of semistable Higgs bundles on a smooth projective curve
C (the Dolbeault side) and coarse moduli spaces of representations of the
fundamental group of C (the Betti side). In the case of coprime rank and
degree\, these spaces are smooth\, and the famous P=W conjecture states t
hat the isomorphism in cohomology provided by the above diffeomorphism tak
es the weight filtration on the Betti side to the perverse filtration on t
he Dolbeault side. The purpose of these talks is to use recent advances i
n cohomological Donaldson-Thomas theory to extend this story to moduli sta
cks.\nFor coprime rank and degree\, two key features in the study of class
ical nonabelian Hodge theory are the perverse filtration with respect to t
he Hitchin base\, and the purity of the cohomology of the Dolbeault moduli
space. I will present an extension of the BBDG decomposition theorem to
moduli stacks of objects in 2CY categories\, which enables us to reproduce
both of the above features for stacks in nonabelian Hodge theory.\nThese
results\, along with cohomological Hall algebras\, allow us to connect the
intersection cohomology of coarse moduli spaces with the Borel-Moore homo
logy of the above stacks\, providing the connection between three versions
of the P=W conjecture: the original conjecture for smooth moduli spaces\,
the version for intersection cohomology of singular moduli spaces\, and a
new version for stacks.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kontsevich (IHES)
DTSTART:20211104T160000Z
DTEND:20211104T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/58
DESCRIPTION:Title: On the perturbation theory for spectra in quantum mechanics\
nby Maxim Kontsevich (IHES) as part of M-seminar\n\n\nAbstract\nConsider a
polynomial differential operator in one variable\, depending on a small p
arameter (Planck constant). Under appropriate conditions\, the low-energy
spectrum admits an asymptotic expansion in hbar. I will present a way to c
alculate such series via a purely "commutative problem"\, a mixture of var
iations of Hodge structures and of the Stirling formula. This result came
from discussions with A. Soibelman.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Goncharov (Yale University)
DTSTART:20211111T213000Z
DTEND:20211111T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/59
DESCRIPTION:Title: Spectral description of non-commutative local systems on surface
s\nby Alexander Goncharov (Yale University) as part of M-seminar\n\n\n
Abstract\nLet R be a non-commutative field. I plan to give a cluster desc
ription of the following moduli spaces:\n\ni) Triples of flags in generic
position.\n\nii) Moduli spaces R-vector bundles with flat framed connectio
ns over topological surfaces with corners.\n\niii) Moduli spaces of non-co
mmutative Stokes data.\n\nEach of the last two examples includes the previ
ous one as a special case. This is a joint work with Maxim Kontsevich.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Padurariu (Columbia University)
DTSTART:20211118T213000Z
DTEND:20211118T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/60
DESCRIPTION:Title: Relative stable pairs and a non-Calabi-Yau wall crossing\nby
Tudor Padurariu (Columbia University) as part of M-seminar\n\n\nAbstract\
nFor complex smooth threefolds\, there are enumerative theories of curves
defined using sheaves\, such as Donaldson-Thomas (DT) theory using ideal s
heaves and Pandharipande-Thomas (PT) theory using stable pairs. These theo
ries are conjecturally related among themselves and conjecturally related
to other enumerative theories of curves\, such as Gromov-Witten theory. T
he conjectural relation between DT and PT theories is known only for Calab
i-Yau threefolds by work of Bridgeland\, Toda\, where one can use the powe
rful machinery of motivic Hall algebras due to Joyce and his collaborators
.\n\nBryan-Steinberg (BS) defined enumerative invariants for Calabi-Yau th
reefolds Y with certain contraction maps Y→X. I plan to explain how to e
xtend their definition beyond the Calabi-Yau case and what is the conjectu
ral relation to the other enumerative theories. This conjectural relation
is known in the Calabi-Yau case by work of Bryan-Steinberg using the motiv
ic Hall algebra. In contrast to the DT/ PT correspondence\, we manage to e
stablish the BS/ PT correspondence in some non-Calabi-Yau situations.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miroslav Rapcak (UC Berkeley)
DTSTART:20211202T213000Z
DTEND:20211202T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/61
DESCRIPTION:Title: $W_\\infty$ modules and melted crystals of DT and PT\nby Mir
oslav Rapcak (UC Berkeley) as part of M-seminar\n\n\nAbstract\n$W_\\infty$
algebra is a vertex operator algebra extending the Virasoro algebra by fi
elds of spin $3\,4\,\\dots$. It is known to admit a nice class of modules
labelled by a triple of partitions. $W_\\infty$ is also known to admit an
alternative description in terms of the affine Yangian of $gl_1$ admitting
a very concrete definition of such modules. As we will see in this talk\,
utilizing the charge-conjugation automorphism of $W_\\infty$ in the langu
age of the affine Yangian leads to a new class of affine Yangian modules w
ith non-diagonalizable action of Cartan generators and striking connection
with Pandharipande-Thomas invariants.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenji Fukaya (Simons Center for Geometry and Physics)
DTSTART:20211209T213000Z
DTEND:20211209T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/62
DESCRIPTION:Title: A note on homological mirror symmetry over Novikov ring\nby
Kenji Fukaya (Simons Center for Geometry and Physics) as part of M-seminar
\n\n\nAbstract\nHomological Mirror symmetry is a symmetry between symplect
ic and complex geometries. In the symplectic side\, Lagrangian Floer homol
ogy is the main object of the study. In most of the results on homological
mirror symmetry in the literature\, Lagrangian Floer homology is consider
ed over the coefficient ring which is either a ground ring (such as Z\, Q\
, C) or a Novikov field\, where the formal parameter is inverted. Lagrang
ian Floer homology over Novikov ring is known to contain much more informa
tions than one over Novikov field. In this talk\, I will explain certain i
deas and preliminary results to study homological Mirror symmetry over No
vikov ring. I will explain how the notion of Gromov-Hausdorff convergence
of A infinity category is used for this purpose.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Ginzburg (University of Chicago)
DTSTART:20220121T220000Z
DTEND:20220121T230000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/63
DESCRIPTION:Title: Chern classes of quantizable sheaves and characteristic cycles\nby Victor Ginzburg (University of Chicago) as part of M-seminar\n\n\nA
bstract\nLet A be a formal deformation quantization of the structure sheaf
of an algebraic symplectic manifold X. Given a coherent sheaf E on X we
define a characteristic class s(E) as a product of the Chern character of
E and a certain class associated with the quantization A. We show that if
E can be quantized to an A-module then all homogeneous components of s(E)
in a certain range of degrees vanish. The proof is based on relating the C
hern characters of E and of its quantization. The latter lives in the nega
tive cyclic homology of A and we show that the negative cyclic homology gr
oups of relevant degrees vanish.\n\nIn the holonomic case our result says
that if the support of the quantizable sheaf E is a (possibly singular) L
agrangian subvariety\, then the only nonvanishing Chern class of E is the
top degree class which is the Poincare dual of support cycle of E. As an a
pplication\, let X be a conical symplectic resolution and B the algebra of
global sections of a filtered quantization of X. We prove\, motivated by
a question by Bezrukavnikov and Losev\, that the characteristic cycles of
finite dimensional simple B-modules are linearly independent.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Rozansky (University of North Carolina)
DTSTART:20220127T213000Z
DTEND:20220127T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/64
DESCRIPTION:Title: Link homology from a stack of D2 branes with a B-twist\nby L
ev Rozansky (University of North Carolina) as part of M-seminar\n\n\nAbstr
act\nThis is a joint work with A. Oblomkov. The HOMFLY-PT polynomial invar
iant of a link in S^3 is `a sibling' of the DT invariant of a Calabi-Yau 3
-fold X: the difference is that the HOMFLY-PT polynomial counts the curves
in X in the presence of special Lagrangian submanifolds related to link c
omponents. We construct a categorification of the HOMFLY-PT polynomial bas
ed on a particular way of curve counting\, when the curves are almost coin
cident and one has to account for their joint vibrations in a transverse C
^2. Thus we select a special object FL in a 2-category associated with the
Hilbert scheme of n points in C^2\, define a homomorphism from the n-stra
nd braid group to the monoidal category End(FL) and use it to associate a
graded vector space (homology) to the closure of a braid. I will explain t
he details of the mathematical construction and its interpretation within
the M-theory.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Mozgovoy (Trinity College (Dublin))
DTSTART:20220203T180000Z
DTEND:20220203T190000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/65
DESCRIPTION:Title: DT invariants and vertex algebras\nby Sergey Mozgovoy (Trini
ty College (Dublin)) as part of M-seminar\n\n\nAbstract\nCohomological Hal
l algebras (CoHAs) can be understood as a mathematical incarnation of alge
bras of BPS states in string theory. Their Poincare series can be used to
determine DT invariants of the corresponding categories.\nFor a symmetric
quiver Q\, the corresponding CoHA is commutative and I will explain how it
s dual can be naturally equipped with a structure of a vertex bialgebra. I
t can also be identified with 1) the universal enveloping algebra of some
Lie algebra\, 2) the universal enveloping vertex algebra of some vertex Li
e algebra\, 3) the principal free vertex algebra embedded into some lattic
e vertex algebra.\nThis identification leads to a new proof of the positiv
ity of DT invariants. It also allows one to interpret duals of CoHA module
s\, arising from moduli spaces of stable framed representations\, as certa
in subspaces of principal free vertex algebras.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech)
DTSTART:20220207T193000Z
DTEND:20220207T203000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/66
DESCRIPTION:Title: Quantum Topology at generic q (part 1)\nby Sergei Gukov (Cal
tech) as part of M-seminar\n\n\nAbstract\nThis is the first of a 4-lecture
miniseries.\n\nQuantum topology is a blend of topology and quantum algebr
a\, where topological invariants of knots and 3-manifolds are constructed
from basic building blocks of algebraic origin. The latter\, in turn\, can
come from symmetries of solvable lattice models\, from vertex operator al
gebras\, from quantum field theories\, and from various constructions in g
eometric representation theory\, thus providing "algebraic bridges" betwee
n these different areas of mathematics and physics. Many invariants of 3-m
anifolds --- e.g. the Rokhlin invariant\, Witten-Reshetikhin-Turaev invari
ants and their non-semisimple generalizations (ADO and CGP invariants) ---
arise in this way and involve quantum groups at roots of unity. Construct
ing q-series invariants associated with quantum groups at generic q requir
es qualitatively new techniques. The main goal of these lectures is to off
er a slow introduction and a practical guide to these techniques\, illustr
ated by many examples and\, hopefully\, led by many questions and suggesti
ons from the audience.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech)
DTSTART:20220209T193000Z
DTEND:20220209T203000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/67
DESCRIPTION:Title: Quantum Topology at generic q (part 2)\nby Sergei Gukov (Cal
tech) as part of M-seminar\n\n\nAbstract\nThis is the second of a 4-lectur
e miniseries.\n\nQuantum topology is a blend of topology and quantum algeb
ra\, where topological invariants of knots and 3-manifolds are constructed
from basic building blocks of algebraic origin. The latter\, in turn\, ca
n come from symmetries of solvable lattice models\, from vertex operator a
lgebras\, from quantum field theories\, and from various constructions in
geometric representation theory\, thus providing "algebraic bridges" betwe
en these different areas of mathematics and physics. Many invariants of 3-
manifolds --- e.g. the Rokhlin invariant\, Witten-Reshetikhin-Turaev invar
iants and their non-semisimple generalizations (ADO and CGP invariants) --
- arise in this way and involve quantum groups at roots of unity. Construc
ting q-series invariants associated with quantum groups at generic q requi
res qualitatively new techniques. The main goal of these lectures is to of
fer a slow introduction and a practical guide to these techniques\, illust
rated by many examples and\, hopefully\, led by many questions and suggest
ions from the audience.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech)
DTSTART:20220210T213000Z
DTEND:20220210T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/68
DESCRIPTION:Title: Quantum Topology at generic q (part 3)\nby Sergei Gukov (Cal
tech) as part of M-seminar\n\n\nAbstract\nThis is the third of a 4-lecture
miniseries.\n\nQuantum topology is a blend of topology and quantum algebr
a\, where topological invariants of knots and 3-manifolds are constructed
from basic building blocks of algebraic origin. The latter\, in turn\, can
come from symmetries of solvable lattice models\, from vertex operator al
gebras\, from quantum field theories\, and from various constructions in g
eometric representation theory\, thus providing "algebraic bridges" betwee
n these different areas of mathematics and physics. Many invariants of 3-m
anifolds --- e.g. the Rokhlin invariant\, Witten-Reshetikhin-Turaev invari
ants and their non-semisimple generalizations (ADO and CGP invariants) ---
arise in this way and involve quantum groups at roots of unity. Construct
ing q-series invariants associated with quantum groups at generic q requir
es qualitatively new techniques. The main goal of these lectures is to off
er a slow introduction and a practical guide to these techniques\, illustr
ated by many examples and\, hopefully\, led by many questions and suggesti
ons from the audience.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech)
DTSTART:20220211T193000Z
DTEND:20220211T203000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/69
DESCRIPTION:Title: Quantum Topology at generic q (part 4)\nby Sergei Gukov (Cal
tech) as part of M-seminar\n\n\nAbstract\nThis is the fourth of a 4-lectur
e miniseries.\n\nQuantum topology is a blend of topology and quantum algeb
ra\, where topological invariants of knots and 3-manifolds are constructed
from basic building blocks of algebraic origin. The latter\, in turn\, ca
n come from symmetries of solvable lattice models\, from vertex operator a
lgebras\, from quantum field theories\, and from various constructions in
geometric representation theory\, thus providing "algebraic bridges" betwe
en these different areas of mathematics and physics. Many invariants of 3-
manifolds --- e.g. the Rokhlin invariant\, Witten-Reshetikhin-Turaev invar
iants and their non-semisimple generalizations (ADO and CGP invariants) --
- arise in this way and involve quantum groups at roots of unity. Construc
ting q-series invariants associated with quantum groups at generic q requi
res qualitatively new techniques. The main goal of these lectures is to of
fer a slow introduction and a practical guide to these techniques\, illust
rated by many examples and\, hopefully\, led by many questions and suggest
ions from the audience.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Latyntsev (Oxford University)
DTSTART:20220218T190000Z
DTEND:20220218T200000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/70
DESCRIPTION:Title: Quantum vertex algebras and cohomological Hall algebras\nby
Alexei Latyntsev (Oxford University) as part of M-seminar\n\n\nAbstract\nT
here is an extremely rich history of interaction between string theory and
the mathematics of moduli spaces\, for instance cohomological Hall algebr
as/algebras of BPS states\, or vertex/chiral algebras.\nIn this talk\, I w
ill explain a link between two of these: Joyce's vertex algebras attached
to the moduli stack of objects in an abelian category\, and one dimensiona
l CoHAs. This is based on my recent paper 2110.14356\, whose main result s
ays that the cohomologies of such stacks are ``quantum vertex algebras": t
he factorisation/vertex analogues of quasitriangular bialgebras. The main
technical tool is a ``bivariant" Euler class which makes torus localisatio
n work in this context. I will discuss applications of these techniques to
CoHAs of coherent sheaves on a curve and future directions.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitrii Galakhov (IPMU)
DTSTART:20220224T230000Z
DTEND:20220225T000000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/71
DESCRIPTION:Title: Quiver BPS Algebras\nby Dmitrii Galakhov (IPMU) as part of M
-seminar\n\n\nAbstract\nThe quiver Yangian is the algebra underlying BPS s
tate counting problems for toric Calabi-Yau three-folds. In this talk I wi
ll discuss a physical construction of this algebra as it emerges from an e
ffective quantum field theory (QFT) describing the IR physics of D-branes
wrapping the three-fold. QFT setup provides as well natural trigonometric
and elliptic analogues of quiver Yangians\, which could be called toroidal
quiver algebras and elliptic quiver algebras\, respectively. The represen
tations of the shifted rational\, trigonometric and elliptic algebras can
be constructed in terms of the statistical model of crystal melting. The
analysis of supersymmetric gauge theories suggests that there exist even r
icher classes of algebras associated with higher-genus Riemann surfaces an
d generalized cohomology theories.\nIf time permits\, I would mention poss
ible developments and relations to (possibly novel) integrable models.\nTh
is talk is based on arXiv:2008.07006\, arXiv:2106.01230\, arXiv:2108.10286
.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Voronov (University of Minnesota)
DTSTART:20220310T213000Z
DTEND:20220310T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/72
DESCRIPTION:Title: Mysterious Triality\nby Alexander Voronov (University of Min
nesota) as part of M-seminar\n\n\nAbstract\nMysterious duality was discove
red by Iqbal\, Neitzke\, and Vafa in 2002 as a convincing\, yet mysterious
correspondence between certain symmetry patterns in toroidal compactifica
tions of M-theory and del Pezzo surfaces\, both governed by the root syste
m series E_k. It turns out that the sequence of del Pezzo surfaces is not
the only sequence of objects in mathematics which gives rise to the same E
_k symmetry pattern. I will present a sequence of topological spaces\, sta
rting with the four-sphere S^4\, and then forming its iterated cyclic loop
spaces L_c^k S^4\, within which we will see the E_k symmetry pattern via
rational homotopy theory. For this sequence of spaces\, the correspondence
between its E_k symmetry pattern and that of toroidal compactifications o
f M-theory is no longer a mystery\, as each space L_c^k S^4 is naturally r
elated to the compactification of M-theory on the k-torus via identificati
on of the equations of motion of (11-k)-dimensional supergravity as the de
fining equations of the Sullivan minimal model of L_c^k S^4. This gives an
explicit duality between rational homotopy theory and physics. Thereby\,
Iqbal\, Neitzke\, and Vafa’s mysterious duality between algebraic geomet
ry and physics is extended to a triality involving algebraic topology\, wi
th the duality between topology and physics made explicit\, i.e.\, demysti
fied. The mystery is now transferred to the mathematical realm as duality
between algebraic geometry and algebraic topology. This is a report on а
recent work\, arXiv:2111.14810 [hep-th]\
, with Hisham Sati.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Gorsky (UC Davis)
DTSTART:20220303T213000Z
DTEND:20220303T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/73
DESCRIPTION:Title: Algebraic weaves and braid varieties\nby Evgeny Gorsky (UC D
avis) as part of M-seminar\n\n\nAbstract\nIn the talk I will define braid
varieties\, a class of affine algebraic varieties associated to positive b
raids\, and explain their relation to Richardson and positroid varieties\,
HOMFLY polynomial and Khovanov-Rozansky homology. I will also develop a S
oergel-like diagrammatic calculus for correspondences between the braid va
rieties. This is a joint work with Roger Casals\, Mikhail Gorsky and Jose
Simental Rodriguez.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Haiden (Center for Quantum Mathematics\, SDU)
DTSTART:20220321T183000Z
DTEND:20220321T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/74
DESCRIPTION:Title: Quadratic differentials\, stability conditions\, and DT invarian
ts\, lecture 1\nby Fabian Haiden (Center for Quantum Mathematics\, SDU
) as part of M-seminar\n\n\nAbstract\nLecture 1: Quadratic differentials\,
Fukaya categories of surfaces\, and stability conditions\n\nCombining ide
as from string theory and geometric invariant theory\, Bridgeland introduc
ed the notion of a stability condition on a triangulated category. Since t
hen\, the problem of determining the structure of spaces of all stability
conditions on triangulated categories\, which are complex analytic manifol
ds\, has proven to be quite challenging and has only been solved in a hand
ful of examples. In some cases though\, spaces of stability conditions tur
n out to have a very concrete and geometric interpretation as spaces of qu
adratic differentials\, or equivalently flat surfaces - objects of intense
study in ergodic theory. In these cases\, the triangulated category is th
e (partially wrapped) Fukaya category of a surface. However\, one can also
instead consider certain 3-d Calabi-Yau triangulated categories\, and thi
s is necessary to make contact with the theory of motivic Donaldson-Thomas
invariants of Kontsevich-Soibelman. As an application one obtains wall-cr
ossing formulas for counts of finite-length geodesics on flat surfaces.\nT
his lecture series will be based on arXiv:1409.8611\, arXiv:2104.06018\, a
s well as unpublished work. The aim will be to present a unified picture o
f existing results as well as indicate open questions and future direction
s of research.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Haiden (Center for Quantum Mathematics\, SDU)
DTSTART:20220323T183000Z
DTEND:20220323T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/75
DESCRIPTION:Title: Quadratic differentials\, stability conditions\, and DT invarian
ts\, lecture 2\nby Fabian Haiden (Center for Quantum Mathematics\, SDU
) as part of M-seminar\n\n\nAbstract\nLecture 2: Calabi-Yau categories of
surfaces\n\nCombining ideas from string theory and geometric invariant the
ory\, Bridgeland introduced the notion of a stability condition on a trian
gulated category. Since then\, the problem of determining the structure of
spaces of all stability conditions on triangulated categories\, which are
complex analytic manifolds\, has proven to be quite challenging and has o
nly been solved in a handful of examples. In some cases though\, spaces of
stability conditions turn out to have a very concrete and geometric inter
pretation as spaces of quadratic differentials\, or equivalently flat surf
aces - objects of intense study in ergodic theory. In these cases\, the tr
iangulated category is the (partially wrapped) Fukaya category of a surfac
e. However\, one can also instead consider certain 3-d Calabi-Yau triangul
ated categories\, and this is necessary to make contact with the theory of
motivic Donaldson-Thomas invariants of Kontsevich-Soibelman. As an applic
ation one obtains wall-crossing formulas for counts of finite-length geode
sics on flat surfaces.\nThis lecture series will be based on arXiv:1409.86
11\, arXiv:2104.06018\, as well as unpublished work. The aim will be to pr
esent a unified picture of existing results as well as indicate open quest
ions and future directions of research.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Haiden (Center for Quantum Mathematics\, SDU)
DTSTART:20220324T183000Z
DTEND:20220324T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/76
DESCRIPTION:Title: Quadratic differentials\, stability conditions\, and DT invarian
ts\, lecture 3\nby Fabian Haiden (Center for Quantum Mathematics\, SDU
) as part of M-seminar\n\n\nAbstract\nLecture 3: DT-invariants and wall-cr
ossing for quadratic differentials\n\nCombining ideas from string theory a
nd geometric invariant theory\, Bridgeland introduced the notion of a stab
ility condition on a triangulated category. Since then\, the problem of de
termining the structure of spaces of all stability conditions on triangula
ted categories\, which are complex analytic manifolds\, has proven to be q
uite challenging and has only been solved in a handful of examples. In som
e cases though\, spaces of stability conditions turn out to have a very co
ncrete and geometric interpretation as spaces of quadratic differentials\,
or equivalently flat surfaces - objects of intense study in ergodic theor
y. In these cases\, the triangulated category is the (partially wrapped) F
ukaya category of a surface. However\, one can also instead consider certa
in 3-d Calabi-Yau triangulated categories\, and this is necessary to make
contact with the theory of motivic Donaldson-Thomas invariants of Kontsevi
ch-Soibelman. As an application one obtains wall-crossing formulas for cou
nts of finite-length geodesics on flat surfaces.\nThis lecture series will
be based on arXiv:1409.8611\, arXiv:2104.06018\, as well as unpublished w
ork. The aim will be to present a unified picture of existing results as w
ell as indicate open questions and future directions of research.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Koroteev (UC Berkeley and Rutgers University)
DTSTART:20220331T203000Z
DTEND:20220331T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/77
DESCRIPTION:Title: q-Opers — what they are and what are they good for?\nby Pe
ter Koroteev (UC Berkeley and Rutgers University) as part of M-seminar\n\n
\nAbstract\nI will introduce the new geometric object - (G\,q)-opers on a
Riemann surface where G is a simple simply connected Lie algebra. I will
describe their applications in geometric Langlands and integrable systems.
Using the formalism of (G\,q)-opers we can describe spectrum of quantum i
ntegrable models\, like XXZ spin chains and their generalizations in repre
sentation theory (so called quantum/classical duality). As a different app
lication we can study wall crossing transformations between fundamental so
lutions of Fuchsian ODEs with regular singularities (ODE/IM correspondence
) using (G\,q)-oper connections.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Losev (Yale University)
DTSTART:20220408T203000Z
DTEND:20220408T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/78
DESCRIPTION:Title: Harish-Chandra modules and quantizations\nby Ivan Losev (Yal
e University) as part of M-seminar\n\n\nAbstract\nLet G be a complex semis
imple algebraic group\, g its Lie algebra and K a symmetric subgroup of G.
In this situation one can talk about Harish-Chandra (g\,K)-modules. Their
study is a classical chapter of Lie representation theory\, largely motiv
ated by the study of representations of semisimple real groups and\, in pa
rticular\, the classification of unitary representations. It is classicall
y expected that Harish-Chandra modules arising from the latter are related
to quantizations of nilpotent orbits and their covers. In the recent year
s\, there has been a lot of progress understanding the latter that in part
icular shed some light on the geometric classification of certain classes
of Harish-Chandra modules that should come from unitary representations. I
will survey some of this progress in my talk. Based on the joint work wit
h Mason-Brown and Matvieievskyi\, arXiv:2108.03453 .\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Sheridan (University of Edinburgh)
DTSTART:20220422T203000Z
DTEND:20220422T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/79
DESCRIPTION:Title: Quantum cohomology as a deformation of symplectic cohomology
\nby Nick Sheridan (University of Edinburgh) as part of M-seminar\n\n\nAbs
tract\nLet X be a compact symplectic manifold\, and D a normal crossings s
ymplectic divisor in X. We give a criterion under which the quantum cohomo
logy of X is the cohomology of a natural deformation of the symplectic coc
hain complex of X \\ D. The criterion can be thought of in terms of the Ko
daira dimension of X (which should be non-positive)\, and the log Kodaira
dimension of X \\ D (which should be non-negative). We will discuss applic
ations to mirror symmetry. This is joint work with Strom Borman and Umut V
arolgunes.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adeel Khan (Academia Sinica)
DTSTART:20220414T203000Z
DTEND:20220414T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/80
DESCRIPTION:Title: Cohomology and intersection theory on stacks\nby Adeel Khan
(Academia Sinica) as part of M-seminar\n\n\nAbstract\nI will give an overv
iew of some recent work on extending cohomological and intersection-theore
tic methods to stacks. This formalism subsumes equivariant intersection t
heory in the sense of Edidin-Graham and also incorporates virtual phenomen
a via a derived version of specialization to the normal cone. I will also
discuss a very general new localization theorem for stacks which recovers
Atiyah-Bott localization in the case of quotients by torus actions. Fina
lly\, I will explain a categorification of this story\, involving a derive
d microlocalization functor for constructible sheaves\, which is closely c
onnected with categorified Donaldson-Thomas theory. The localization theo
rem is joint with Aranha\, Latyntsev\, Park and Ravi\, and the application
s to DT theory are joint with Kinjo.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksander Doan (Columbia & Trinity College\, Cambridge)
DTSTART:20220428T203000Z
DTEND:20220428T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/81
DESCRIPTION:Title: Holomorphic Floer theory and the Fueter equation\nby Aleksan
der Doan (Columbia & Trinity College\, Cambridge) as part of M-seminar\n\n
\nAbstract\nI will discuss an idea of constructing a category associated w
ith a pair of holomorphic Lagrangians in a hyperkahler manifold\, or\, mor
e generally\, a manifold equipped with a triple of almost complex structur
es I\,J\,K satisfying the quaternionic relation IJ =-JI= K. This category
can be seen as an infinite-dimensional version of the Fukaya-Seidel catego
ry associated with a Lefschetz fibration. While many analytic aspects of t
his proposal remain unexplored\, I will argue that in the case of the cota
ngent bundle of a Lefschetz fibration\, our construction recovers the Fuka
ya-Seidel category. This talk is based on joint work with Semon Rezchikov\
, and builds on earlier ideas of Haydys\, Gaiotto-Moore-Witten\, and Kapra
nov-Kontsevich-Soibelman.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Kivinen (EPFL)
DTSTART:20220505T173000Z
DTEND:20220505T183000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/82
DESCRIPTION:Title: Weight polynomials of compactified Jacobians and link invariants
\nby Oscar Kivinen (EPFL) as part of M-seminar\n\n\nAbstract\nUsing a
recursive algorithm for orbital integrals of tamely ramified elliptic elem
ents in p-adic GL_n\, we compute the weight polynomials of (local) compact
ified Jacobians of planar curves. Depending on one's taste\, these can be
also interpreted as point-counts on Hitchin fibers or affine Springer fibe
rs in type A. The algorithm is based on old work of Waldspurger and can be
interpreted using an action of the affine Yangian of gl(1) on the Fock sp
ace\, where it becomes clear that there is a relationship to knot invarian
ts of HOMFLY type. This also proves a virtual version of the Cherednik-Dan
ilenko conjecture on Betti numbers of Jacobian factors.\nIn fact\, the alg
orithm yields more\, such as so called Shalika germs for the elements in q
uestion. These have a geometric interpretation on the Hilbert scheme of po
ints on C^2\, which I will also discuss. This is joint work with Cheng-Chi
ang Tsai.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiro Lee Tanaka (Texas State University)
DTSTART:20220922T203000Z
DTEND:20220922T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/83
DESCRIPTION:Title: Stable Weinstein geometry through localizations\nby Hiro Lee
Tanaka (Texas State University) as part of M-seminar\n\n\nAbstract\nMuch
of computational math is formula-driven\, while much of categorical math i
s formalism-driven. Mirror symmetry is rich in part because many of its re
sults are driven by both. With the advent of stable-homotopy-theoretic inv
ariants in symplectic geometry\, there has been a real need for better-beh
aved formalisms in symplectic geometry. In this talk\, we will talk about
recent success in constructing the formalism\, especially in the setting o
f certain non-compact symplectic manifolds called Weinstein sectors. The r
esults have concrete geometric consequences\, like showing that spaces of
embeddings of these manifolds map continuously to spaces of maps between c
ertain invariants. (And in particular\, leads to higher-homotopy-group gen
eralizations\, in the Weinstein setting\, of the Seidel homomorphism\, sim
ilar to works of Savelyev and Oh-Tanaka.) The main result we'll discuss is
that the infinity-category of stabilized sectors can be constructed using
the categorically formal process of localization. Most of what we discuss
is joint with Oleg Lazarev and Zachary Sylvan.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Pomerleano (University of Massachusetts Boston)
DTSTART:20221007T203000Z
DTEND:20221007T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/84
DESCRIPTION:Title: Singularities of the quantum connection on a Fano variety\nb
y Daniel Pomerleano (University of Massachusetts Boston) as part of M-semi
nar\n\n\nAbstract\nThe small quantum connection on a Fano variety is one o
f the simplest objects in enumerative geometry. Nevertheless\, it is the s
ubject of far-reaching conjectures known as the Dubrovin/Gamma conjectures
. Traditionally\, these conjectures are made for manifolds with semi-simpl
e quantum cohomology or more generally for Fano manifolds whose quantum co
nnection is of unramified exponential type at $q=\\infty$. I will explain
a program\, joint with Paul Seidel\, to show that this unramified exponent
ial type property holds for all Fano manifolds M carrying a smooth antican
onical divisor D. The basic idea of our argument is to view these structur
es through the lens of a noncommutative Landau-Ginzburg model intrinsicall
y attached to (M\,D).\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Soibelman (IHES)
DTSTART:20221013T173000Z
DTEND:20221013T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/85
DESCRIPTION:Title: Quantized integrable systems\, normal forms\, and variation of H
odge structures\nby Alexander Soibelman (IHES) as part of M-seminar\n\
n\nAbstract\nA classical theorem due to Birkhoff states that on a complex
symplectic manifold a function near its Morse critical point can be transf
ormed by a formal symplectomorphism into a normal form given by a power se
ries in the pairwise sums of squares of the coordinates. Using a quantum a
nalog of this normal form\, one can compute the eigenvalues of the Schröd
inger operator\, given certain conditions. In my talk\, I will explain how
to obtain the Birkhoff normal form of a quantum Hamiltonian geometrically
\, relating it to the quantization of integrable systems and to formal def
ormations of variations of Hodge structures. This is joint work in progres
s with Maxim Kontsevich.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Hilburn (Perimeter Institute)
DTSTART:20221020T203000Z
DTEND:20221020T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/86
DESCRIPTION:Title: Towards 2-Categorical 3d Mirror Symmetry\nby Justin Hilburn
(Perimeter Institute) as part of M-seminar\n\n\nAbstract\nBy now it is kno
wn that many interesting phenomena in geometry and representation theory c
an be understood as aspects of mirror symmetry of 3d N=4 SUSY QFTs. Such a
QFT is associated to a hyper-Kähler manifold X equipped with a hyper-Ham
iltonian action of a compact Lie group G and admits two topological twists
. The first twist\, which is known as the 3d B-model or Rozansky-Witten th
eory\, is a TQFT of algebro-geometric flavor and has been studied extensiv
ely by Kapustin\, Rozansky and Saulina. The second twist\, which is known
as the 3d A-model or 3d Seiberg-Witten theory\, is a more mysterious TQFT
of symplecto-topological flavor. In this talk I will discuss what is known
about the 2-categories of boundary conditions for these two TQFTs. They a
re expected to provide two distinct categorifications of category O for th
e hyperkahler quotient X///G and 3d mirror symmetry is expected to induce
a categorification of the Koszul duality between categories O for mirror s
ymplectic resolutions. For abelian gauge theories this picture is work in
progress with Ben Gammage and Aaron Mazel-Gee. This generalizes the works
of Kapustin-Vyas-Setter and Teleman on pure gauge theory.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Bridgeland (University of Sheffield)
DTSTART:20221027T150000Z
DTEND:20221027T160000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/87
DESCRIPTION:Title: Geometry from Donaldson-Thomas invariants\nby Tom Bridgeland
(University of Sheffield) as part of M-seminar\n\n\nAbstract\nOur general
aim is to use the Donaldson-Thomas invariants of a 3-Calabi-Yau triangul
ated category to define a geometric structure on its space of stability co
nditions. So far we only understand how to do this in a few classes of exa
mples. In the talk I'll explain (i) the geometry we expect to obtain (whic
h involves a hyperkahler structure)\, and (ii) a moduli-theoretic construc
tion of this geometry in the case of "categories of class S[A_1]" (where t
he stability space parameterises algebraic curves equipped with quadratic
differentials).\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arkadij Bojko (ETH Zurich)
DTSTART:20221103T190000Z
DTEND:20221103T200000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/88
DESCRIPTION:Title: Wall-crossing for Calabi-Yau fourfolds and applications\nby
Arkadij Bojko (ETH Zurich) as part of M-seminar\n\n\nAbstract\nThere are m
ultiple existing theories studying wall-crossing of sheaf-counting invaria
nts in dimensions less than or equal to three. Recently these invariants w
ere also extended to Calabi-Yau fourfolds where it was reasonable to ask a
bout an analogous story. I will explain the framework leading to the wall-
crossing formulae proposed by Joyce and describe their proof. The main goa
l of this project is the proof of existing conjectures relating different
stable pairs counting points\, curves and surfaces in Calabi-Yau fourfolds
. For example\, it proves my previous computations for Hilbert schemes of
points.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanki Lekili (Imperial College London)
DTSTART:20221201T160000Z
DTEND:20221201T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/89
DESCRIPTION:Title: Equivariant Fukaya categories at the singular value\nby Yank
i Lekili (Imperial College London) as part of M-seminar\n\n\nAbstract\nWe
have some new conjectures and examples where we relate wrapped Fukaya cate
gories of symplectic manifolds with Hamiltonian S^1 actions and the wrappe
d Fukaya categories of their Hamiltonian reductions.\nJoint work with Ed S
egal.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Davison (University of Edinburgh)
DTSTART:20221110T193000Z
DTEND:20221110T203000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/90
DESCRIPTION:Title: Affine BPS algebras and W algebras\nby Ben Davison (Universi
ty of Edinburgh) as part of M-seminar\n\n\nAbstract\nOne may associate to
a quiver Q with potential W a certain Lie algebra\, called the BPS Lie alg
ebra. On the one hand this Lie algebra generates the Kontsevich-Soibelman
cohomological Hall algebra (CoHA) associated to Q and W under a Yangian-t
ype PBW theorem\, and on the other hand it partially categorifies the BPS
invariants of the Jacobi algebra associated to (Q\,W). For special choice
s of (Q\,W)\, the resulting cohomological Hall algebra is isomorphic to th
e cohomological Hall algebra studied by Schiffamnn and Vasserot in their s
olution of the AGT conjecture.\nI will explain how a special case of a joi
nt result with Kinjo enables us to affinize the BPS Lie algebra for these
CoHAs\, and express the CoHA as a universal enveloping algebra. I will ex
plain how for the three-loop quiver with its canonical cubic potential\, a
one-parameter deformation of the affine BPS Lie algebra recovers one half
of the Lie algebra of differential operators on the complex torus. In pa
rticular\, this implies that the associated CoHA is spherically generated\
, so that we can use a result of Rapčák\, Soibelman\, Yang and Zhou to c
ompletely describe the fully deformed version of this algebra in terms of
half of the affine Yangian of gl(1).\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Schiffmann (Université de Paris-Sud ORSAY)
DTSTART:20221118T150000Z
DTEND:20221118T160000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/91
DESCRIPTION:Title: COHA of zero dimensional sheaves on surfaces and the P=W conject
ure\nby Olivier Schiffmann (Université de Paris-Sud ORSAY) as part of
M-seminar\n\n\nAbstract\nCohomological Hall algebras of 2CY categories fe
ature in several recent geometric constructions of infinite dimensional qu
antum groups (such as affine Yangians) and their representations. The case
of zero dimensional sheaves on smooth surfaces (such as projective surfac
es\, or line bundles over smooth projective curves) has attracted particul
ar attention due to the analogy with usual Hecke operators (acting on modu
li spaces of sheaves on curves as opposed to surfaces). We will describe t
he COHA in this case (a joint work with Mellit\, Minets and Vasserot)\, an
d we will sketch its use in a recent proof of the P=W conjecture of de Cat
lado\, Hausel and Migliorini relating the Hodge structure of character var
ieties and the perverse cohomology of the Hitchin fiibration (a joint work
with Hausel\, Mellit and Minets).\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lino Amorim (Kansas State University)
DTSTART:20230201T213000Z
DTEND:20230201T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/92
DESCRIPTION:Title: Enumerative invariants from categories\nby Lino Amorim (Kans
as State University) as part of M-seminar\n\n\nAbstract\nKontsevich sugges
ted that enumerative predictions of Mirror Symmetry should follow directly
from Homological Mirror Symmetry. This requires a natural construction of
analogues of Gromov-Witten invariants associated to any dg or A-infinity
Calabi-Yau category (with some extra choices). I will discuss two approach
es to this construction: 1) categorical primitive forms\, a non-commutativ
e version of Saito's theory of primitive forms for singularities\, which g
ives only genus zero invariants\; 2) Costello's enumerative invariants whi
ch conjecturally give invariants in all genera.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semon Rezchikov (IAS/Princeton University)
DTSTART:20230209T213000Z
DTEND:20230209T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/93
DESCRIPTION:Title: Categorical aspects of the Fueter Equation\nby Semon Rezchik
ov (IAS/Princeton University) as part of M-seminar\n\n\nAbstract\nThe (3d)
Fueter equation is the three-dimensional analog of the pseudoholomorphic
map equation\, and as such underlies a three-dimensional topological quant
um field theory. This PDE underlies the mathematics of the A-type twist of
the 3D N=4 sigma model\, which has a hyperkahler manifold as its target.
One can think of this topological quantum field theory as a simultaneous c
omplexification and categorification of the Fukaya category\; in particula
r\, it assigns to a ("weak") hyperkahler manifold a 2-category with object
s holomorphic Lagrangians\, which in an appropriate sense categorifies the
Fukaya category. Certain basic open problems remain about the analysis of
the Fueter equation\, but this categorical viewpoint suggests new tractab
le directions in the differential geometry of this equation. In particular
\, just as holomorphic strips between nearby Lagrangans are in bijection w
ith Morse trajectories of a real morse function\, Fueter maps between near
by holomorphic Lagrangians are in bijection with complex gradient trajecto
ries of a holomorphic morse function\, also known as zeta-instantons. Thus
\, in the (A-twist) Fueter 2-category\, hom-categories are locally modeled
on Fukaya-Seidel categories\, just as in the B-twist Kapustin-Rozansky-Sa
ulinas category\, hom-categories are locally modeled on matrix factorizati
on categories. Categorical 3D mirror symmetry should exchange these pairs
of 2-categories associated to pairs of 3d mirror manifolds. I will survey
these ideas and describe interesting directions and puzzles in this story.
This is based on joint work with Aleksander Doan\, as well as on discussi
ons with Justin Hilburn and Benjamin Gammage.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Danilenko (UC Berkeley)
DTSTART:20230216T213000Z
DTEND:20230216T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/94
DESCRIPTION:Title: Stable envelopes from 2d mirror symmetry\nby Ivan Danilenko
(UC Berkeley) as part of M-seminar\n\n\nAbstract\nHomological mirror symme
try predicts an equivalence between the derived category of equivariant co
herent sheaves on the additive Coulomb branch X and a version of the wrapp
ed Fukaya category on multiplicative Coulomb branch Y with superpotential
W. If one decategorifies both sides by taking K-theory\, the construction
still gives an interesting identification between well-known objects in th
e equivariant K-theory of X and cycles with coefficients in local systems
on Y. The talk will show how it works for the fixed point basis and the st
able envelopes. Work in progress with Andrey Smirnov\, with many insights
from the joint project with Mina Aganagic\, Peng Zhou and Yixuan Li.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolai Reshetikhin (UC Berkeley and BIMSA)
DTSTART:20230223T213000Z
DTEND:20230223T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/95
DESCRIPTION:Title: Solitons in infinite relativistic Toda system\nby Nicolai Re
shetikhin (UC Berkeley and BIMSA) as part of M-seminar\n\n\nAbstract\nThis
system is a "relativistic" generalization of the infinite Toda chain. In
is a $GL(\\infty)$ version of the Toda-Coxeter system for $SL(N)$ with the
standard Poisson Lie structure. The phase space of this system is an exam
ple of an infinite cluster variety. Assuming an analog of rapidly decaying
boundary conditions we construct soliton solutions for both\, factorizati
on discrete time dynamics and for continuous time integrable dynamics. We
also construct action-angle variables from scattering data. This is a join
t work with Cory Lansford.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoel Groman (Hebrew University)
DTSTART:20230302T213000Z
DTEND:20230302T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/96
DESCRIPTION:Title: The closed string mirror construction\nby Yoel Groman (Hebre
w University) as part of M-seminar\n\n\nAbstract\nConsider a 2n-dimensiona
l symplectic Calabi Yau manifold equipped with a Maslov 0 Lagrangian torus
fibration with singularities over a base B. According to modern interpret
ations of the SYZ conjecture\, there should be an associated analytic mirr
or variety with a non Archimedean torus fibration over B. I will suggest a
general construction called the closed string mirror which is based on re
lative symplectic cohomologies of the fibers. A priori the closed string m
irror is only a set with a map to the base. I will discuss work in progres
s on some general hypotheses for when it is in fact an n-dimensional rigid
analytic variety with a non Archimedean torus fibration. I will touch on
the relation to enumerative and homological mirror symmetry.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Mellit (University of Vienna)
DTSTART:20230309T160000Z
DTEND:20230309T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/97
DESCRIPTION:Title: P=W via H_2\nby Anton Mellit (University of Vienna) as part
of M-seminar\n\n\nAbstract\nBy $H_2$ we denote the Lie algebra of polynomi
al hamiltonian vector fields on the plane. We consider the moduli space of
stable twisted Higgs bundles on an algebraic curve of given coprime rank
and degree. De Cataldo\, Hausel and Migliorini proved in the case of rank
2 and conjectured in arbitrary rank that two natural filtrations on the co
homology of the moduli space coincide. One is the weight filtration W comi
ng from the Betti realization\, and the other one is the perverse filtrati
on P induced by the Hitchin map. Motivated by computations of the Khovanov
-Rozansky homology of links by Gorsky\, Hogancamp and myself\, we look for
an action of $H_2$ on the cohomology of the moduli space. We find it in t
he algebra generated by two kinds of natural operations: on the one hand w
e have the operations of cup product by tautological classes\, and on the
other hand we have the Hecke operators acting via certain correspondences.
We then show that both P and W coincide with the filtration canonically a
ssociated to the $sl_2$ subalgebra of $H_2$. Based on joint work with Haus
el\, Minets and Schiffmann.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miguel Moreira (ETH)
DTSTART:20230323T203000Z
DTEND:20230323T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/98
DESCRIPTION:Title: Virasoro constraints in sheaf theory\nby Miguel Moreira (ETH
) as part of M-seminar\n\n\nAbstract\nVirasoro constraints for Gromov-Witt
en invariants have a rich history tied to the very beginning of the subjec
t\, but recently there have been many developments on the sheaf side. In t
his talk I will survey those developments and talk about joint work with A
. Bojko and W. Lim where we propose a general conjecture of Virasoro const
raints for moduli spaces of sheaves and formulate it using the vertex alge
bra that D. Joyce recently introduced to study wall-crossing. Using Joyce'
s framework we can show compatibility between wall-crossing and the constr
aints\, which we then use to prove that they hold for moduli of stable she
aves on curves and surfaces with h^0\,1=h^0\,2=0.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Gammage (Harvard University)
DTSTART:20230330T203000Z
DTEND:20230330T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/99
DESCRIPTION:Title: Structural features of 3d mirror symmetry\nby Benjamin Gamma
ge (Harvard University) as part of M-seminar\n\n\nAbstract\n"Homological"
3d mirror symmetry is an equivalence between the Kapustin-Rozansky-Saulina
2-category and an as-yet-undefined "Fukaya-Fueter" 2-category associated
to dual holomorphic symplectic stacks. Many statements\, some classical an
d some new\, may be recovered from such an equivalence by decategorificati
on. We will discuss what is known in the toric setting\, where decategorif
ication can be used to produce both the Braden-Licata-Proudfoot-Webster hy
pertoric Koszul duality and a geometric version of Tate's thesis. This is
based on joint work with Justin Hilburn & Aaron Mazel-Gee.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umut Varolgunes (Bogazici University)
DTSTART:20230407T160000Z
DTEND:20230407T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/100
DESCRIPTION:Title: Mirror formal schemes of symplectic manifolds equipped with gen
eralized cut decompositions\nby Umut Varolgunes (Bogazici University)
as part of M-seminar\n\n\nAbstract\nI will discuss the notion of generaliz
ed Delzant subdomains of graded symplectic manifolds and their relative sy
mplectic cohomology. Assuming that we have an involutive decomposition int
o such domains\, I will construct a mirror formal scheme over the Novikov
ring. The key is to be able to compute the invariants modulo Thbar\, where
hbar is a positive constant depending on the decomposition\, finiteness o
f boundary depth which leads to homology level completeness and an injecti
vity statement mirror to uniqueness of analytic continuation. Then I will
assume the existence of a "homological section" and construct the HMS func
tor. I will end by discussing when one should expect this functor to be co
homologically full and faithful via the notion of local generation.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau (University of Georgia)
DTSTART:20230413T203000Z
DTEND:20230413T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/101
DESCRIPTION:Title: Quivers\, flow trees and log curves\nby Pierrick Bousseau (
University of Georgia) as part of M-seminar\n\n\nAbstract\nDonaldson-Thoma
s (DT) invariants of a quiver with potential can be expressed in terms of
simpler attractor DT invariants by a universal formula. The coefficients i
n this formula are calculated combinatorially using attractor flow trees.
In joint work with Arguz (arXiv:2302.02068)\, we prove that these coeffici
ents are genus 0 log Gromov--Witten invariants of d-dimensional toric vari
eties\, where d is the number of vertices of the quiver. This result follo
ws from a log-tropical correspondence theorem which relates (d-2)-dimensio
nal families of tropical curves obtained as universal deformations of attr
actor flow trees\, and rational log curves in toric varieties.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kai Hugtenburg (University of Edinburgh)
DTSTART:20230420T170000Z
DTEND:20230420T180000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/102
DESCRIPTION:Title: Gromov-Witten invariants from the Fukaya category\nby Kai H
ugtenburg (University of Edinburgh) as part of M-seminar\n\n\nAbstract\nTh
is talk will report on recent progress on obtaining (open) Gromov-Witten i
nvariants from the Fukaya category. A crucial ingredient is showing that t
he cyclic open-closed map\, which maps the cyclic homology of the Fukaya c
ategory of X to its S1-equivariant quantum cohomology\, respects connectio
ns. Along the way we will encounter R-matrices\, which were used in the Gi
vental-Teleman classification of semisimple cohomological field theories\,
and allow one to determine higher genus Gromov-Witten invariants from gen
us 0 invariants. I will then present some evidence that this approach migh
t extend beyond the semisimple case. Time permitting\, I will explain how
one can extend these results to obtain open Gromov-Witten invariants from
the Fukaya category.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuel Diaconescu (Rutgers University)
DTSTART:20230427T170000Z
DTEND:20230427T180000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/103
DESCRIPTION:Title: Flops and Hilbert scheme of space curve singularities\nby E
manuel Diaconescu (Rutgers University) as part of M-seminar\n\n\nAbstract\
nThis is joint work with Mauro Porta\, Francesco Sala and Arian Vosoughini
a using pagoda flop transitions in order to derive explicit results for to
pological invariants of Hilbert schemes of space curve singularities.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilia Itenberg (Sorbonne University)
DTSTART:20230504T160000Z
DTEND:20230504T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/104
DESCRIPTION:Title: Empty real plane sextic curves\nby Ilia Itenberg (Sorbonne
University) as part of M-seminar\n\n\nAbstract\nMany geometric questions a
bout K3-surfaces can be restated and solved in purely arithmetical terms\,
by means of an appropriately defined homological type. For example\, this
works well in the study of singular complex sextic curves or quartic surf
aces\, as well as in that of smooth real ones. However\, when the two are
combined (singular real curves or surfaces)\, the approach fails as the na
tural concept of homological type does not fully reflect the geometry. We
show that the situation can be repaired if the curves in question have emp
ty real part\; then\, one can confine oneself to the homological types con
sisting of the exceptional divisors\, polarization\, and real structure. T
he resulting arithmetical problem can be solved\, and this leads to an equ
ivariant equisingular deformation classification of real plane sextics wit
h empty real part. This is a joint work with Alex Degtyarev.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Bezrukavnikov (MIT)
DTSTART:20230921T211500Z
DTEND:20230921T221500Z
DTSTAMP:20260404T095851Z
UID:M-seminar/105
DESCRIPTION:Title: On Springer theory for homogeneous affine Springer fibers\n
by Roman Bezrukavnikov (MIT) as part of M-seminar\n\n\nAbstract\nSpringer
fibers are subvarieties in the flag variety of a reductive group playing a
key role in geometric representation theory. One of their important featu
res is that they arise as central Lagrangian fibers of a symplectic resolu
tion of a singular space known as the Slodowy slice. Affine Springer fiber
s are loop group analogues of the Springer fibers\, they are closely relat
ed to singular fibers of the Hitchin integrable system. In a joint work wi
th Pablo Boixeda-Alvarez\, Michael McBreen and Zhiwei Yun we construct the
analogue of a Slodowy slice for some (namely\, homogeneous) affine Spring
er fibers. The construction is based on a version of the Hitchin space inv
olving connections with an irregular singularity. Time permitting\, I will
mention applications to quantum groups at a root of unity etc.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Liu (IPMU)
DTSTART:20230928T230000Z
DTEND:20230929T000000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/106
DESCRIPTION:Title: The K-theoretic DT/PT vertex correspondence\nby Henry Liu (
IPMU) as part of M-seminar\n\n\nAbstract\nOn smooth quasi-projective toric
3- and 4-folds\, vertices are the contributions from an affine toric char
t to the enumerative invariants of Donaldson-Thomas (DT) or Pandharipande-
Thomas (PT) moduli spaces. Unlike partition functions\, vertices are funda
mentally torus-equivariant objects\, and they carry a great deal of combin
atorial complexity\, particularly in equivariant K-theory. In joint work w
ith Nick Kuhn and Felix Thimm\, we give two different proofs of the K-theo
retic 3-fold DT/PT vertex correspondence. Both proofs use equivariant wall
-crossing in a setup originally due to Toda\; one uses a Mochizuki-style m
aster space\, while the other uses ideas from Joyce's recent universal wal
l-crossing machine. A crucial new ingredient is the construction of *symme
trized* pullbacks of symmetric obstruction theories on moduli stacks\, usi
ng Kiem-Savvas'étale-local notion of almost-perfect obstruction theory. I
believe our techniques\, particularly the Joyce-style approach\, can also
be applied to related questions such as DT/PT descendent transformations\
, the DT crepant resolution conjecture\, and the 4-fold DT/PT vertex corre
spondence.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Constantin Teleman (UC Berkeley)
DTSTART:20231005T203000Z
DTEND:20231005T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/107
DESCRIPTION:Title: Condensed Thoughts\nby Constantin Teleman (UC Berkeley) as
part of M-seminar\n\n\nAbstract\nTopological Field Theories have recently
gained attention via their control of (extended) topological operators in
QFT. One operation commonly used in that context is ’condensation’\, w
hich however seems to lack a precise definition. In this talk I will descr
ibe a path to a precise construction of condensation and relate it to conn
ectivity in the case of TQFTs coming from homotopy types. This is based on
discussions with Dan Freed and Mike Hopkins\, in turn much inspired by co
nversations with colleagues from the Simons Collaboration on Categorical S
ymmetries.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (MSU)
DTSTART:20231012T180000Z
DTEND:20231012T190000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/108
DESCRIPTION:Title: Cluster Nature of Quantum Groups\nby Linhui Shen (MSU) as p
art of M-seminar\n\n\nAbstract\nWe present a rigid cluster model to realiz
e the quantum group $U_q(g)$ for $g$ of type ADE. That is\, we prove that
there is a natural Hopf algebra isomorphism from the quantum group to a qu
otient algebra of the Weyl group invariants of a Fock-Goncharov quantum cl
uster algebra. By applying the quantum duality of cluster algebras\, we sh
ow that the quantum group admits a cluster canonical basis $\\Theta$ whose
structural coefficients are in $\\mathbb{N}[q^{\\frac{1}{2}}\, q^{-\\frac
{1}{2}}]$. The basis $\\Theta$ satisfies an invariance property under the
braid group action\, the Dynkin automorphisms\, and the star anti-involuti
on. Based on the preprint arXiv: 2209.06258\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niklas Garner (University of Washington)
DTSTART:20231017T203000Z
DTEND:20231017T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/109
DESCRIPTION:Title: Non-semisimple TQFTs from 3d N=4 QFTs - lecture 1\nby Nikla
s Garner (University of Washington) as part of M-seminar\n\n\nAbstract\nTo
pological quantum field theory (TQFT) sits at the rich intersection of man
y disciplines including physics\, topological\, and algebra. Many of the m
ost familiar TQFTs\, such as Chern-Simons theory with compact gauge group
at positive integer level\, can be built from semisimple categories where
homological aspects can be safely avoided\, but this is no longer the case
beyond these simple examples. In these talks I will describe aspects of s
everal non-semisimple TQFTs arising from supersymmetric twists of three-di
mensional field theories and their relations to quantum groups and vertex
operator algebras.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niklas Garner (University of Washington)
DTSTART:20231018T183000Z
DTEND:20231018T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/110
DESCRIPTION:Title: Non-semisimple TQFTs from 3d N=4 QFTs - lecture 2\nby Nikla
s Garner (University of Washington) as part of M-seminar\n\n\nAbstract\nTo
pological quantum field theory (TQFT) sits at the rich intersection of man
y disciplines including physics\, topological\, and algebra. Many of the m
ost familiar TQFTs\, such as Chern-Simons theory with compact gauge group
at positive integer level\, can be built from semisimple categories where
homological aspects can be safely avoided\, but this is no longer the case
beyond these simple examples. In these talks I will describe aspects of s
everal non-semisimple TQFTs arising from supersymmetric twists of three-di
mensional field theories and their relations to quantum groups and vertex
operator algebras.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niklas Garner (University of Washington)
DTSTART:20231019T203000Z
DTEND:20231019T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/111
DESCRIPTION:Title: Non-semisimple TQFTs from 3d N=4 QFTs - lecture 3\nby Nikla
s Garner (University of Washington) as part of M-seminar\n\n\nAbstract\nTo
pological quantum field theory (TQFT) sits at the rich intersection of man
y disciplines including physics\, topological\, and algebra. Many of the m
ost familiar TQFTs\, such as Chern-Simons theory with compact gauge group
at positive integer level\, can be built from semisimple categories where
homological aspects can be safely avoided\, but this is no longer the case
beyond these simple examples. In these talks I will describe aspects of s
everal non-semisimple TQFTs arising from supersymmetric twists of three-di
mensional field theories and their relations to quantum groups and vertex
operator algebras.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Kapranov (IPMU)
DTSTART:20231108T200000Z
DTEND:20231108T210000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/112
DESCRIPTION:Title: Resurgent perverse sheaves\nby Mikhail Kapranov (IPMU) as p
art of M-seminar\n\n\nAbstract\nPerverse sheaves provide a topological cou
nterpart of regular holonomic D-modules whose solutions are multivalued fu
nctions of certain restricted type. Much more general multivalued function
s (on the complex plane C) have been studied in J. Ecalle's theory of resu
rgence using\, as one of the main tools\, additive convolution. The talk\,
based on joint work in progress with Y. Soibelman\, will propose topologi
cal counterpart of the theory of resurgence based on perverse sheaves on C
which are algebras with respect to (middle) additive convolution. Such sh
eaves typically have infinitely many singular points. In particular\, we w
ill argue that the cohomological Hall algebra in a 3-Calabi-Yau situation
localizes to such a "resurgent perverse sheaf".\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jim Bryan (UBC)
DTSTART:20231026T203000Z
DTEND:20231026T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/113
DESCRIPTION:Title: The geometry and arithmetic of banana nano-manifolds\nby Ji
m Bryan (UBC) as part of M-seminar\n\n\nAbstract\nThe Hodge numbers of a C
alabi-Yau threefold X are determined by the two numbers h^{1\,1}(X) and h^
{1\,2}(X) which can be interpreted respectively as the dimensions of the s
pace of Kahler forms and complex deformations respectively. We construct f
our new examples X_N\, where N \\in {5\,6\,8\,9}\, of rigid Calabi-Yau thr
eefolds (h^{2\,1}=0) with Picard number 4 (h^{1\,1}=4). These manifolds ar
e of “banana type” and have among the smallest known values for Calabi
-Yau Hodge numbers. We (partially) compute the Donaldson-Thomas partition
functions of these manifolds and in particular show that the associated ge
nus g Gromov-Witten potential is given by a weight 2g-2 Siegel paramodular
form of index N. These manifolds are also modular in the arithmetic sense
: there is a weight 4 modular form whose Fourier coefficients are obtained
by counting points over finite fields on X_N. We compute this form and ob
serve that it is the unique cusp form of weight 4 and index N. This is joi
nt work with Stephen Pietromonaco.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Butson (Oxford University)
DTSTART:20231030T183000Z
DTEND:20231030T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/114
DESCRIPTION:Title: Vertex algebras from divisors on Calabi-Yau threefolds and perv
erse coherent extensions - lecture 1\nby Dylan Butson (Oxford Universi
ty) as part of M-seminar\n\n\nAbstract\nWe will explain two conjecturally
equivalent constructions of vertex algebras associated to divisors S on ce
rtain toric Calabi-Yau threefolds Y\, and some partial results towards the
proof of their equivalence. One construction is algebraic\, as the kernel
of screening operators on lattice vertex algebras determined by the GKM g
raph of Y and a Jordan-Holder filtration of the structure sheaf of S. The
other is geometric\, as a convolution algebra acting on the homology of ce
rtain moduli spaces of sheaves supported on the divisor\, following the pr
oof of the AGT conjecture by Schiffmann-Vasserot and its generalization to
divisors in C^3 by Rapcak-Soibelman-Yang-Zhao. This provides a correspond
ence between the enumerative geometry of sheaves on Calabi-Yau threefolds
and the representation theory of W-algebras and affine Yangian-type quantu
m groups.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Butson (Oxford University)
DTSTART:20231101T183000Z
DTEND:20231101T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/115
DESCRIPTION:Title: Vertex algebras from divisors on Calabi-Yau threefolds and perv
erse coherent extensions - lecture 2\nby Dylan Butson (Oxford Universi
ty) as part of M-seminar\n\n\nAbstract\nWe will explain two conjecturally
equivalent constructions of vertex algebras associated to divisors S on ce
rtain toric Calabi-Yau threefolds Y\, and some partial results towards the
proof of their equivalence. One construction is algebraic\, as the kernel
of screening operators on lattice vertex algebras determined by the GKM g
raph of Y and a Jordan-Holder filtration of the structure sheaf of S. The
other is geometric\, as a convolution algebra acting on the homology of ce
rtain moduli spaces of sheaves supported on the divisor\, following the pr
oof of the AGT conjecture by Schiffmann-Vasserot and its generalization to
divisors in C^3 by Rapcak-Soibelman-Yang-Zhao. This provides a correspond
ence between the enumerative geometry of sheaves on Calabi-Yau threefolds
and the representation theory of W-algebras and affine Yangian-type quantu
m groups.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Butson (Oxford University)
DTSTART:20231102T183000Z
DTEND:20231102T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/116
DESCRIPTION:Title: Vertex algebras from divisors on Calabi-Yau threefolds and perv
erse coherent extensions - lecture 3\nby Dylan Butson (Oxford Universi
ty) as part of M-seminar\n\n\nAbstract\nWe will explain two conjecturally
equivalent constructions of vertex algebras associated to divisors S on ce
rtain toric Calabi-Yau threefolds Y\, and some partial results towards the
proof of their equivalence. One construction is algebraic\, as the kernel
of screening operators on lattice vertex algebras determined by the GKM g
raph of Y and a Jordan-Holder filtration of the structure sheaf of S. The
other is geometric\, as a convolution algebra acting on the homology of ce
rtain moduli spaces of sheaves supported on the divisor\, following the pr
oof of the AGT conjecture by Schiffmann-Vasserot and its generalization to
divisors in C^3 by Rapcak-Soibelman-Yang-Zhao. This provides a correspond
ence between the enumerative geometry of sheaves on Calabi-Yau threefolds
and the representation theory of W-algebras and affine Yangian-type quantu
m groups.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Butson (Oxford University)
DTSTART:20231103T183000Z
DTEND:20231103T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/117
DESCRIPTION:Title: Vertex algebras from divisors on Calabi-Yau threefolds and perv
erse coherent extensions - lecture 4\nby Dylan Butson (Oxford Universi
ty) as part of M-seminar\n\n\nAbstract\nWe will explain two conjecturally
equivalent constructions of vertex algebras associated to divisors S on ce
rtain toric Calabi-Yau threefolds Y\, and some partial results towards the
proof of their equivalence. One construction is algebraic\, as the kernel
of screening operators on lattice vertex algebras determined by the GKM g
raph of Y and a Jordan-Holder filtration of the structure sheaf of S. The
other is geometric\, as a convolution algebra acting on the homology of ce
rtain moduli spaces of sheaves supported on the divisor\, following the pr
oof of the AGT conjecture by Schiffmann-Vasserot and its generalization to
divisors in C^3 by Rapcak-Soibelman-Yang-Zhao. This provides a correspond
ence between the enumerative geometry of sheaves on Calabi-Yau threefolds
and the representation theory of W-algebras and affine Yangian-type quantu
m groups.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harold Williams (USC)
DTSTART:20231116T213000Z
DTEND:20231116T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/118
DESCRIPTION:Title: Differential operators on the base affine space and quantized C
oulomb branches\nby Harold Williams (USC) as part of M-seminar\n\n\nAb
stract\nWe discuss joint work with Tom Gannon\, showing that the algebra $
D(SL_n/U)$ of differential operators on the base affine space of $SL_n$ is
the quantized Coulomb branch of a certain 3d $\\mathcal{N} = 4$ quiver ga
uge theory. In the semiclassical limit this confirms a conjecture of Dance
r-Hanany-Kirwan on the universal hyperk\\"ahler implosion of $SL_n$. In fa
ct\, we prove a generalization interpreting an arbitrary unipotent reducti
on of $T^* SL_n$ as a Coulomb branch. These results also provide a new int
erpretation of the Gelfand-Graev Weyl group symmetry of $D(SL_n/U)$.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jake Solomon (Hebrew University)
DTSTART:20231130T170000Z
DTEND:20231130T180000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/119
DESCRIPTION:Title: Counting holomorphic disks with boundary on the Chiang Lagrangi
an\nby Jake Solomon (Hebrew University) as part of M-seminar\n\n\nAbst
ract\nI will discuss a computation of open Gromov-Witten invariants counti
ng holomorphic disks with boundary on the Chiang Lagrangian along with var
ious correction terms. The Chiang Lagrangian is not fixed by an anti-sympl
ectic involution and thus techniques from Floer theory are used instead of
those of real algebraic geometry that play a role in other computations.
The invariants exhibit periodic behaviors of periods 8 and 16. Denominator
s of invariants are always powers of two indicating a non-trivial arithmet
ic structure of the open WDVV equations. Background on open Gromov-Witten
theory will be provided. This is joint work with Hollands-Kosloff-Sela-Shu
and Tukachinsky.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Pardon (Simons Center)
DTSTART:20231206T183000Z
DTEND:20231206T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/120
DESCRIPTION:Title: Universally counting curves in Calabi--Yau threefolds\nby J
ohn Pardon (Simons Center) as part of M-seminar\n\n\nAbstract\nEnumerating
curves in algebraic varieties traditionally involves choosing a compactif
ication of the space of smooth embedded curves in the variety. There are m
any such compactifications\, hence many different enumerative invariants.
I will propose a "universal" (very tautological) enumerative invariant whi
ch takes values in a certain Grothendieck group of 1-cycles. It is often t
he case with such "universal" constructions that the resulting Grothendiec
k group is essentially uncomputable. But in this case\, the cluster formal
ism of Ionel and Parker shows that\, in the case of threefolds with nef an
ticanonical bundle\, this Grothendieck group is freely generated by local
curves. This reduces the MNOP conjecture (in the case of nef anticanonical
bundle and primary insertions) to the case of local curves\, where it is
already known due to work of Bryan--Pandharipande and Okounkov--Pandharipa
nde.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Safronov (University of Edinburgh)
DTSTART:20240208T200000Z
DTEND:20240208T210000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/121
DESCRIPTION:Title: Perverse sheaves in deformation quantization\nby Pavel Safr
onov (University of Edinburgh) as part of M-seminar\n\n\nAbstract\nGiven a
holomorphic symplectic manifold\, there is a canonical category of deform
ation quantization modules. Holomorphic Lagrangians equipped with spin str
uctures define objects in this category. I will explain how one can descri
be the RHom perverse sheaf of two such DQ modules in terms of the derived
geometry of the Lagrangian intersection. I will also explain a related res
ult describing the perverse sheaf appearing in BV quantization of a (-1)-s
hifted symplectic scheme. This is a report on work joint with Sam Gunningh
am.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucien Hennecart (University of Edinburgh)
DTSTART:20240219T193000Z
DTEND:20240219T203000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/122
DESCRIPTION:Title: Cohomological Hall algebras of 2-Calabi-Yau categories and appl
ications (lecture 1)\nby Lucien Hennecart (University of Edinburgh) as
part of M-seminar\n\n\nAbstract\nIn this series of four lectures\, I will
explain the interactions between cohomological Hall algebras (CoHAs) and
several questions of interest in algebraic geometry (in particular enumera
tive geometry) and representation theory (Kac-Moody algebras and their rep
resentations).\n\nCoHAs are associative algebra structures on the Borel-Mo
ore homology of the stack of objects in some Abelian categories. We consid
er the CoHAs of various categories: sheaves on surfaces\, representations
of quivers\, and representations of fundamental groups\, which are 2-Calab
i-Yau. CoHAs lead to a fine understanding of the cohomology of the stacks
and moduli spaces involved. They provide tools to study various conjecture
s in the subject: cohomological integrality\, positivity\, and purity. In
the first two lectures\, I will detail how CoHAs give a geometric construc
tion of generalised Kac-Moody algebras (in the sense of Borcherds). The la
st two lectures will develop applications of CoHAs to the study of the coh
omology of quiver varieties (following the groundbreaking work of Nakajima
from the 1990s) and to nonabelian Hodge theory (following questions of Si
mpson).\n\nThe four lectures will\, to a large extent\, be independent fro
m each other and are largely based on joint work with Ben Davison and Seba
stian Schlegel Mejia.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucien Hennecart (University of Edinburgh)
DTSTART:20240221T193000Z
DTEND:20240221T203000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/123
DESCRIPTION:Title: Cohomological Hall algebras of 2-Calabi-Yau categories and appl
ications (lecture 2)\nby Lucien Hennecart (University of Edinburgh) as
part of M-seminar\n\n\nAbstract\nIn this series of four lectures\, I will
explain the interactions between cohomological Hall algebras (CoHAs) and
several questions of interest in algebraic geometry (in particular enumera
tive geometry) and representation theory (Kac-Moody algebras and their rep
resentations).\n\nCoHAs are associative algebra structures on the Borel-Mo
ore homology of the stack of objects in some Abelian categories. We consid
er the CoHAs of various categories: sheaves on surfaces\, representations
of quivers\, and representations of fundamental groups\, which are 2-Calab
i-Yau. CoHAs lead to a fine understanding of the cohomology of the stacks
and moduli spaces involved. They provide tools to study various conjecture
s in the subject: cohomological integrality\, positivity\, and purity. In
the first two lectures\, I will detail how CoHAs give a geometric construc
tion of generalised Kac-Moody algebras (in the sense of Borcherds). The la
st two lectures will develop applications of CoHAs to the study of the coh
omology of quiver varieties (following the groundbreaking work of Nakajima
from the 1990s) and to nonabelian Hodge theory (following questions of Si
mpson).\n\nThe four lectures will\, to a large extent\, be independent fro
m each other and are largely based on joint work with Ben Davison and Seba
stian Schlegel Mejia.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucien Hennecart (University of Edinburgh)
DTSTART:20240222T213000Z
DTEND:20240222T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/124
DESCRIPTION:Title: Cohomological Hall algebras of 2-Calabi-Yau categories and appl
ications (lecture 3)\nby Lucien Hennecart (University of Edinburgh) as
part of M-seminar\n\n\nAbstract\nIn this series of four lectures\, I will
explain the interactions between cohomological Hall algebras (CoHAs) and
several questions of interest in algebraic geometry (in particular enumera
tive geometry) and representation theory (Kac-Moody algebras and their rep
resentations).\n\nCoHAs are associative algebra structures on the Borel-Mo
ore homology of the stack of objects in some Abelian categories. We consid
er the CoHAs of various categories: sheaves on surfaces\, representations
of quivers\, and representations of fundamental groups\, which are 2-Calab
i-Yau. CoHAs lead to a fine understanding of the cohomology of the stacks
and moduli spaces involved. They provide tools to study various conjecture
s in the subject: cohomological integrality\, positivity\, and purity. In
the first two lectures\, I will detail how CoHAs give a geometric construc
tion of generalised Kac-Moody algebras (in the sense of Borcherds). The la
st two lectures will develop applications of CoHAs to the study of the coh
omology of quiver varieties (following the groundbreaking work of Nakajima
from the 1990s) and to nonabelian Hodge theory (following questions of Si
mpson).\n\nThe four lectures will\, to a large extent\, be independent fro
m each other and are largely based on joint work with Ben Davison and Seba
stian Schlegel Mejia.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucien Hennecart (University of Edinburgh)
DTSTART:20240223T193000Z
DTEND:20240223T203000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/125
DESCRIPTION:Title: Cohomological Hall algebras of 2-Calabi-Yau categories and appl
ications (lecture 4)\nby Lucien Hennecart (University of Edinburgh) as
part of M-seminar\n\n\nAbstract\nIn this series of four lectures\, I will
explain the interactions between cohomological Hall algebras (CoHAs) and
several questions of interest in algebraic geometry (in particular enumera
tive geometry) and representation theory (Kac-Moody algebras and their rep
resentations).\n\nCoHAs are associative algebra structures on the Borel-Mo
ore homology of the stack of objects in some Abelian categories. We consid
er the CoHAs of various categories: sheaves on surfaces\, representations
of quivers\, and representations of fundamental groups\, which are 2-Calab
i-Yau. CoHAs lead to a fine understanding of the cohomology of the stacks
and moduli spaces involved. They provide tools to study various conjecture
s in the subject: cohomological integrality\, positivity\, and purity. In
the first two lectures\, I will detail how CoHAs give a geometric construc
tion of generalised Kac-Moody algebras (in the sense of Borcherds). The la
st two lectures will develop applications of CoHAs to the study of the coh
omology of quiver varieties (following the groundbreaking work of Nakajima
from the 1990s) and to nonabelian Hodge theory (following questions of Si
mpson).\n\nThe four lectures will\, to a large extent\, be independent fro
m each other and are largely based on joint work with Ben Davison and Seba
stian Schlegel Mejia.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gus Schrader (Northwestern University)
DTSTART:20240215T190000Z
DTEND:20240215T200000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/126
DESCRIPTION:Title: Skeins\, clusters and wavefunctions\nby Gus Schrader (North
western University) as part of M-seminar\n\n\nAbstract\nEkholm and Shende
have proposed a version of open Gromov-Witten theory in which holomorphic
maps from Riemann surfaces with boundary landing on a Lagrangian 3-manifol
d L are counted via the image of the boundary in the HOMFLYPT skein module
of L. I'll describe joint work with Mingyuan Hu and Eric Zaslow which giv
es a method to compute the Ekholm-Shende generating function ('wavefunctio
n') enumerating such maps for a class of Lagrangian branes L in C^3. The m
ethod uses a skein-theoretic analog of cluster theory\, in which skein-val
ued wavefunctions for different Lagrangians are related by skein mutation
operators.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT)
DTSTART:20240227T213000Z
DTEND:20240227T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/127
DESCRIPTION:Title: Periodic pencils of flat connections and their p-curvature\
nby Pavel Etingof (MIT) as part of M-seminar\n\n\nAbstract\nA periodic pen
cil of flat connections on a smooth algebraic variety $X$ is a linear fami
ly of flat connections $\\nabla(s_1\,...\,s_n)=d-\\sum_{i=1}^r\\sum_{j=1}^
ns_jB_{ij}dx_i$\, where $\\lbrace x_i\\rbrace$ are local coordinates on $X
$ and $B_{ij}: X\\to {\\rm Mat}_N$ are matrix-valued regular functions. A
pencil is periodic if it is generically invariant under the shifts $s_j\\m
apsto s_j+1$ up to isomorphism. I will explain that periodic pencils have
many remarkable properties\, and there are many interesting examples of th
em\, e.g. Knizhnik-Zamolodchikov\, Dunkl\, Casimir connections and equivar
iant quantum connections for conical symplectic resolutions with finitely
many torus fixed points. I will also explain that in characteristic $p$\,
the $p$-curvature operators $\\lbrace C_i\,1\\le i\\le r\\rbrace$ of a per
iodic pencil $\\nabla$ are isospectral to the commuting endomorphisms $C_i
^*:=\\sum_{j=1}^n (s_j-s_j^p)B_{ij}^{(1)}$\, where $B_{ij}^{(1)}$ is the F
robenius twist of $B_{ij}$. This allows us to compute the eigenvalues of t
he $p$-curvature for the above examples\, and also to show that a periodic
pencil of connections always has regular singularites. This is joint work
with Alexander Varchenko.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre Minets (MPI Bonn)
DTSTART:20240307T213000Z
DTEND:20240307T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/128
DESCRIPTION:Title: COHAs of 0-dimensional sheaves on surfaces\nby Alexandre Mi
nets (MPI Bonn) as part of M-seminar\n\n\nAbstract\nGiven an abelian categ
ory C of low homological dimension\, one can construct a cohomological Hal
l algebra (COHA) of C\, whose product encodes extensions between objects i
n C. An important example of such C is the category Coh(S) of coherent she
aves on a smooth surface S. While understanding the whole CoHA algebraical
ly is more or less hopeless for a general S\, we can restrict our attentio
n to the CoHA of 0-dimensional sheaves. I will give an explicit descriptio
n of this algebra\, which builds on the seminal work of Nakajima and Lehn.
I will also discuss how this description can be used to deduce structural
results about cohomology of moduli spaces of sheaves with positive-dimens
ional support on S\, such as our recent proof of P=W conjecture. This is a
report on joint work with A. Mellit\, O. Schiffmann and E. Vasserot.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Botta (ETH)
DTSTART:20240321T193000Z
DTEND:20240321T203000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/129
DESCRIPTION:Title: Maulik-Okounkov Lie algebras and BPS Lie algebras\nby Tomma
so Botta (ETH) as part of M-seminar\n\n\nAbstract\nThe Maulik-Okounkov (MO
) Lie algebra associated to a quiver Q controls the R-matrix formalism dev
eloped by Maulik and Okounkov in the context of (quantum) cohomology of Na
kajima quiver varieties. On the other hand\, the BPS Lie algebra originate
s from cohomological DT theory\, and in particular from the theory of coho
mological Hall algebras associated to 3 Calabi-Yau categories. In this tal
k\, I will explain how to identify the MO Lie algebra of Q with the BPS Li
e algebra of the tripled quiver Q̃ with its canonical cubic potential. Th
e bridge to compare these similarly diverse words is the theory of non-abe
lian stable envelopes\, which can be exploited to relate representations o
f the MO Lie algebra to representations of the BPS Lie algebra. As a bypro
duct\, I will present a proof of Okounkov's conjecture\, equating the grad
ed dimensions of the MO Lie algebra with the coefficients of Kac polynomia
ls. This is joint work with Ben Davison.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiwei Yun (MIT)
DTSTART:20240328T203000Z
DTEND:20240328T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/130
DESCRIPTION:Title: An irregular Deligne-Simpson problem\nby Zhiwei Yun (MIT) a
s part of M-seminar\n\n\nAbstract\nThe Deligne-Simpson problem asks for a
criterion for the existence of connections on an algebraic curve with pres
cribed singularities at punctures. We give a solution to a generalization
of this problem to G-connections on P^1 with a regular singularity and an
irregular singularity (satisfying a condition called isoclinic). Here G ca
n be any complex reductive group. Perhaps surprisingly\, the solution can
be expressed in terms of rational Cherednik algebras. This is joint work w
ith Konstantin Jakob\, and the proof uses recent joint work with Bezrukavn
ikov\, Boixeda Alvarez and McBreen\, and previous joint work with Oblomkov
.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Nekrasov (Simons Center)
DTSTART:20240404T203000Z
DTEND:20240404T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/131
DESCRIPTION:Title: Infinite-dimensional spin chains from gauge theory\nby Niki
ta Nekrasov (Simons Center) as part of M-seminar\n\n\nAbstract\nSpin chain
s are quantum mechanical models of interacting degrees of freedom\, such a
s (anti)ferromagnetic atoms. The celebrated Bethe ansatz for the eigenstat
es of the Heisenberg spin chain Hamiltonian has been a source of inspirati
on for physicists and mathematicians for almost a century now\, leading to
the invention of quantum groups\, among other achievements. In my talk I
will describe several infinite-dimensional generalizations of spin chains\
, which are believed to play an important role in the studies of strong in
teractions of elementary particles: L.Lipatov's reggeized gluons\, planar
N=4 super-Yang-Mills anomalous dimensions and\, closer to the seminar's th
eme: surface defects in N=2 super-QCD. Mathematically\, the latter is the
generating function of equivariant DT-type invariants defined via the modu
li spaces of parabolic sheaves on complex surfaces. Surprisingly\, the Hec
ke operators of geometric and analytic Langlands programs make appearances
\, and gauge theory allows them to generalize outside the critical level.
Based on the recent work with Saebyeok Jeong\, Norton Lee\, and on the rec
ent work and work in progress with Andrey Grekov\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Halpern-Leistner (Cornell University)
DTSTART:20240408T183000Z
DTEND:20240408T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/132
DESCRIPTION:Title: Dispatches from the ends of the stability manifold - part 1
\nby Daniel Halpern-Leistner (Cornell University) as part of M-seminar\n\n
\nAbstract\nThis is the first lecture of four.\n\nThe manifold of Bridgela
nd stability conditions parameterizes a homological structure on a triangu
lated category that is analogous to a Kaehler structure on a projective va
riety. Recently\, I have proposed a "noncommutative minimal model program"
in which the quantum differential equation of a projective variety determ
ines paths toward infinity in the stability manifold of that variety\, and
that these paths can be used to define canonical (semiorthogonal)decompos
itions of its derived category.\nIn fact\, these paths converge in a certa
in partial compactification of the stability manifold\, the space of "augm
ented stability conditions." In order to define this partial compactificat
ion\, I will introduce a structure on a triangulated category that we call
a multi-scale decomposition\, which generalizes a semiorthogonal decompos
ition\, and a new moduli space of multi-scale lines that is closely relate
d to the moduli spaces of multi-scale differentials which are of recent in
terest in dynamics. The main conjecture about the space of augmented stabi
lity conditions is that it is a manifold with corners (in a specific way t
hat I will explain). One consequence: If this conjecture holds for any smo
oth and proper dg-category\, then any stability condition on a smooth and
proper dg-category admits proper moduli spaces of semistable objects.\nThe
plan for the lectures is\, loosely:\n1) The noncommutative MMP\n2) The sp
ace of n-pointed multi-scale lines (lecture on Wednesday will be given by
Alekos Robotis)\n3) The space of augmented stability conditions\n4) Struct
ure of the boundary: the manifold-with-corners conjecture and consequences
\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Halpern-Leistner (Cornell University)
DTSTART:20240410T183000Z
DTEND:20240410T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/133
DESCRIPTION:Title: Dispatches from the ends of the stability manifold - part 2
\nby Daniel Halpern-Leistner (Cornell University) as part of M-seminar\n\n
\nAbstract\nThis is the second lecture of four.\n\nThe manifold of Bridgel
and stability conditions parameterizes a homological structure on a triang
ulated category that is analogous to a Kaehler structure on a projective v
ariety. Recently\, I have proposed a "noncommutative minimal model program
" in which the quantum differential equation of a projective variety deter
mines paths toward infinity in the stability manifold of that variety\, an
d that these paths can be used to define canonical (semiorthogonal)decompo
sitions of its derived category.\nIn fact\, these paths converge in a cert
ain partial compactification of the stability manifold\, the space of "aug
mented stability conditions." In order to define this partial compactifica
tion\, I will introduce a structure on a triangulated category that we cal
l a multi-scale decomposition\, which generalizes a semiorthogonal decompo
sition\, and a new moduli space of multi-scale lines that is closely relat
ed to the moduli spaces of multi-scale differentials which are of recent i
nterest in dynamics. The main conjecture about the space of augmented stab
ility conditions is that it is a manifold with corners (in a specific way
that I will explain). One consequence: If this conjecture holds for any sm
ooth and proper dg-category\, then any stability condition on a smooth and
proper dg-category admits proper moduli spaces of semistable objects.\nTh
e plan for the lectures is\, loosely:\n1) The noncommutative MMP\n2) The s
pace of n-pointed multi-scale lines (lecture on Wednesday will be given by
Alekos Robotis)\n3) The space of augmented stability conditions\n4) Struc
ture of the boundary: the manifold-with-corners conjecture and consequence
s\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Halpern-Leistner (Cornell University)
DTSTART:20240411T203000Z
DTEND:20240411T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/134
DESCRIPTION:Title: Dispatches from the ends of the stability manifold - part 3
\nby Daniel Halpern-Leistner (Cornell University) as part of M-seminar\n\n
\nAbstract\nThis is the third lecture of four.\n\nThe manifold of Bridgela
nd stability conditions parameterizes a homological structure on a triangu
lated category that is analogous to a Kaehler structure on a projective va
riety. Recently\, I have proposed a "noncommutative minimal model program"
in which the quantum differential equation of a projective variety determ
ines paths toward infinity in the stability manifold of that variety\, and
that these paths can be used to define canonical (semiorthogonal)decompos
itions of its derived category.\nIn fact\, these paths converge in a certa
in partial compactification of the stability manifold\, the space of "augm
ented stability conditions." In order to define this partial compactificat
ion\, I will introduce a structure on a triangulated category that we call
a multi-scale decomposition\, which generalizes a semiorthogonal decompos
ition\, and a new moduli space of multi-scale lines that is closely relate
d to the moduli spaces of multi-scale differentials which are of recent in
terest in dynamics. The main conjecture about the space of augmented stabi
lity conditions is that it is a manifold with corners (in a specific way t
hat I will explain). One consequence: If this conjecture holds for any smo
oth and proper dg-category\, then any stability condition on a smooth and
proper dg-category admits proper moduli spaces of semistable objects.\nThe
plan for the lectures is\, loosely:\n1) The noncommutative MMP\n2) The sp
ace of n-pointed multi-scale lines (lecture on Wednesday will be given by
Alekos Robotis)\n3) The space of augmented stability conditions\n4) Struct
ure of the boundary: the manifold-with-corners conjecture and consequences
\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Halpern-Leistner (Cornell University)
DTSTART:20240412T183000Z
DTEND:20240412T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/135
DESCRIPTION:Title: Dispatches from the ends of the stability manifold - part 4
\nby Daniel Halpern-Leistner (Cornell University) as part of M-seminar\n\n
\nAbstract\nThis is the fourth lecture of four.\n\nThe manifold of Bridgel
and stability conditions parameterizes a homological structure on a triang
ulated category that is analogous to a Kaehler structure on a projective v
ariety. Recently\, I have proposed a "noncommutative minimal model program
" in which the quantum differential equation of a projective variety deter
mines paths toward infinity in the stability manifold of that variety\, an
d that these paths can be used to define canonical (semiorthogonal)decompo
sitions of its derived category.\nIn fact\, these paths converge in a cert
ain partial compactification of the stability manifold\, the space of "aug
mented stability conditions." In order to define this partial compactifica
tion\, I will introduce a structure on a triangulated category that we cal
l a multi-scale decomposition\, which generalizes a semiorthogonal decompo
sition\, and a new moduli space of multi-scale lines that is closely relat
ed to the moduli spaces of multi-scale differentials which are of recent i
nterest in dynamics. The main conjecture about the space of augmented stab
ility conditions is that it is a manifold with corners (in a specific way
that I will explain). One consequence: If this conjecture holds for any sm
ooth and proper dg-category\, then any stability condition on a smooth and
proper dg-category admits proper moduli spaces of semistable objects.\nTh
e plan for the lectures is\, loosely:\n1) The noncommutative MMP\n2) The s
pace of n-pointed multi-scale lines (lecture on Wednesday will be given by
Alekos Robotis)\n3) The space of augmented stability conditions\n4) Struc
ture of the boundary: the manifold-with-corners conjecture and consequence
s\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiroshi Iritani (Kyoto University)
DTSTART:20240418T140000Z
DTEND:20240418T150000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/136
DESCRIPTION:Title: Decomposition of quantum cohomology under blowups\nby Hiros
hi Iritani (Kyoto University) as part of M-seminar\n\n\nAbstract\nQuantum
cohomology is a deformation of the cohomology ring defined by counting rat
ional curves. A close relationship between quantum cohomology and biration
al geometry has been expected. For example\, when the quantum parameter q
approaches an "extremal ray"\, the spectrum of the quantum cohomology ring
clusters in a certain way (predicted by the corresponding extremal contra
ction)\, inducing a decomposition of the quantum cohomology. In this talk\
, I will discuss such a decomposition for blowups: quantum cohomology of t
he blowup of X along a smooth center Z will decompose into QH(X) and (codi
m Z-1) copies of QH(Z). The proof relies on Fourier analysis and shift ope
rators for equivariant quantum cohomology. We can describe blowups as a va
riation of GIT of a certain space W with C^* action. The equivariant quant
um cohomology of W acts as a "global" mirror family connecting X and its b
lowup.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Murad Alim (Heriot-Watt University)
DTSTART:20240425T203000Z
DTEND:20240425T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/137
DESCRIPTION:Title: From Gromov-Witten to Donaldson-Thomas invariants via resurgenc
e\nby Murad Alim (Heriot-Watt University) as part of M-seminar\n\n\nAb
stract\nThe generating function of higher genus Gromov-Witten invariants o
f Calabi-Yau threefolds can be computed by topological string theory and i
s given by an asymptotic series in the topological string coupling. I will
discuss how a piecewise analytic function in the string coupling can be o
btained from this series via resurgence analysis and how Donaldson-Thomas
invariants of the same geometry can be obtained from the corresponding Sto
kes factors. This is based on various joint works with Lotte Hollands\, Ar
pan Saha\, Iván Tulli and Jörg Teschner as well as on work in progress.\
n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sheel Ganatra (USC)
DTSTART:20240502T180000Z
DTEND:20240502T190000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/138
DESCRIPTION:Title: Arclike Lagrangians in Liouville sectors\nby Sheel Ganatra
(USC) as part of M-seminar\n\n\nAbstract\nSectorial descent\, established
in earlier joint work with Pardon-Shende\, gives a local-to-global formula
computing the wrapped Fukaya category of a Weinstein manifold from a sect
orial cover. If one has a specific fixed global Lagrangian in mind that is
n't contained in a single subsector\, the resulting formula is only implic
it\, as it begins by appealing to the generation of this object by "local"
Lagrangians. In this talk I will introduce and study the class of (global
) "arclike" Lagrangian submanifolds with respect to a sectorial covering\,
which are allowed to run through subsector boundaries but in a controlled
fashion. For arclike Lagrangians\, a more explicit local-to-global analys
is is possible. Based on works in progress with Hanlon-Hicks-Pomerleano-Sh
eridan and Hanlon-Hicks-Ward.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gwyn Bellamy (University of Glasgow)
DTSTART:20240905T150000Z
DTEND:20240905T160000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/139
DESCRIPTION:Title: Koszul Duality on quantizations of bionic symplectic varieties<
/a>\nby Gwyn Bellamy (University of Glasgow) as part of M-seminar\n\n\nAbs
tract\nVia localization theorems à la Beilinson-Bernstein\, representatio
ns of quantizations of symplectic singularities are equivalent to modules
over sheaves of deformation-quantization algebras (DQ-modules) on symplect
ic resolutions of the singularity. This applies for instance to (spherical
) rational Cherednik algebras and finite W-algebras as well as the primiti
ve central quotients of enveloping algebras appearing in the original Beil
inson-Bernstein theorem. Usually\, the sympletic resolution is equipped wi
th a Hamiltonian C*-action\, who attracting locus is a Lagrangian (with mo
dules supported on this Lagrangian belonging to geometric category O). I'l
l explain that it's possible to construct a "local generator" in geometric
category O such that the bounded derived category of coherent DQ-modules
is equivalent to the derived category of coherent modules over the dg-endo
morphism ring of the generator. This is a generalization of the classical
D-Omega duality of Kapranov\, Beilinson-Drinfeld and Positselski and thus
an example of filtered Koszul duality. This talk is based on recent joint
work with Chris Dodd\, Kevin McGerty and Tom Nevins.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mingyuan Hu (Northwestern University)
DTSTART:20240912T193000Z
DTEND:20240912T203000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/140
DESCRIPTION:Title: Skein valued open Gromov-Witten invariants and cluster mutation
s\nby Mingyuan Hu (Northwestern University) as part of M-seminar\n\n\n
Abstract\nWe consider a class of Lagrangians living in [\\mathbb{C}^3] . T
heir Ekholm-Shende wavefunctions\, living in the HOMFLY-PT skein module\,
will encode open Gromov-Witten invariants in all genus and with arbitrary
numbers of boundary components. We develop a skein valued cluster theory t
o compute these wavefunctions. In the case of Aganagic-Vafa brane\, our co
mputation matches up with the prediction of the topological vertex. We als
o define a skein-valued dilogarithm and prove a relation. which will imply
the 5-term relation of Garsia and Mellit. This talk is based on arXiv:231
2.10186 (joint with Gus Schrader and Eric Zaslow) and arXiv:2401.10817.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hulya Arguz (U Georgia)
DTSTART:20240926T203000Z
DTEND:20240926T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/141
DESCRIPTION:Title: The KSBA moduli space of stable log Calabi-Yau surfaces\nby
Hulya Arguz (U Georgia) as part of M-seminar\n\n\nAbstract\nThe KSBA modu
li space\, introduced by Kollár--Shepherd-Barron\, and Alexeev\, is a nat
ural generalization of "the moduli space of stable curves" to higher dimen
sions. It parametrizes stable pairs (X\,B)\, where X is a projective algeb
raic variety satisfying certain conditions and B is a divisor such that K_
X+B is ample. This moduli space is described concretely only in a handful
of situations: for instance\, if X is a toric variety and B=D+\\epsilon C\
, where D is the toric boundary divisor and C is an ample divisor\, it is
shown by Alexeev that the KSBA moduli space is a toric variety. Generally\
, for a log Calabi-Yau variety (X\,D) consisting of a projective variety X
and an anticanonical divisor D\, with B=D+\\epsilon C where C is an ample
divisor\, it was conjectured by Hacking--Keel--Yu that the KSBA moduli sp
ace is still toric (up to passing to a finite cover). In joint work with A
lexeev and Bousseau\, we prove this conjecture for all log Calabi-Yau surf
aces. This uses tools from the minimal model program\, log smooth deformat
ion theory and mirror symmetry.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Hicks (University of Edinburgh)
DTSTART:20241003T203000Z
DTEND:20241003T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/142
DESCRIPTION:Title: Superabundance and Unobstructedness\nby Jeff Hicks (Univers
ity of Edinburgh) as part of M-seminar\n\n\nAbstract\nConsider a tropical
curve in the base of a Lagrangian torus fibration. Then there exists a "La
grangian realization" of this curve: a Lagrangian submanifold in the total
space of the fibration whose projection to the base can be made to lie (v
ia Hamiltonian isotopy) arbitrarily close to your original tropical curve.
In this talk\, we'll show that in the 3-dimensional setting a combinatori
al criterion (non-superabundance of the tropical curve) determines unobstr
uctedness of the corresponding Lagrangian lift.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shivang Jingdal (University of Edinburgh)
DTSTART:20241010T150000Z
DTEND:20241010T160000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/143
DESCRIPTION:Title: CoHA of cyclic quivers and an integral form of affine Yangians<
/a>\nby Shivang Jingdal (University of Edinburgh) as part of M-seminar\n\n
\nAbstract\nIn 2012\, Schiffmann and Vasserot considered a Hall algebra-ty
pe construction on the cohomology of the moduli space of sheaves supported
on points in a plane\, using it to prove the AGT conjecture. However\, du
e to the mysterious nature of the moduli space of representations of the p
reprojective algebra\, these algebras are very difficult to study and are
often highly nontrivial. In this talk\, my goal is to explain how one can
study this algebra by employing tools from cohomological Donaldson-Thomas
theory. In particular\, I will explain how\, in the case of the cyclic qui
ver\, this algebra turns out to be the universal enveloping algebra of the
positive half of a certain extension of matrix differential operators on
the torus\, while its deformation turns out to be an explicit integral for
m of the affine Yangian of gl(n).\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Mclean (Stony Brook)
DTSTART:20241017T203000Z
DTEND:20241017T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/144
DESCRIPTION:Title: Symplectic Orbifold Gromov-Witten Invariants\nby Mark Mclea
n (Stony Brook) as part of M-seminar\n\n\nAbstract\nChen and Ruan construc
ted symplectic orbifold Gromov-Witten invariants more than 20 years ago. I
n ongoing work with Alex Ritter\, we show that moduli spaces of pseudo-hol
omorphic curves mapping to a symplectic orbifold admit global Kuranishi ch
arts. This allows us to construct other types of Gromov-Witten invariants\
, such as K-theoretic counts. The construction relies on an orbifold embed
ding theorem of Ross and Thomas.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Hoskins (Radboud University)
DTSTART:20241024T150000Z
DTEND:20241024T160000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/145
DESCRIPTION:Title: Moduli spaces of bundles on curves with abelian motives\nby
Victoria Hoskins (Radboud University) as part of M-seminar\n\n\nAbstract\
nI will explain how several different moduli spaces of bundles on a curve
have abelian motives and how conservatively properties for abelian motives
can be harnessed to obtain motivic formulas and provide motivic lifts of
known cohomological phenomena\, such as chi-independence and mirror symmet
ry. This is joint work with Simon Pepin Lehalleur.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zihong Chen (MIT)
DTSTART:20241031T203000Z
DTEND:20241031T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/146
DESCRIPTION:Title: The exponential type conjecture for quantum connections\nby
Zihong Chen (MIT) as part of M-seminar\n\n\nAbstract\nThe (small) quantum
connection is one of the simplest objects built out of Gromov-Witten theo
ry\, yet it gives rise to a repertoire of rich and important questions suc
h as the Gamma conjectures and the Dubrovin conjectures. There is a very b
asic question one can ask about this connection: what is its formal singul
arity type? People's (e.g. Kontsevich-Katzarkov-Pantev\, Iritani) expectat
ion for this is packaged into the so-called exponential type conjecture\,
and the goal of this talk is to discuss a proof in the case of closed mono
tone symplectic manifolds. My approach uses a reduction mod p argument\, a
nd I will start by introducing some basic ordinary differential equations
(in particular in characteristic p) and Katz's local monodromy theorem. Th
en I will demonstrate the key idea of proof pretending we were working in
a B-side mirror situation---matrix factorizations\, where it is particular
ly simple. Finally\, I will explain how to adapt the proof to the case of
quantum connections using certain equivariant operations on quantum cohomo
logy.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Sala (University of Pisa)
DTSTART:20241107T160000Z
DTEND:20241107T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/147
DESCRIPTION:Title: Cohomological Hall algebras\, their representations\, and Nakaj
ima operators\nby Francesco Sala (University of Pisa) as part of M-sem
inar\n\n\nAbstract\nIn the first part of the talk\, I will briefly introdu
ce the theory of 2d cohomological Hall algebras (COHAs)\, focusing on the
example of COHAs arising from zero-dimensional sheaves on smooth surfaces.
I will also describe certain geometric representations of these COHAs and
introduce Nakajima-type operators. In the second part\, I will discuss a
generalization and categorification of this framework.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ran Tessler (Weizmann Institute of Science)
DTSTART:20241114T190000Z
DTEND:20241114T200000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/148
DESCRIPTION:Title: Open Mirror Symmetry for Landau-Ginzburg Models\nby Ran Tes
sler (Weizmann Institute of Science) as part of M-seminar\n\n\nAbstract\nW
e will start with a short overview of mirror symmetry. We will then descri
be Saito-Givental's theory and its mirror dual using FJRW theory and open
FJRW theory. Based on joint works with Mark Gross and Tyler Kelly.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Grekov (Simons Center)
DTSTART:20241121T160000Z
DTEND:20241121T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/149
DESCRIPTION:Title: Many-body integrable systems and the moduli space of instantons
: Quantum spectral curves and classical Lax operators\nby Andrei Greko
v (Simons Center) as part of M-seminar\n\n\nAbstract\nIn this talk\, I wil
l explore the relation between the generalized equivariant cohomology theo
ries of the moduli space of instantons on \\mathbb{C}^2 and the famous fam
ily of integrable systems: Calogero-Moser\, Ruijsennars-Schneider\, and DE
LL. We introduce the so-called \\theta-transforms of the qq-characters vev
’s\, defined as integrals of certain classes in these cohomology theorie
s\, and relate them to quantum spectral curves of the corresponding integr
able systems. The solution to the quantum spectral curve equation is const
ructed in a natural way as well. In the second half\, I will explain the o
rbifolded version of all the notions defined above\, which corresponds to
the replacement of the moduli space of instantons with the affine Laumon s
pace. Such treatment allows one to obtain the Lax matrices of the integrab
le systems in question in a new form\, as well as the eigenvectors of thes
e matrices. In the end\, I will briefly explain how the above results help
to rederive the quantum-classical duality between the trigonometric degen
erations of the considered integrable systems and the corresponding spin c
hains\, as well as shed some light on the spectral duality for them.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amina Abdurrahman (IHES)
DTSTART:20241205T190000Z
DTEND:20241205T200000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/150
DESCRIPTION:Title: Hyperbolic homology 3-spheres\, spectral gaps and torsion homol
ogy growth\nby Amina Abdurrahman (IHES) as part of M-seminar\n\n\nAbst
ract\nWhen does a sequence of hyperbolic 3-manifolds with volume going to
infinity have exponentially growing torsion homology? For arithmetic tower
s\, the work of Bergeron-Sengun-Venkatesh suggests a set of conditions tha
t conjecturally imply exponential growth of torsion homology. Their work r
elies on Cheeger-Mueller's theorem\, linking torsion homology and analytic
torsion. For nice sequences of hyperbolic 3-manifolds we use a different
approach to find a condition implying exponential torsion homology growth:
we give a condition on the spectrum of the Laplacian. I will give several
motivations for this condition and show how to construct concrete example
s of sequences satisfying it. This is based on joint work with Anshul Adve
\, Vikram Giri\, Ben Lowe and Jonathan Zung.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Markarian (University of Strasbourg)
DTSTART:20250206T160000Z
DTEND:20250206T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/151
DESCRIPTION:Title: Multiplicative convolution and double shuffle relations\nby
Nikita Markarian (University of Strasbourg) as part of M-seminar\n\n\nAbs
tract\nMultiple zeta values (and their motivic version) is the gadget lyin
g in the heart of many subjects\, such as mixed Tate motives over Z.\nThe
geometric relations between them are\, therefore\, crucial for these subje
cts. The associator relations are supposed to be the strongest among all r
elations. Regularized double shuffle relations form another set of relatio
ns. The interaction between these two sets seems to be an important questi
on. Deligne and Terasoma initiated a geometric approach to interpreting re
gularized double shuffle relations. This approach explains the form of the
se relations: group-likeness of a certain element of a Hopf algebra. The t
ensor category standing behind this Hopf algebra is a certain category bui
lt of perverse sheaves\, the tensor product being given by convolution. I
will present my version of this approach\, which (in my opinion) clarifies
and simplifies some points. The first part of this story is published as
preprint https://arxiv.org/abs/2412.15694 .\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Nikolaev (University of Birmingham)
DTSTART:20250213T160000Z
DTEND:20250213T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/152
DESCRIPTION:Title: Geometry and Resurgence of WKB Solutions of Schrödinger Equati
ons - Part 1\nby Nikita Nikolaev (University of Birmingham) as part of
M-seminar\n\n\nAbstract\nI will recall the WKB method for Schrödinger eq
uations and explain how to make sense of it in more invariant and geometri
c terms. I will then explain how to prove that Schrödinger equations on c
ompact Riemann surfaces have the so-called quantum resurgence property: th
e Borel transform of a formal WKB solution is a holomorphic germ that exte
nds to a global holomorphic function on an infinite Riemann surface with e
xponential bounds at infinity. This infinite Riemann surface has a rich ge
ometry that is built out of the geometry of the spectral curve and complet
ely governs the Stokes phenomenon in the WKB method. Based on arXiv:2410.1
7224.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Nikolaev (University of Birmingham)
DTSTART:20250220T160000Z
DTEND:20250220T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/153
DESCRIPTION:Title: Geometry and Resurgence of WKB Solutions of Schrödinger Equati
ons - Part 2\nby Nikita Nikolaev (University of Birmingham) as part of
M-seminar\n\n\nAbstract\nI will recall the WKB method for Schrödinger eq
uations and explain how to make sense of it in more invariant and geometri
c terms. I will then explain how to prove that Schrödinger equations on c
ompact Riemann surfaces have the so-called quantum resurgence property: th
e Borel transform of a formal WKB solution is a holomorphic germ that exte
nds to a global holomorphic function on an infinite Riemann surface with e
xponential bounds at infinity. This infinite Riemann surface has a rich ge
ometry that is built out of the geometry of the spectral curve and complet
ely governs the Stokes phenomenon in the WKB method. Based on arXiv:2410.1
7224.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Dumanski (MIT)
DTSTART:20250227T160000Z
DTEND:20250227T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/154
DESCRIPTION:Title: From quantum loop group to coherent Satake category via fusion
product\nby Ilya Dumanski (MIT) as part of M-seminar\n\n\nAbstract\nCa
utis and Williams considered the category of perverse coherent sheaves on
the affine Grassmanian and proved for GL and conjectured for other types t
hat this category has a cluster structure. I will speak about partial prog
ress towards the proof of this conjecture for simply-laced types. Our appr
oach is based on relating the coherent Satake category with the category o
f finite-dimensional modules over the affine quantum group. The bridge bet
ween these two categories is provided by the notion of Feigin-Loktev fusio
n product for modules over the current algebra. In particular\, it helps t
o construct cluster short exact sequences of perverse coherent sheaves usi
ng the existence of exact sequences of modules over the quantum affine gro
up\, called the Q-systems.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Haiden (Center for Quantum Mathematics)
DTSTART:20250306T160000Z
DTEND:20250306T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/155
DESCRIPTION:Title: Counting in Calabi-Yau categories - Part 1\nby Fabian Haide
n (Center for Quantum Mathematics) as part of M-seminar\n\n\nAbstract\nI w
ill discuss a replacement for homotopy cardinality in situations where it
is a priori ill-defined\, including Z/2-graded dg-categories. A key ingred
ient are Calabi-Yau structures and their relative generalizations. As an a
pplication we obtain a Hall algebra for many pre-triangulated dg-categorie
s for which it was previously undefined. This also gives an intrinsic repl
acement for many ad-hoc constructions\, such as that of the elliptic Hall
algebra via the Drinfeld double. Another application is the proof of a con
jecture of Ng-Rutherford-Shende-Sivek expressing the ruling polynomial of
a Z/2m-graded Legendrian knot (which is part of the HOMFLY polynomial if m
=1) in terms of the homotopy cardinality of its augmentation category. Thi
s is joint work with Mikhail Gorsky\, arxiv:2409.10154.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Haiden (Center for Quantum Mathematics)
DTSTART:20250313T160000Z
DTEND:20250313T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/156
DESCRIPTION:Title: Counting in Calabi-Yau categories - Part 2\nby Fabian Haide
n (Center for Quantum Mathematics) as part of M-seminar\n\n\nAbstract\nI w
ill discuss a replacement for homotopy cardinality in situations where it
is a priori ill-defined\, including Z/2-graded dg-categories. A key ingred
ient are Calabi-Yau structures and their relative generalizations. As an a
pplication we obtain a Hall algebra for many pre-triangulated dg-categorie
s for which it was previously undefined. This also gives an intrinsic repl
acement for many ad-hoc constructions\, such as that of the elliptic Hall
algebra via the Drinfeld double. Another application is the proof of a con
jecture of Ng-Rutherford-Shende-Sivek expressing the ruling polynomial of
a Z/2m-graded Legendrian knot (which is part of the HOMFLY polynomial if m
=1) in terms of the homotopy cardinality of its augmentation category. Thi
s is joint work with Mikhail Gorsky\, arxiv:2409.10154.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/156/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Haney (Columbia University)
DTSTART:20250327T203000Z
DTEND:20250327T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/157
DESCRIPTION:Title: Infinity inner products and open Gromov-Witten invariants\n
by Sebastian Haney (Columbia University) as part of M-seminar\n\n\nAbstrac
t\nThe open Gromov-Witten (OGW) potential is a function defined on the Mau
rer-Cartan space of a closed Lagrangian submanifold in a symplectic manifo
ld with values in the Novikov ring. From the values of the OGW potential\,
one can extract so-called open Gromov-Witten invariants\, which count pse
udoholomorphic disks with boundary on the Lagrangian. Standard definitions
of the OGW potential only allow for the construction of OGW invariants wi
th values in the real or complex numbers. In this talk\, we will present a
construction of the OGW potential which gives invariants valued in any fi
eld of characteristic zero. The main algebraic input for our construction
is a homotopy cyclic inner product on the (curved) Fukaya A-infinity algeb
ra\, which generalizes the notion of a cyclically symmetric inner product
and is determined by a strong proper Calabi-Yau structure on the Fukaya ca
tegory.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/157/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martijn Kool (Utrecht University)
DTSTART:20250403T150000Z
DTEND:20250403T160000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/158
DESCRIPTION:Title: Virtual structure on Hilbert schemes of affine 4-space\nby
Martijn Kool (Utrecht University) as part of M-seminar\n\n\nAbstract\nWe c
onsider the generating series of certain K-theoretic invariants of Hilbert
schemes of points on affine 4-space. Using torus localization\, it reduce
s to an interesting weighted count of solid partitions for which Nekrasov
provided a (conjectural) closed formula. We prove this formula by showing
that the K-theoretic insertions lift to spin modules and give rise to a fa
ctorizable sequence of sheaves in the sense of Okounkov. Time permitting\,
we discuss relations to Nekrasov’s origami gauge theory.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/158/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wenjun Niu (Perimeter Institute)
DTSTART:20250409T150000Z
DTEND:20250409T160000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/159
DESCRIPTION:Title: Quantum algebras and spectral R-matrices from equivariant affin
e Grassmannians - Part 1\nby Wenjun Niu (Perimeter Institute) as part
of M-seminar\n\n\nAbstract\nIn these two talks I will explain my joint wor
k with R. Abedin\, in which we construct new quantum algebras and spectral
solutions of quantum Yang-Baxter equations. These quantum algebras are qu
antizations of Yang’s r matrix associated to the cotangent Lie algebra d
=T^*g of a Lie algebra g. Our construction is based on the geometry of the
equivariant affine Grassmannian associated to g\, and is related to holom
orphic-topological twist of 4d N=2 gauge theories. I will start by giving
a brief review of the holomorphic-topological twist of 4d N=2 gauge theori
es\, especially its relation to equivariant affine Grassmannians. I will a
lso review the work of Costello-Witten-Yamazaki\, in which the authors giv
e a gauge-theoretic origin to spectral solutions of YB equations. Our cons
tructions are inspired by these physical considerations. After that\, I wi
ll explain our results in relation to the geometry of equivariant affine G
rassmannians. Time permitting\, I will also explain how we can dynamically
twist the quantum algebra over formal neighborhoods of the moduli space o
f G-bundles\, and obtain dynamical R-matrices as a consequence.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/159/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wenjun Niu (Perimeter Institute)
DTSTART:20250416T150000Z
DTEND:20250416T160000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/160
DESCRIPTION:Title: Quantum algebras and spectral R-matrices from equivariant affin
e Grassmannians - Part 2\nby Wenjun Niu (Perimeter Institute) as part
of M-seminar\n\n\nAbstract\nIn these two talks I will explain my joint wor
k with R. Abedin\, in which we construct new quantum algebras and spectral
solutions of quantum Yang-Baxter equations. These quantum algebras are qu
antizations of Yang’s r matrix associated to the cotangent Lie algebra d
=T^*g of a Lie algebra g. Our construction is based on the geometry of the
equivariant affine Grassmannian associated to g\, and is related to holom
orphic-topological twist of 4d N=2 gauge theories. I will start by giving
a brief review of the holomorphic-topological twist of 4d N=2 gauge theori
es\, especially its relation to equivariant affine Grassmannians. I will a
lso review the work of Costello-Witten-Yamazaki\, in which the authors giv
e a gauge-theoretic origin to spectral solutions of YB equations. Our cons
tructions are inspired by these physical considerations. After that\, I wi
ll explain our results in relation to the geometry of equivariant affine G
rassmannians. Time permitting\, I will also explain how we can dynamically
twist the quantum algebra over formal neighborhoods of the moduli space o
f G-bundles\, and obtain dynamical R-matrices as a consequence.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/160/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominic Joyce (University of Oxford)
DTSTART:20250424T150000Z
DTEND:20250424T160000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/161
DESCRIPTION:Title: Orientations on moduli spaces of coherent sheaves on Calabi-Yau
4-folds - Part I\nby Dominic Joyce (University of Oxford) as part of
M-seminar\n\n\nAbstract\nLet X be a compact Calabi-Yau 4-fold. To define D
T4 invariants of X\, one needs an orientation on moduli spaces of semistab
le coherent sheaves on X\, or (better) an orientation on the moduli stack
M of all perfect complexes on X\, in the sense of Borisov-Joyce 2017. Cao-
Gross-Joyce 2020 claimed to prove that M is orientable for any Calabi-Yau
4-fold X. Unfortunately\, we have found a mistake in their proof\, and the
theorem itself may be false\, though we do not have a counterexample. I w
ill explain how to fix the mistake in Cao-Gross-Joyce under an extra hypot
hesis on the cohomology H^3(X\,Z) (for example\, H^3(X\,Z)=0 is sufficient
). We also explain a choice of extra data (a "flag structure” on H^4(X\,
Z)) which determines a canonical orientation on M. This is part of a large
r project studying orientability and orientations of moduli spaces of conn
ections in gauge theory\, and of moduli spaces of special submanifolds. We
define "bordism categories” Bord_n(BG) with objects pairs (X\,P) of a c
ompact spin n-manifold X and a principal G-bundle P —> X. Then orientati
ons of gauge theory moduli spaces of connections on P can be encoded in a
functor from Bord_n(BG) to Z_2-torsors\, and an orientation of the gauge t
heory moduli space B_P corresponds to a trivialization of this functor on
a subcategory [X\,P] of Bord_n(BG). It turns out that Bord_n(BG) is a "Pic
ard groupoid”\, and can be understood in terms of the spin bordism group
s Omega_m^{Spin}(BG) for m=n\,n+1. So we reduce orientability questions to
(difficult) calculations involving spin bordism groups of classifying spa
ces in Algebraic Topology. This is joint work with Markus Upmeier.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/161/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominic Joyce (University of Oxford)
DTSTART:20250501T150000Z
DTEND:20250501T160000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/162
DESCRIPTION:Title: Orientations on moduli spaces of coherent sheaves on Calabi-Yau
4-folds - Part II\nby Dominic Joyce (University of Oxford) as part of
M-seminar\n\n\nAbstract\nLet X be a compact Calabi-Yau 4-fold. To define
DT4 invariants of X\, one needs an orientation on moduli spaces of semista
ble coherent sheaves on X\, or (better) an orientation on the moduli stack
M of all perfect complexes on X\, in the sense of Borisov-Joyce 2017. Cao
-Gross-Joyce 2020 claimed to prove that M is orientable for any Calabi-Yau
4-fold X. Unfortunately\, we have found a mistake in their proof\, and th
e theorem itself may be false\, though we do not have a counterexample. I
will explain how to fix the mistake in Cao-Gross-Joyce under an extra hypo
thesis on the cohomology H^3(X\,Z) (for example\, H^3(X\,Z)=0 is sufficien
t). We also explain a choice of extra data (a "flag structure” on H^4(X\
,Z)) which determines a canonical orientation on M. This is part of a larg
er project studying orientability and orientations of moduli spaces of con
nections in gauge theory\, and of moduli spaces of special submanifolds. W
e define "bordism categories” Bord_n(BG) with objects pairs (X\,P) of a
compact spin n-manifold X and a principal G-bundle P —> X. Then orientat
ions of gauge theory moduli spaces of connections on P can be encoded in a
functor from Bord_n(BG) to Z_2-torsors\, and an orientation of the gauge
theory moduli space B_P corresponds to a trivialization of this functor on
a subcategory [X\,P] of Bord_n(BG). It turns out that Bord_n(BG) is a "Pi
card groupoid”\, and can be understood in terms of the spin bordism grou
ps Omega_m^{Spin}(BG) for m=n\,n+1. So we reduce orientability questions t
o (difficult) calculations involving spin bordism groups of classifying sp
aces in Algebraic Topology. This is joint work with Markus Upmeier.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/162/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ailsa Keating (University of Cambridge)
DTSTART:20250508T150000Z
DTEND:20250508T160000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/163
DESCRIPTION:Title: Homological mirror symmetry for projective K3 surfaces\nby
Ailsa Keating (University of Cambridge) as part of M-seminar\n\n\nAbstract
\nJoint work with Paul Hacking. We outline a proof that the Fukaya categor
y of a projective K3 surface is equivalent to the derived category of cohe
rent sheaves on the mirror\, which is a K3 surface of Picard rank 19 over
the field C((q)) of formal Laurent series. This builds on prior work of Se
idel\, who proved the theorem in the case of the quartic surface\, Gross-S
iebert\, Kontsevich-Soibelman\, Sheridan\, and others.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/163/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yash Deshmukh (IAS)
DTSTART:20251002T203000Z
DTEND:20251002T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/164
DESCRIPTION:Title: Categorical and geometric enumerative invariants\nby Yash D
eshmukh (IAS) as part of M-seminar\n\n\nAbstract\nCostello introduced cate
gorical enumerative invariants for a smooth and proper Calabi--Yau categor
y equipped with a splitting of the non-commutative Hodge--de Rham spectral
sequence. I will discuss an extension of this to a chain-level CohFT stru
cture on the Hochschild homology of the category. This construction will b
e universal in a precise sense\, and I will explain how to exploit this to
compare the categorical CohFT of a Fukaya category with the geometric Coh
FT of the underlying symplectic manifold whenever a chain-level open-close
d Gromov--Witten CohFT satisfying suitable properties exists.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/164/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Descombes (Imperial College)
DTSTART:20251006T173000Z
DTEND:20251006T183000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/165
DESCRIPTION:Title: Hyperbolic localization in Donaldson-Thomas theory - 1\nby
Pierre Descombes (Imperial College) as part of M-seminar\n\n\nAbstract\nGi
ven a scheme X with an action of a one-dimensional torus\, the hyperbolic
localization functor\, which restricts constructible complexes from X to t
he attracting variety X^+ and then projects with compact support to the fi
xed variety X^0\, was introduced by Braden in order to study generalizatio
ns of Białynicki-Birula decompositions beyond the smooth case. Richarz ha
s then proven that this functor commutes with vanishing cycles.\nUsing shi
fted symplectic geometry and a shifted Darboux theorem\, moduli spaces of
sheaves on Calabi-Yau threefolds are described locally by critical loci of
functions on smooth spaces\, which are related locally by adding quadrati
c forms to the functions. On such moduli spaces\, a DT perverse sheaf\, wh
ose cohomology gives the cohomological DT invariants\, was defined by Brav
\, Bussi\, Dupont\, Joyce\, and Szendroï by gluing vanishing cycles on su
ch local models\, involving a subtle trivialization of the action of quadr
atic forms using orientation data.\nWe will explain here how to prove a fo
rmula for the hyperbolic localization of the DT perverse sheaf\, combining
the results of Białynicki-Birula and Richarz with a study of the behavio
r of hyperbolic localization with quadratic forms and orientations. One ob
tains in particular from this result a critical version of Białynicki-Bir
ula decomposition in cohomological DT theory.\nWe will also explain how to
obtain a stacky version of the above result\, replacing X^+ and X^0 by th
e stacks of filtered and graded points\, which has recently led to the pro
of of fundamental results in DT theory\, namely the proof of the Kontsevic
h-Soibelman wall-crossing formula and the construction of the cohomologica
l Hall algebra for CY3 categories.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/165/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Descombes (Imperial College)
DTSTART:20251008T173000Z
DTEND:20251008T183000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/166
DESCRIPTION:Title: Hyperbolic localization in Donaldson-Thomas theory - 2\nby
Pierre Descombes (Imperial College) as part of M-seminar\n\n\nAbstract\nGi
ven a scheme X with an action of a one-dimensional torus\, the hyperbolic
localization functor\, which restricts constructible complexes from X to t
he attracting variety X^+ and then projects with compact support to the fi
xed variety X^0\, was introduced by Braden in order to study generalizatio
ns of Białynicki-Birula decompositions beyond the smooth case. Richarz ha
s then proven that this functor commutes with vanishing cycles.\nUsing shi
fted symplectic geometry and a shifted Darboux theorem\, moduli spaces of
sheaves on Calabi-Yau threefolds are described locally by critical loci of
functions on smooth spaces\, which are related locally by adding quadrati
c forms to the functions. On such moduli spaces\, a DT perverse sheaf\, wh
ose cohomology gives the cohomological DT invariants\, was defined by Brav
\, Bussi\, Dupont\, Joyce\, and Szendroï by gluing vanishing cycles on su
ch local models\, involving a subtle trivialization of the action of quadr
atic forms using orientation data.\nWe will explain here how to prove a fo
rmula for the hyperbolic localization of the DT perverse sheaf\, combining
the results of Białynicki-Birula and Richarz with a study of the behavio
r of hyperbolic localization with quadratic forms and orientations. One ob
tains in particular from this result a critical version of Białynicki-Bir
ula decomposition in cohomological DT theory.\nWe will also explain how to
obtain a stacky version of the above result\, replacing X^+ and X^0 by th
e stacks of filtered and graded points\, which has recently led to the pro
of of fundamental results in DT theory\, namely the proof of the Kontsevic
h-Soibelman wall-crossing formula and the construction of the cohomologica
l Hall algebra for CY3 categories.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/166/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Descombes (Imperial College)
DTSTART:20251009T173000Z
DTEND:20251009T183000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/167
DESCRIPTION:Title: Hyperbolic localization in Donaldson-Thomas theory - 3\nby
Pierre Descombes (Imperial College) as part of M-seminar\n\n\nAbstract\nGi
ven a scheme X with an action of a one-dimensional torus\, the hyperbolic
localization functor\, which restricts constructible complexes from X to t
he attracting variety X^+ and then projects with compact support to the fi
xed variety X^0\, was introduced by Braden in order to study generalizatio
ns of Białynicki-Birula decompositions beyond the smooth case. Richarz ha
s then proven that this functor commutes with vanishing cycles.\nUsing shi
fted symplectic geometry and a shifted Darboux theorem\, moduli spaces of
sheaves on Calabi-Yau threefolds are described locally by critical loci of
functions on smooth spaces\, which are related locally by adding quadrati
c forms to the functions. On such moduli spaces\, a DT perverse sheaf\, wh
ose cohomology gives the cohomological DT invariants\, was defined by Brav
\, Bussi\, Dupont\, Joyce\, and Szendroï by gluing vanishing cycles on su
ch local models\, involving a subtle trivialization of the action of quadr
atic forms using orientation data.\nWe will explain here how to prove a fo
rmula for the hyperbolic localization of the DT perverse sheaf\, combining
the results of Białynicki-Birula and Richarz with a study of the behavio
r of hyperbolic localization with quadratic forms and orientations. One ob
tains in particular from this result a critical version of Białynicki-Bir
ula decomposition in cohomological DT theory.\nWe will also explain how to
obtain a stacky version of the above result\, replacing X^+ and X^0 by th
e stacks of filtered and graded points\, which has recently led to the pro
of of fundamental results in DT theory\, namely the proof of the Kontsevic
h-Soibelman wall-crossing formula and the construction of the cohomologica
l Hall algebra for CY3 categories.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/167/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sabin Cautis (UBC)
DTSTART:20251014T210000Z
DTEND:20251014T220000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/168
DESCRIPTION:Title: Abelian Hall categories - 1\nby Sabin Cautis (UBC) as part
of M-seminar\n\n\nAbstract\nAfter reviewing some background\, we will expl
ain how to associate to any\nquiver a finite length abelian category which
categorifies the corresponding K-theoretic Hall algebra. The simples in t
his category provide a (dual) canonical basis of the Hall algebra. In part
icular\, if the quiver is affine\, this provides a basis for the positive
half of the corresponding quantum toroidal algebra. We also explain how th
is abelian category is naturally endowed with renormalized r-matrices.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/168/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sabin Cautis (UBC)
DTSTART:20251015T210000Z
DTEND:20251015T220000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/169
DESCRIPTION:Title: Abelian Hall categories - 2\nby Sabin Cautis (UBC) as part
of M-seminar\n\n\nAbstract\nAfter reviewing some background\, we will expl
ain how to associate to any\nquiver a finite length abelian category which
categorifies the corresponding K-theoretic Hall algebra. The simples in t
his category provide a (dual) canonical basis of the Hall algebra. In part
icular\, if the quiver is affine\, this provides a basis for the positive
half of the corresponding quantum toroidal algebra. We also explain how th
is abelian category is naturally endowed with renormalized r-matrices.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/169/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sabin Cautis (UBC)
DTSTART:20251016T210000Z
DTEND:20251016T220000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/170
DESCRIPTION:Title: Abelian Hall categories - 3\nby Sabin Cautis (UBC) as part
of M-seminar\n\n\nAbstract\nAfter reviewing some background\, we will expl
ain how to associate to any\nquiver a finite length abelian category which
categorifies the corresponding K-theoretic Hall algebra. The simples in t
his category provide a (dual) canonical basis of the Hall algebra. In part
icular\, if the quiver is affine\, this provides a basis for the positive
half of the corresponding quantum toroidal algebra. We also explain how th
is abelian category is naturally endowed with renormalized r-matrices.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/170/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiu-Chu Melissa Liu (Columbia University)
DTSTART:20251023T203000Z
DTEND:20251023T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/171
DESCRIPTION:Title: Remodeling Conjecture with descendants\nby Chiu-Chu Melissa
Liu (Columbia University) as part of M-seminar\n\n\nAbstract\nThe Remodel
ing Conjecture proposed by Bouchard-Klemm-Mariño-Pasquetti relates Gromov
-Witten (GW) invariants counting holomorphic curves in a toric Calabi-Yau
3-manifold/3-orbifold to the Chekhov-Eynard-Orantin Topological Recursion
(TR) invariants of its mirror curve. In this talk\, I will describe the Re
modeling Conjecture with descendants\, which is a correspondence between a
ll-genus equivariant descendant GW invariants and oscillatory integrals (L
aplace transforms) of TR invariants along relative 1-cycles on the equivar
iant mirror curve. Our genus-zero correspondence is a version of equivaria
nt Hodge-theoretic mirror symmetry with integral structures. In the non-eq
uivariant setting\, we prove a conjecture of Hosono which equates quantum
cohomology central charges of compactly supported coherent sheaves with pe
riod integrals of a holomorphic 3-form along integral 3-cycles on the Hori
-Vafa mirror. This talk is based on joint work with Bohan Fang\, Song Yu\,
and Zhengyu Zong.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/171/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Yue Yu (CalTech)
DTSTART:20251030T200000Z
DTEND:20251030T210000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/172
DESCRIPTION:by Tony Yue Yu (CalTech) as part of M-seminar\n\nAbstract: TBA
\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/172/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruoxi Li (University of Pittsburgh)
DTSTART:20251106T213000Z
DTEND:20251106T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/173
DESCRIPTION:Title: Motivic classes of varieties and stacks with applications to Hi
ggs bundles and bundles with connections\nby Ruoxi Li (University of P
ittsburgh) as part of M-seminar\n\n\nAbstract\nIn this talk\, we will firs
t discuss the motivations for motivic classes coming from point counting o
ver finite fields. Then we will give the definitions of the motivic classe
s of varieties\, in particular we explain that an extra relation is needed
in finite characteristic. We will introduce symmetric powers and motivic
zeta functions that are universal versions of local zeta functions.\nFor t
he second part of the talk\, we will focus on the motivic classes of stack
s. In particular\, we will give the explicit formulas for the motivic clas
ses of moduli of Higgs bundles. If time permits\, we will discuss future w
ork on the motivic classes of moduli of bundles with connections.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/173/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Alexandrov (Université de Montpellier)
DTSTART:20251110T160000Z
DTEND:20251110T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/174
DESCRIPTION:Title: Mock modularity of Calabi-Yau threefolds - 1\nby Sergey Ale
xandrov (Université de Montpellier) as part of M-seminar\n\n\nAbstract\nT
he seminars aim to explain modular properties of rank 0 generalized Donald
son-Thomas (DT) invariants\, how these properties can be used to compute t
he invariants\, and their implications for other topological invariants su
ch as Vafa-Witten and Gopakumar-Vafa.\n\n1. In the first part\, I'll expla
in basic facts about modular forms\, mock modular forms\, Jacobi forms and
indefinite theta series. In the end\, I'll switch the topic and explain a
few facts about generalized DT invariants associated to Calabi-Yau threef
olds.\n\n2. In the second part\, I'll explain how one can derive precise m
odular properties of the generating functions of rank 0 DT invariants whic
h turn out to be (higher depth) mock modular forms. I'll present an equati
on encoding the modular anomaly\, its extensions and how it can be solved
for compact and non-compact CY threefolds.\n\n3. In the compact case\, the
solution of the modular anomaly allows us to fix the generating functions
up to a finite number of coefficients\, the so-called polar terms. In the
third part\, I'll show how these terms can be computed using wall-crossin
g and direct integration of topological string\, which for a set of compac
t one-parameter threefolds resulted in explicit modular and mock modular f
orms encoding rank 0 DT invariants. In turn\, they have been used to gener
ate new Gopakumar-Vafa invariants overcoming the limitations of the direct
integration method.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/174/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Alexandrov (Université de Montpellier)
DTSTART:20251112T160000Z
DTEND:20251112T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/175
DESCRIPTION:Title: Mock modularity of Calabi-Yau threefolds - 2\nby Sergey Ale
xandrov (Université de Montpellier) as part of M-seminar\n\n\nAbstract\nT
he seminars aim to explain modular properties of rank 0 generalized Donald
son-Thomas (DT) invariants\, how these properties can be used to compute t
he invariants\, and their implications for other topological invariants su
ch as Vafa-Witten and Gopakumar-Vafa.\n\n1. In the first part\, I'll expla
in basic facts about modular forms\, mock modular forms\, Jacobi forms and
indefinite theta series. In the end\, I'll switch the topic and explain a
few facts about generalized DT invariants associated to Calabi-Yau threef
olds.\n\n2. In the second part\, I'll explain how one can derive precise m
odular properties of the generating functions of rank 0 DT invariants whic
h turn out to be (higher depth) mock modular forms. I'll present an equati
on encoding the modular anomaly\, its extensions and how it can be solved
for compact and non-compact CY threefolds.\n\n3. In the compact case\, the
solution of the modular anomaly allows us to fix the generating functions
up to a finite number of coefficients\, the so-called polar terms. In the
third part\, I'll show how these terms can be computed using wall-crossin
g and direct integration of topological string\, which for a set of compac
t one-parameter threefolds resulted in explicit modular and mock modular f
orms encoding rank 0 DT invariants. In turn\, they have been used to gener
ate new Gopakumar-Vafa invariants overcoming the limitations of the direct
integration method.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/175/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Alexandrov (Université de Montpellier)
DTSTART:20251113T160000Z
DTEND:20251113T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/176
DESCRIPTION:Title: Mock modularity of Calabi-Yau threefolds - 3\nby Sergey Ale
xandrov (Université de Montpellier) as part of M-seminar\n\n\nAbstract\nT
he seminars aim to explain modular properties of rank 0 generalized Donald
son-Thomas (DT) invariants\, how these properties can be used to compute t
he invariants\, and their implications for other topological invariants su
ch as Vafa-Witten and Gopakumar-Vafa.\n\n1. In the first part\, I'll expla
in basic facts about modular forms\, mock modular forms\, Jacobi forms and
indefinite theta series. In the end\, I'll switch the topic and explain a
few facts about generalized DT invariants associated to Calabi-Yau threef
olds.\n\n2. In the second part\, I'll explain how one can derive precise m
odular properties of the generating functions of rank 0 DT invariants whic
h turn out to be (higher depth) mock modular forms. I'll present an equati
on encoding the modular anomaly\, its extensions and how it can be solved
for compact and non-compact CY threefolds.\n\n3. In the compact case\, the
solution of the modular anomaly allows us to fix the generating functions
up to a finite number of coefficients\, the so-called polar terms. In the
third part\, I'll show how these terms can be computed using wall-crossin
g and direct integration of topological string\, which for a set of compac
t one-parameter threefolds resulted in explicit modular and mock modular f
orms encoding rank 0 DT invariants. In turn\, they have been used to gener
ate new Gopakumar-Vafa invariants overcoming the limitations of the direct
integration method.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/176/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Padurariu (Institut de Mathématiques de Jussieu-Paris Rive
Gauche)
DTSTART:20251117T183000Z
DTEND:20251117T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/177
DESCRIPTION:Title: BPS cohomology and quasi-BPS categories (1 of 4)\nby Tudor
Padurariu (Institut de Mathématiques de Jussieu-Paris Rive Gauche) as par
t of M-seminar\n\n\nAbstract\nBPS invariants were initially introduced as
counts of objects in Calabi-Yau 3-categories\, generalizing Donaldson-Thom
as invariants counting ideal sheaves\, or stable sheaves (in the absence o
f strictly semistable sheaves) on a Calabi-Yau 3-fold. BPS invariants may
be defined more generally for symmetric stacks\, and they can be also refi
ned to BPS cohomology and (partially) to quasi-BPS categories. \nI will di
scuss the construction and some of the fundamental results about BPS cohom
ology and quasi-BPS categories of symmetric stacks. I will focus mostly on
the case of quivers with potential and Higgs bundles on a curve. More pre
cisely\, I will talk about the construction of the Hall product in (singul
ar or critical) cohomology and for categories of coherent sheaves or matri
x factorizations\, cohomological integrality\, semiorthogonal decompositio
ns of relevant categories in terms of quasi-BPS categories\, and propertie
s of quasi-BPS categories. Lastly\, I will discuss the \\chi-independence
phenomenon for moduli of sheaves supported on curves in a Calabi-Yau 3-fol
d for both BPS cohomology and quasi-BPS categories\, and its relation to m
irror symmetry and Langlands duality for local curves. \nThe results discu
ssed are due to many people\, including Kontsevich-Soibelman\, Joyce et.al
\, Meinhardt-Reineke\, Davison-Meinhardt\, Toda etc. I will also mention r
esults from joint work with Yukinobu Toda\, and joint work with Chenjing B
u\, Ben Davison\, Andrés Ibáñez Núñez\, and Tasuki Kinjo.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/177/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Padurariu (Institut de Mathématiques de Jussieu-Paris Rive
Gauche)
DTSTART:20251118T173000Z
DTEND:20251118T183000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/178
DESCRIPTION:Title: BPS cohomology and quasi-BPS categories (2 of 4)\nby Tudor
Padurariu (Institut de Mathématiques de Jussieu-Paris Rive Gauche) as par
t of M-seminar\n\n\nAbstract\nBPS invariants were initially introduced as
counts of objects in Calabi-Yau 3-categories\, generalizing Donaldson-Thom
as invariants counting ideal sheaves\, or stable sheaves (in the absence o
f strictly semistable sheaves) on a Calabi-Yau 3-fold. BPS invariants may
be defined more generally for symmetric stacks\, and they can be also refi
ned to BPS cohomology and (partially) to quasi-BPS categories. \nI will di
scuss the construction and some of the fundamental results about BPS cohom
ology and quasi-BPS categories of symmetric stacks. I will focus mostly on
the case of quivers with potential and Higgs bundles on a curve. More pre
cisely\, I will talk about the construction of the Hall product in (singul
ar or critical) cohomology and for categories of coherent sheaves or matri
x factorizations\, cohomological integrality\, semiorthogonal decompositio
ns of relevant categories in terms of quasi-BPS categories\, and propertie
s of quasi-BPS categories. Lastly\, I will discuss the \\chi-independence
phenomenon for moduli of sheaves supported on curves in a Calabi-Yau 3-fol
d for both BPS cohomology and quasi-BPS categories\, and its relation to m
irror symmetry and Langlands duality for local curves. \nThe results discu
ssed are due to many people\, including Kontsevich-Soibelman\, Joyce et.al
\, Meinhardt-Reineke\, Davison-Meinhardt\, Toda etc. I will also mention r
esults from joint work with Yukinobu Toda\, and joint work with Chenjing B
u\, Ben Davison\, Andrés Ibáñez Núñez\, and Tasuki Kinjo.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/178/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Padurariu (Institut de Mathématiques de Jussieu-Paris Rive
Gauche)
DTSTART:20251119T173000Z
DTEND:20251119T183000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/179
DESCRIPTION:Title: BPS cohomology and quasi-BPS categories (3 of 4)\nby Tudor
Padurariu (Institut de Mathématiques de Jussieu-Paris Rive Gauche) as par
t of M-seminar\n\n\nAbstract\nBPS invariants were initially introduced as
counts of objects in Calabi-Yau 3-categories\, generalizing Donaldson-Thom
as invariants counting ideal sheaves\, or stable sheaves (in the absence o
f strictly semistable sheaves) on a Calabi-Yau 3-fold. BPS invariants may
be defined more generally for symmetric stacks\, and they can be also refi
ned to BPS cohomology and (partially) to quasi-BPS categories. \nI will di
scuss the construction and some of the fundamental results about BPS cohom
ology and quasi-BPS categories of symmetric stacks. I will focus mostly on
the case of quivers with potential and Higgs bundles on a curve. More pre
cisely\, I will talk about the construction of the Hall product in (singul
ar or critical) cohomology and for categories of coherent sheaves or matri
x factorizations\, cohomological integrality\, semiorthogonal decompositio
ns of relevant categories in terms of quasi-BPS categories\, and propertie
s of quasi-BPS categories. Lastly\, I will discuss the \\chi-independence
phenomenon for moduli of sheaves supported on curves in a Calabi-Yau 3-fol
d for both BPS cohomology and quasi-BPS categories\, and its relation to m
irror symmetry and Langlands duality for local curves. \nThe results discu
ssed are due to many people\, including Kontsevich-Soibelman\, Joyce et.al
\, Meinhardt-Reineke\, Davison-Meinhardt\, Toda etc. I will also mention r
esults from joint work with Yukinobu Toda\, and joint work with Chenjing B
u\, Ben Davison\, Andrés Ibáñez Núñez\, and Tasuki Kinjo.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/179/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Padurariu (Institut de Mathématiques de Jussieu-Paris Rive
Gauche)
DTSTART:20251120T173000Z
DTEND:20251120T183000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/180
DESCRIPTION:Title: BPS cohomology and quasi-BPS categories (4 of 4)\nby Tudor
Padurariu (Institut de Mathématiques de Jussieu-Paris Rive Gauche) as par
t of M-seminar\n\n\nAbstract\nBPS invariants were initially introduced as
counts of objects in Calabi-Yau 3-categories\, generalizing Donaldson-Thom
as invariants counting ideal sheaves\, or stable sheaves (in the absence o
f strictly semistable sheaves) on a Calabi-Yau 3-fold. BPS invariants may
be defined more generally for symmetric stacks\, and they can be also refi
ned to BPS cohomology and (partially) to quasi-BPS categories. \nI will di
scuss the construction and some of the fundamental results about BPS cohom
ology and quasi-BPS categories of symmetric stacks. I will focus mostly on
the case of quivers with potential and Higgs bundles on a curve. More pre
cisely\, I will talk about the construction of the Hall product in (singul
ar or critical) cohomology and for categories of coherent sheaves or matri
x factorizations\, cohomological integrality\, semiorthogonal decompositio
ns of relevant categories in terms of quasi-BPS categories\, and propertie
s of quasi-BPS categories. Lastly\, I will discuss the \\chi-independence
phenomenon for moduli of sheaves supported on curves in a Calabi-Yau 3-fol
d for both BPS cohomology and quasi-BPS categories\, and its relation to m
irror symmetry and Langlands duality for local curves. \nThe results discu
ssed are due to many people\, including Kontsevich-Soibelman\, Joyce et.al
\, Meinhardt-Reineke\, Davison-Meinhardt\, Toda etc. I will also mention r
esults from joint work with Yukinobu Toda\, and joint work with Chenjing B
u\, Ben Davison\, Andrés Ibáñez Núñez\, and Tasuki Kinjo.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/180/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Smirnov (University of North Carolina)
DTSTART:20251202T213000Z
DTEND:20251202T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/181
DESCRIPTION:Title: Frobenius structures for quantum differential and q-difference
equations (1 of 3)\nby Andrey Smirnov (University of North Carolina) a
s part of M-seminar\n\n\nAbstract\nThere is a known connection between the
Kloosterman sum in number theory and the Bessel differential equation. Th
is connection was explained by B. Dwork in 1974 through his discovery of F
robenius structures in the p-adic theory of the Bessel equation. In this t
alk\, I will speculate that this connection extends to the quantum differe
ntial equations appearing in the quantum cohomology of Nakajima varieties.
As an example\, I will present an explicit conjectural description of the
corresponding Frobenius structures. The traces of these Frobenius structu
res serve as natural finite-field analogs of the integral solutions to qua
ntum differential equations known from mirror symmetry. Some of these resu
lts also extend to the setting of q-difference equations\, where a similar
picture emerges when q is close to a root of unity in the p-adic norm. I
will review these developments and discuss their connections to other rece
nt advances\, including quantum Steenrod operations\, Habiro cohomology\,
and related topics.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/181/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Smirnov (University of North Carolina)
DTSTART:20251203T213000Z
DTEND:20251203T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/182
DESCRIPTION:Title: Frobenius structures for quantum differential and q-difference
equations (2 of 3)\nby Andrey Smirnov (University of North Carolina) a
s part of M-seminar\n\n\nAbstract\nThere is a known connection between the
Kloosterman sum in number theory and the Bessel differential equation. Th
is connection was explained by B. Dwork in 1974 through his discovery of F
robenius structures in the p-adic theory of the Bessel equation. In this t
alk\, I will speculate that this connection extends to the quantum differe
ntial equations appearing in the quantum cohomology of Nakajima varieties.
As an example\, I will present an explicit conjectural description of the
corresponding Frobenius structures. The traces of these Frobenius structu
res serve as natural finite-field analogs of the integral solutions to qua
ntum differential equations known from mirror symmetry. Some of these resu
lts also extend to the setting of q-difference equations\, where a similar
picture emerges when q is close to a root of unity in the p-adic norm. I
will review these developments and discuss their connections to other rece
nt advances\, including quantum Steenrod operations\, Habiro cohomology\,
and related topics.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/182/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Smirnov (University of North Carolina)
DTSTART:20251204T213000Z
DTEND:20251204T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/183
DESCRIPTION:Title: Frobenius structures for quantum differential and q-difference
equations (3 of 3)\nby Andrey Smirnov (University of North Carolina) a
s part of M-seminar\n\n\nAbstract\nThere is a known connection between the
Kloosterman sum in number theory and the Bessel differential equation. Th
is connection was explained by B. Dwork in 1974 through his discovery of F
robenius structures in the p-adic theory of the Bessel equation. In this t
alk\, I will speculate that this connection extends to the quantum differe
ntial equations appearing in the quantum cohomology of Nakajima varieties.
As an example\, I will present an explicit conjectural description of the
corresponding Frobenius structures. The traces of these Frobenius structu
res serve as natural finite-field analogs of the integral solutions to qua
ntum differential equations known from mirror symmetry. Some of these resu
lts also extend to the setting of q-difference equations\, where a similar
picture emerges when q is close to a root of unity in the p-adic norm. I
will review these developments and discuss their connections to other rece
nt advances\, including quantum Steenrod operations\, Habiro cohomology\,
and related topics.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/183/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Sulkowski (University of Warsaw)
DTSTART:20251210T183000Z
DTEND:20251210T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/184
DESCRIPTION:Title: Symmetric quivers for 2d\, 3d and 4d theories and topological s
trings (1 of 2)\nby Piotr Sulkowski (University of Warsaw) as part of
M-seminar\n\n\nAbstract\nI will present how invariants of symmetric quiver
s capture various\nobservables of physical theories in 2\, 3 and 4 dimensi
ons\, as well as of topological string theory. The observables in question
include or are immediately related to knot invariants\, (wild) BPS degene
racies of 4d N=2 theories\, superconformal indices\, wall-crossing identit
ies\, 2d CFT or VOA characters\, LMOV invariants\, etc. Such a unifying ro
le of symmetric quivers is very useful and intriguing and calls for deeper
\nunderstanding.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/184/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Sulkowski (University of Warsaw)
DTSTART:20251211T183000Z
DTEND:20251211T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/185
DESCRIPTION:Title: Symmetric quivers for 2d\, 3d and 4d theories and topological s
trings (2 of 2)\nby Piotr Sulkowski (University of Warsaw) as part of
M-seminar\n\n\nAbstract\nI will present how invariants of symmetric quiver
s capture various\nobservables of physical theories in 2\, 3 and 4 dimensi
ons\, as well as of topological string theory. The observables in question
include or are immediately related to knot invariants\, (wild) BPS degene
racies of 4d N=2 theories\, superconformal indices\, wall-crossing identit
ies\, 2d CFT or VOA characters\, LMOV invariants\, etc. Such a unifying ro
le of symmetric quivers is very useful and intriguing and calls for deeper
\nunderstanding.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/185/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Tsygan (Northwestern University)
DTSTART:20260205T213000Z
DTEND:20260205T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/186
DESCRIPTION:Title: The Gauss-Manin connection in noncommutative geometry\nby B
oris Tsygan (Northwestern University) as part of M-seminar\n\n\nAbstract\n
In noncommutative geometry\, a variety is replaced by an associative ring
or\, more generally\, by an appropriate version of a category\, and the De
Rham cohomology is replaced by the periodic cyclic complex. As shown by G
etzler\, the periodic cyclic homology of a family of algebras carries a fl
at connection\, which is analogous to the De Rham cohomology of a family o
f varieties carrying the Gauss-Manin connection. The structure living on t
he periodic cyclic complex (as opposed to homology) had been studied exten
sively\, for example by Dolgushev\, Tamarkin and the author\, by Kontsevic
h and Soibelman\, by Willwacher\, and others. The question was recently re
visited by the author and\, from a different perspective\, by Antieu. I wi
ll review the main results and concentrate on explicit formulas. Those for
mulas seem to have good convergence properties\, both p-adic and Archimede
an\; also\, they bear intriguing resemblance to some known constructions f
rom mathematical physics\, D-module theory\, and formal groups.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/186/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Dumanski (MIT)
DTSTART:20260209T183000Z
DTEND:20260209T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/187
DESCRIPTION:Title: Perverse coherent sheaves on symplectic singularities (part 1 o
f 3)\nby Ilya Dumanski (MIT) as part of M-seminar\n\n\nAbstract\nPerve
rse constructible sheaves are ubiquitous in algebraic geometry and geometr
ic representation theory. Bezrukavnikov introduced their coherent analog\,
called perverse coherent sheaves. For technical reasons\, there are essen
tially two interesting examples when this notion is well-behaved: the nilp
otent cone and the affine Grassmannian. In both these cases\, this categor
y is very meaningful and well-studied. It is related to modular representa
tion theory\, local geometric Langlands\, line defects in 4d gauge theorie
s\, and cluster categorifications. We will discuss these questions and the
n present a generalization of this construction to an arbitrary Poisson va
riety with finitely many symplectic leaves\, most notably the symplectic s
ingularities. This may be seen as a step towards building the Kazhdan-Lusz
tig theory in this setting.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/187/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Dumanski (MIT)
DTSTART:20260211T183000Z
DTEND:20260211T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/188
DESCRIPTION:Title: Perverse coherent sheaves on symplectic singularities (part 2 o
f 3)\nby Ilya Dumanski (MIT) as part of M-seminar\n\n\nAbstract\nPerve
rse constructible sheaves are ubiquitous in algebraic geometry and geometr
ic representation theory. Bezrukavnikov introduced their coherent analog\,
called perverse coherent sheaves. For technical reasons\, there are essen
tially two interesting examples when this notion is well-behaved: the nilp
otent cone and the affine Grassmannian. In both these cases\, this categor
y is very meaningful and well-studied. It is related to modular representa
tion theory\, local geometric Langlands\, line defects in 4d gauge theorie
s\, and cluster categorifications. We will discuss these questions and the
n present a generalization of this construction to an arbitrary Poisson va
riety with finitely many symplectic leaves\, most notably the symplectic s
ingularities. This may be seen as a step towards building the Kazhdan-Lusz
tig theory in this setting.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/188/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Dumanski (MIT)
DTSTART:20260212T213000Z
DTEND:20260212T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/189
DESCRIPTION:Title: Perverse coherent sheaves on symplectic singularities (part 3 o
f 3)\nby Ilya Dumanski (MIT) as part of M-seminar\n\n\nAbstract\nPerve
rse constructible sheaves are ubiquitous in algebraic geometry and geometr
ic representation theory. Bezrukavnikov introduced their coherent analog\,
called perverse coherent sheaves. For technical reasons\, there are essen
tially two interesting examples when this notion is well-behaved: the nilp
otent cone and the affine Grassmannian. In both these cases\, this categor
y is very meaningful and well-studied. It is related to modular representa
tion theory\, local geometric Langlands\, line defects in 4d gauge theorie
s\, and cluster categorifications. We will discuss these questions and the
n present a generalization of this construction to an arbitrary Poisson va
riety with finitely many symplectic leaves\, most notably the symplectic s
ingularities. This may be seen as a step towards building the Kazhdan-Lusz
tig theory in this setting.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/189/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rina Anno (KSU)
DTSTART:20260226T213000Z
DTEND:20260226T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/190
DESCRIPTION:Title: The Hochschild homology of a noncommutative symmetric quotient
stack\nby Rina Anno (KSU) as part of M-seminar\n\n\nAbstract\nFor a sm
all DG category $A$\, its symmetric power $S^nA$ may be considered a nonco
mmutative symmetric quotient stack of $A$. We establish an isomorphism bet
ween $\\bigoplus HH_\\bullet(S^nA)$ and the symmetric algebra $S^*(HH_\\bu
llet(A) \\otimes t k[t])$ by chaining explicit maps of complexes. These gr
aded vector spaces being isomorphic has been established before by Baranov
sky in the commutative case and conjectured by Belmans\, Fu\, and Krug in
the form that we prove it. The explicit nature of the isomorphism allows u
s to transfer a number of structures from the symmetric algebra to $\\bigo
plus HH_\\bullet(S^nA)$\, since the former is a Hopf algebra\, the Fock sp
ace for the Heisenberg algebra of $A$\, and a $\\lambda$-ring. In this tal
k\, I will go over (some of the) history of the results this one is buildi
ng upon\, describe the quasiisomorphism\, and compare the result to the (m
uch more studied) commutative case. This talk is based on a joint work wit
h V. Baranovsky and T. Logvinenko\, https://arxiv.org/abs/2512.25039\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/190/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Gaiotto (Perimeter Institute)
DTSTART:20260302T183000Z
DTEND:20260302T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/191
DESCRIPTION:Title: The categorical 't Hooft expansion - part 1 of 3\nby Davide
Gaiotto (Perimeter Institute) as part of M-seminar\n\n\nAbstract\nThe 't
Hooft expansion is the key structure underlying dualities between gauge th
eories of large matrices and string theories. I will review categorical as
pects of the 't Hooft expansion\, matching the formal deformation space of
certain ``fundamental modifications'' of the gauge theory to the formal d
eformation space of a category of boundary conditions ("D-branes") for a 2
d dg-TFT\, to be identified with the world-volume theory for the string th
eory. I will illustrate this by reviewing the holographic description of c
orrelation functions for a 2d chiral algebra/VOA deforming H^*(gl_N[A[z]]\
;gl_N) for a 2d CY algebra A\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/191/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Gaiotto (Perimeter Institute)
DTSTART:20260304T183000Z
DTEND:20260304T193000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/192
DESCRIPTION:Title: The categorical 't Hooft expansion - part 2 of 3\nby Davide
Gaiotto (Perimeter Institute) as part of M-seminar\n\n\nAbstract\nThe 't
Hooft expansion is the key structure underlying dualities between gauge th
eories of large matrices and string theories. I will review categorical as
pects of the 't Hooft expansion\, matching the formal deformation space of
certain ``fundamental modifications'' of the gauge theory to the formal d
eformation space of a category of boundary conditions ("D-branes") for a 2
d dg-TFT\, to be identified with the world-volume theory for the string th
eory. I will illustrate this by reviewing the holographic description of c
orrelation functions for a 2d chiral algebra/VOA deforming H^*(gl_N[A[z]]\
;gl_N) for a 2d CY algebra A\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/192/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Gaiotto (Perimeter Institute)
DTSTART:20260305T213000Z
DTEND:20260305T223000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/193
DESCRIPTION:Title: The categorical 't Hooft expansion - part 3 of 3\nby Davide
Gaiotto (Perimeter Institute) as part of M-seminar\n\n\nAbstract\nThe 't
Hooft expansion is the key structure underlying dualities between gauge th
eories of large matrices and string theories. I will review categorical as
pects of the 't Hooft expansion\, matching the formal deformation space of
certain ``fundamental modifications'' of the gauge theory to the formal d
eformation space of a category of boundary conditions ("D-branes") for a 2
d dg-TFT\, to be identified with the world-volume theory for the string th
eory. I will illustrate this by reviewing the holographic description of c
orrelation functions for a 2d chiral algebra/VOA deforming H^*(gl_N[A[z]]\
;gl_N) for a 2d CY algebra A\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/193/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Dimofte (University of Edinburgh)
DTSTART:20260309T173000Z
DTEND:20260309T183000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/194
DESCRIPTION:Title: Tannaka/Koszul duality and line operators - part 1 of 3\nby
Tudor Dimofte (University of Edinburgh) as part of M-seminar\n\n\nAbstrac
t\nThese seminars will focus on the representing line operators in topolog
ical and/or holomorphic QFT’s\, from the perspective of categorical reco
nstruction theory. In particular\, I’ll explain how fiber functors have
several natural constructions in QFT\, leading to field-theoretic incarnat
ions of Tannaka and Koszul duality (following my own work but also many ot
hers\, in particular work of Costello and collaborators). In the first tal
k\, I’ll set up a general QFT framework for reconstruction theory\, and
discuss a basic application to constructing (generalized) quantum groups f
rom 3d TQFT’s. In the second talk\, I’ll consider 4d holomorphic-topol
ogical theories. I’ll review the work of Costello-Yamazaki-Witten on Yan
gians in 4d Chern-Simons theory\, and explain how to generalize this to se
e structures such as Drinfeld coproducts. I’ll also generalize further t
o relate line operators in 4d Seiberg-Witten theories to CoHA’s of BPS s
tates. In the final talk\, I’ll consider 3d holomorphic-topological theo
ries\, and derive a new structure that I call a “dg-shifted” Yangian.\
n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/194/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Dimofte (University of Edinburgh)
DTSTART:20260311T173000Z
DTEND:20260311T183000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/195
DESCRIPTION:Title: Tannaka/Koszul duality and line operators - part 2 of 3\nby
Tudor Dimofte (University of Edinburgh) as part of M-seminar\n\n\nAbstrac
t\nThese seminars will focus on the representing line operators in topolog
ical and/or holomorphic QFT’s\, from the perspective of categorical reco
nstruction theory. In particular\, I’ll explain how fiber functors have
several natural constructions in QFT\, leading to field-theoretic incarnat
ions of Tannaka and Koszul duality (following my own work but also many ot
hers\, in particular work of Costello and collaborators). In the first tal
k\, I’ll set up a general QFT framework for reconstruction theory\, and
discuss a basic application to constructing (generalized) quantum groups f
rom 3d TQFT’s. In the second talk\, I’ll consider 4d holomorphic-topol
ogical theories. I’ll review the work of Costello-Yamazaki-Witten on Yan
gians in 4d Chern-Simons theory\, and explain how to generalize this to se
e structures such as Drinfeld coproducts. I’ll also generalize further t
o relate line operators in 4d Seiberg-Witten theories to CoHA’s of BPS s
tates. In the final talk\, I’ll consider 3d holomorphic-topological theo
ries\, and derive a new structure that I call a “dg-shifted” Yangian.\
n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/195/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Dimofte (University of Edinburgh)
DTSTART:20260312T160000Z
DTEND:20260312T170000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/196
DESCRIPTION:Title: Tannaka/Koszul duality and line operators - part 3 of 3\nby
Tudor Dimofte (University of Edinburgh) as part of M-seminar\n\n\nAbstrac
t\nThese seminars will focus on the representing line operators in topolog
ical and/or holomorphic QFT’s\, from the perspective of categorical reco
nstruction theory. In particular\, I’ll explain how fiber functors have
several natural constructions in QFT\, leading to field-theoretic incarnat
ions of Tannaka and Koszul duality (following my own work but also many ot
hers\, in particular work of Costello and collaborators). In the first tal
k\, I’ll set up a general QFT framework for reconstruction theory\, and
discuss a basic application to constructing (generalized) quantum groups f
rom 3d TQFT’s. In the second talk\, I’ll consider 4d holomorphic-topol
ogical theories. I’ll review the work of Costello-Yamazaki-Witten on Yan
gians in 4d Chern-Simons theory\, and explain how to generalize this to se
e structures such as Drinfeld coproducts. I’ll also generalize further t
o relate line operators in 4d Seiberg-Witten theories to CoHA’s of BPS s
tates. In the final talk\, I’ll consider 3d holomorphic-topological theo
ries\, and derive a new structure that I call a “dg-shifted” Yangian.\
n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/196/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasily Krylov (Harvard University)
DTSTART:20260323T203000Z
DTEND:20260323T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/197
DESCRIPTION:Title: Higgs and Coulomb branches for quiver gauge theories: geometry
and representation theory (part 1 of 3)\nby Vasily Krylov (Harvard Uni
versity) as part of M-seminar\n\n\nAbstract\nHiggs and Coulomb branches of
quiver gauge theories form two important families of Poisson varieties th
at are expected to be exchanged under so-called 3D mirror symmetry. One im
portant approach to studying modules over quantized Coulomb branches is by
analyzing their graded traces. Graded traces generalize the notion of cha
racters and are closely related to the q-characters introduced by Frenkel
and Reshetikhin. Any graded trace defines a solution of the D-module of gr
aded traces introduced by Kamnitzer\, McBreen\, and Proudfoot. In this ser
ies of talks\, I will discuss various techniques that allow us to explicit
ly compute characters and graded traces of certain important modules over
quantized Coulomb branches\, as well as shifted Yangians and affine quantu
m affine groups. These techniques combine geometry\, representation theory
\, and analytic methods. I will explain how some of these results naturall
y appear on the Higgs side\, leading to an explicit description of the D-m
odule of graded traces for a quantized Coulomb branch via the geometry of
the Higgs branch. We will prove these results for ADE quivers and formulat
e explicit conjectures in the general case. We will also discuss how the p
icture changes when Coulomb branches are replaced by their "multiplicative
" versions.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/197/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasily Krylov (Harvard University)
DTSTART:20260325T203000Z
DTEND:20260325T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/198
DESCRIPTION:Title: Higgs and Coulomb branches for quiver gauge theories: geometry
and representation theory (part 2 of 3)\nby Vasily Krylov (Harvard Uni
versity) as part of M-seminar\n\n\nAbstract\nHiggs and Coulomb branches of
quiver gauge theories form two important families of Poisson varieties th
at are expected to be exchanged under so-called 3D mirror symmetry. One im
portant approach to studying modules over quantized Coulomb branches is by
analyzing their graded traces. Graded traces generalize the notion of cha
racters and are closely related to the q-characters introduced by Frenkel
and Reshetikhin. Any graded trace defines a solution of the D-module of gr
aded traces introduced by Kamnitzer\, McBreen\, and Proudfoot. In this ser
ies of talks\, I will discuss various techniques that allow us to explicit
ly compute characters and graded traces of certain important modules over
quantized Coulomb branches\, as well as shifted Yangians and affine quantu
m affine groups. These techniques combine geometry\, representation theory
\, and analytic methods. I will explain how some of these results naturall
y appear on the Higgs side\, leading to an explicit description of the D-m
odule of graded traces for a quantized Coulomb branch via the geometry of
the Higgs branch. We will prove these results for ADE quivers and formulat
e explicit conjectures in the general case. We will also discuss how the p
icture changes when Coulomb branches are replaced by their "multiplicative
" versions.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/198/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasily Krylov (Harvard University)
DTSTART:20260326T203000Z
DTEND:20260326T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/199
DESCRIPTION:Title: Higgs and Coulomb branches for quiver gauge theories: geometry
and representation theory (part 3 of 3)\nby Vasily Krylov (Harvard Uni
versity) as part of M-seminar\n\n\nAbstract\nHiggs and Coulomb branches of
quiver gauge theories form two important families of Poisson varieties th
at are expected to be exchanged under so-called 3D mirror symmetry. One im
portant approach to studying modules over quantized Coulomb branches is by
analyzing their graded traces. Graded traces generalize the notion of cha
racters and are closely related to the q-characters introduced by Frenkel
and Reshetikhin. Any graded trace defines a solution of the D-module of gr
aded traces introduced by Kamnitzer\, McBreen\, and Proudfoot. In this ser
ies of talks\, I will discuss various techniques that allow us to explicit
ly compute characters and graded traces of certain important modules over
quantized Coulomb branches\, as well as shifted Yangians and affine quantu
m affine groups. These techniques combine geometry\, representation theory
\, and analytic methods. I will explain how some of these results naturall
y appear on the Higgs side\, leading to an explicit description of the D-m
odule of graded traces for a quantized Coulomb branch via the geometry of
the Higgs branch. We will prove these results for ADE quivers and formulat
e explicit conjectures in the general case. We will also discuss how the p
icture changes when Coulomb branches are replaced by their "multiplicative
" versions.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/199/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam DeHority (Yale University)
DTSTART:20260330T173000Z
DTEND:20260330T183000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/200
DESCRIPTION:Title: Orientifold lines from CoHA modules (part 1 of 3)\nby Sam D
eHority (Yale University) as part of M-seminar\n\n\nAbstract\nWe will disc
uss a category of modules for the cohomological Hall algebra which have a
vertex coaction compatible with the vertex coproduct of the CoHA. This cat
egory is a mathematical model for line operators in a 4d N = 2 theory. Lin
e operators which live at an orientifold singularity in the 4d theory are
then described using a different category of modules for the CoHA which ar
ise from a folding procedure. These modules possess their own version of a
vertex coproduct. We will discuss these structures\, their compatibility
and applications including the construction of representations of quantize
d coulomb branch algebras.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/200/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam DeHority (Yale University)
DTSTART:20260401T173000Z
DTEND:20260401T183000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/201
DESCRIPTION:Title: Orientifold lines from CoHA modules (part 2 of 3)\nby Sam D
eHority (Yale University) as part of M-seminar\n\n\nAbstract\nWe will disc
uss a category of modules for the cohomological Hall algebra which have a
vertex coaction compatible with the vertex coproduct of the CoHA. This cat
egory is a mathematical model for line operators in a 4d N = 2 theory. Lin
e operators which live at an orientifold singularity in the 4d theory are
then described using a different category of modules for the CoHA which ar
ise from a folding procedure. These modules possess their own version of a
vertex coproduct. We will discuss these structures\, their compatibility
and applications including the construction of representations of quantize
d coulomb branch algebras.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/201/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam DeHority (Yale University)
DTSTART:20260402T203000Z
DTEND:20260402T213000Z
DTSTAMP:20260404T095851Z
UID:M-seminar/202
DESCRIPTION:Title: Orientifold lines from CoHA modules (part 3 of 3)\nby Sam D
eHority (Yale University) as part of M-seminar\n\n\nAbstract\nWe will disc
uss a category of modules for the cohomological Hall algebra which have a
vertex coaction compatible with the vertex coproduct of the CoHA. This cat
egory is a mathematical model for line operators in a 4d N = 2 theory. Lin
e operators which live at an orientifold singularity in the 4d theory are
then described using a different category of modules for the CoHA which ar
ise from a folding procedure. These modules possess their own version of a
vertex coproduct. We will discuss these structures\, their compatibility
and applications including the construction of representations of quantize
d coulomb branch algebras.\n
LOCATION:https://stable.researchseminars.org/talk/M-seminar/202/
END:VEVENT
END:VCALENDAR