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BEGIN:VEVENT
SUMMARY:Maxence Mayrand (University of Toronto)
DTSTART:20200903T185000Z
DTEND:20200903T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/1
DESCRIPTION:Title: Symplectic reduction along a submanifold and the Moore-Tachikawa T
QFT\nby Maxence Mayrand (University of Toronto) as part of Geometry\,
Physics\, and Representation Theory Seminar\n\n\nAbstract\nIn 2011\, Moore
and Tachikawa conjectured the existence of certain complex Hamiltonian va
rieties which generate two-dimensional TQFTs where the target category has
complex reductive groups as objects and holomorphic symplectic varieties
as arrows. It was solved by Ginzburg and Kazhdan using an ad hoc technique
which can be thought of as a kind of "symplectic reduction by a group sch
eme." We clarify their construction by introducing a general notion of "sy
mplectic reduction by a groupoid along a submanifold\," which generalizes
many constructions at once\, such as standard symplectic reduction\, preim
ages of Slodowy slices\, the Mikami-Weinstein reduction\, and the Ginzburg
-Kazhdan examples. This is joint work with Peter Crooks.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svetlana Makarova (University of Pennsylvania)
DTSTART:20200910T185000Z
DTEND:20200910T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/2
DESCRIPTION:Title: Moduli spaces of stable sheaves over quasipolarized K3 surfaces an
d Strange Duality\nby Svetlana Makarova (University of Pennsylvania) a
s part of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbst
ract\nIn this talk\, I will show a construction of relative moduli spaces
of stable sheaves over the stack of quasipolarized K3 surfaces of degree t
wo. For this\, we use the theory of good moduli spaces\, whose study was i
nitiated by Alper. As a corollary\, we obtain the generic Strange Duality
for K3 surfaces of degree two\, extending the results of Marian and Oprea
on the generic Strange Duality for K3 surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Jeffrey (University of Toronto)
DTSTART:20200917T185000Z
DTEND:20200917T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/3
DESCRIPTION:Title: Flat connections and the $SU(2)$ commutator map\nby Lisa Jeffr
ey (University of Toronto) as part of Geometry\, Physics\, and Representat
ion Theory Seminar\n\n\nAbstract\nThis talk is joint work with Nan-Kuo Ho\
, Paul Selick and Eugene Xia. We describe the space of conjugacy classes o
f representations of the fundamental group of a genus 2 oriented 2-manifol
d into $G := SU(2)$.\n\nWe identify the cohomology ring and a cell decompo
sition of a\; space homotopy equivalent to the space of commuting pairs in
$SU(2)$.\n\nWe compute the cohomology of the space $M:= \\mu^{-1}(-I)$\,
where $\\mu:G^4 \\to G$ is the product of commutators.\n\nWe give a new pr
oof of the cohomology of $A:= M/G$\, both as a group and as a ring. The gr
oup structure is due to Atiyah and Bott in their landmark 1983 paper. The
ring structure is due to Michael Thaddeus 1992.\n\nWe compute the cohomolo
gy of the total space of the prequantum line bundle over $A$.\n\nWe identi
fy the transition functions of the induced $SO(3)$ bundle $M\\to A$.\n\nTo
appear in QJM (Atiyah memorial special issue). arXiv:2005.07390\n\nRefere
nces:\n\n[1] M.F. Atiyah\, R. Bott\, The Yang-Mills equations over Riemann
surfaces\, Phil. Trans. Roy. Soc. Lond. A308 (1983) 523-615.\n\n[2] T. Ba
ird\, L. Jeffrey\, P. Selick\, The space of commuting n-tuples in $SU(2)$\
, Illinois J. Math. 55 (2011)\, no. 3\, 805–813.\n\n[3] M. Crabb\, Space
s of commuting elements in $SU(2)$\, Proc. Edin. Math. Soc. 54 (2011)\, no
. 1\, 67–75.\n\n[4] N. Ho\, L. Jeffrey\, K. Nguyen\, E. Xia\, The $SU(2)
$-character variety of the closed surface of genus 2. Geom. Dedicata 192 (
2018)\, 171–187.\n\n[5] N. Ho\, L. Jeffrey\, P. Selick\, E. Xia\, Flat c
onnections and the commutator map for $SU(2)$\, Oxford Quart. J. Math.\, t
o appear (in the Atiyah memorial special issue).\n\n[6] L. Jeffrey\, A. Li
ndberg\, S. Rayan\, Explicit Poincar´e duality in the cohomology ring of
the $SU(2)$ character variety of a surface. Expos. Math.\, to appear.\n\n[
7] M.S. Narasimhan and C.S. Seshadri\, Stable and unitary vector bundles o
n a compact Riemann surface. Ann. of Math. 82 (1965) 540–567.\n\n[8] P.
Newstead\, Topological properties of some spaces of stable bundles\, Topol
ogy 6 (1967)\, 241–262.\n\n[9] C.T.C Wall\, Classification problems in d
ifferential topology. V. On certain 6-manifolds. Invent. Math. 1 (1966)\,
355–374\; corrigendum\, ibid.\, 2 (1966) 306.\n\n[10] M. Thaddeus\, Conf
ormal field theory and the cohomology of the moduli space of stable bundle
s. J. Differential Geom. 35 (1992) 131–149.\n\n[11] E. Witten\, Two dime
nsional gauge theories revisited\, J. Geom. Phys. 9 (1992) 303-368.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Smirnov (University of North Carolina at Chapel Hill)
DTSTART:20201001T185000Z
DTEND:20201001T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/4
DESCRIPTION:Title: Quantum difference equations\, monodromies and mirror symmetry
\nby Andrey Smirnov (University of North Carolina at Chapel Hill) as part
of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nA
n important enumerative invariant of a symplectic variety $X$ is its verte
x function. The vertex function is the analog of J-function in Gromov-Witt
en theory: it is the generating function for the numbers of rational curve
s in $X$.\n\nIn representation theory these functions feature as solutions
of various $q$-difference and differential equations associated with $X$\
, with examples including qKZ and quantum dynamical equations for quantum
loop groups\, Casimir connections for Yangians and other objects.\n\nIn th
is talk I explain how these equations can be extracted from algebraic topo
logy of symplectic dual variety $X^!$\, also known as $3D$-mirror of $X$.
This can be summarized as "identity"\n$$\n\\text{Enumerative geometry of }
X = \\text{algebraic topology of }X^!\n$$\nThe talk is based on work in pr
ogress with Y.Kononov arXiv:2004.07862\; arXiv:2008.06309.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soheyla Feyzbakhsh (Imperial College)
DTSTART:20201015T185000Z
DTEND:20201015T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/5
DESCRIPTION:Title: An application of Bogomolov-Gieseker type inequality to counting i
nvariants\nby Soheyla Feyzbakhsh (Imperial College) as part of Geometr
y\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nIn this tal
k\, I will work on a smooth projective threefold $X$ which satisfies the B
ogomolov-Gieseker conjecture of Bayer-Macrì-Toda\, such as the projective
space $\\mathbb{P}^3$ or the quintic threefold. I will show certain modul
i spaces of 2-dimensional torsion sheaves on $X$ are smooth bundles over H
ilbert schemes of ideal sheaves of curves and points in $X$. When $X$ is C
alabi-Yau this gives a simple wall crossing formula expressing curve count
s (and so ultimately Gromov-Witten invariants) in terms of counts of D4-D2
-D0 branes. This is joint work with Richard Thomas\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Alekseev (University of Geneva)
DTSTART:20201022T185000Z
DTEND:20201022T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/6
DESCRIPTION:Title: Poisson-Lie groups\, integrable systems and the Berenstein-Kazhdan
potential\nby Anton Alekseev (University of Geneva) as part of Geomet
ry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nIntegrable
systems and Poisson-Lie groups are closely related topics. In this talk\,
we will explain how integrability helps in understanding Poisson geometry
of the dual Poisson-Lie group $K^*$ of a compact Lie group $K$. One of ou
r main tools will be the Berenstein-Kazhdan potential from the theory of c
anonical bases.\n\nThe talk is based on joint works with A. Berenstein\, I
. Davidenkova\, B. Hoffman\, J. Lane and Y. Li.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balázs Elek (Cornell University)
DTSTART:20200924T185000Z
DTEND:20200924T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/7
DESCRIPTION:Title: Heaps\, Crystals and Preprojective algebra modules\nby Balázs
Elek (Cornell University) as part of Geometry\, Physics\, and Representat
ion Theory Seminar\n\n\nAbstract\nKashiwara crystals are combinatorial gad
gets associated to a representation of a reductive algebraic group that en
able us to understand the structure of the representation in purely combin
atorial terms. We will describe a type-independent construction of crystal
s of certain representations\, using the heap associated to a fully commut
ative element in the Weyl group. Then we will discuss how these heaps also
lead us to the construction of modules for the preprojective algebra of t
he Dynkin quiver. Using the rank-nullity theorem\, we will see how the Kas
hiwara operators have a surprisingly nice description in terms of these pr
eprojective algebra modules. This is work in progress joint with Anne Dran
owski\, Joel Kamnitzer\, Tanny Libman and Calder Morton-Ferguson.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolle González (University of California at Los Angeles)
DTSTART:20201008T185000Z
DTEND:20201008T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/8
DESCRIPTION:Title: A Skein theoretic Carlsson-Mellit algebra\nby Nicolle Gonzále
z (University of California at Los Angeles) as part of Geometry\, Physics\
, and Representation Theory Seminar\n\n\nAbstract\nThe Carlsson-Mellit alg
ebra arose for the first time in the proof of the shuffle conjecture\, whi
ch gives an explicit combinatorial formula for the Frobenius character of
the space of diagonal harmonics in terms of parking functions. Its polynom
ial representation\, given by certain complicated plethystic operators ove
r extensions of the ring of symmetric functions\, plays a particularly imp
ortant role as it encodes much of the underlying combinatorial theory. By
various results of Gorsky\, Mellit and Carlsson it was shown that this alg
ebra can be used to construct generators of the Elliptic Hall algebra in a
ddition to having deep connections to the homology of torus knots. Thus\,
a natural starting point in the search to categorify these structures is t
he categorification of the Carlsson-Mellit algebra and its polynomial repr
esentation. \n\nIn this talk I will explain joint work with Matt Hogancamp
where we constructed a purely skein theoretic formulation of this algebra
and realized its generators as certain braid diagrams on a thickened annu
lus. Consequently\, we used this framework to categorify the polynomial re
presentation of the Carlsson-Mellit algebra as a family of functors over t
he derived trace of the Soergel category.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Simental Rodríguez (University of California at Davis)
DTSTART:20201029T185000Z
DTEND:20201029T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/9
DESCRIPTION:Title: Parabolic Hilbert schemes and representation theory\nby José
Simental Rodríguez (University of California at Davis) as part of Geometr
y\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nWe explicit
ly construct an action of type A rational Cherednik algebras and\, more ge
nerally\, quantized Gieseker varieties\, on the equivariant homology of th
e parabolic Hilbert scheme of points on the plane curve singularity $C = \
\{x^{m} = y^{n}\\}$ where $m$ and $n$ are coprime positive integers. We sh
ow that the representation we get is a highest weight irreducible represen
tation and explicitly identify its highest weight. We will also place thes
e results in the recent context of Coulomb branches and BFN Springer theor
y. This is joint work with Eugene Gorsky and Monica Vazirani.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah White (Australian National University)
DTSTART:20201105T195000Z
DTEND:20201105T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/10
DESCRIPTION:Title: Cactus group actions and cell modules\nby Noah White (Austral
ian National University) as part of Geometry\, Physics\, and Representatio
n Theory Seminar\n\n\nAbstract\nThe cactus group associated to a Coxeter g
roup can be thought of as an asymptotic version of the braid group. It has
been observed by many authors that interesting cactus group actions can b
e constructed in many situations when one has a representation of the brai
d group. In this talk I will explain what the cactus group is\, and what i
s meant by "asymptotic". I will also explain how to construct cactus group
actions associated to cell modules of the Hecke algebra\, a description o
f this action using Lusztig’s isomorphism between the Hecke algebra and
group algebra and point to some interesting questions along the way. Much
of this talk is work joint with Raphael Rouquier.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrike Rieß (ETH Zürich)
DTSTART:20201112T195000Z
DTEND:20201112T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/11
DESCRIPTION:Title: On the Kähler cone of irreducible symplectic orbifolds\nby U
lrike Rieß (ETH Zürich) as part of Geometry\, Physics\, and Representati
on Theory Seminar\n\n\nAbstract\nIn this talk I report on recent joint wor
k with G. Menet: We generalize a series of classical results on irreducibl
e symplectic manifolds to the orbifold setting. In particular we prove a c
haracterization of the Kähler cone using wall divisors. This generalizes
results of Mongardi for the smooth case. I will finish the talk by applyin
g these results to study a concrete example.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rekha Biswal (University of Edinburgh)
DTSTART:20201119T195000Z
DTEND:20201119T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/12
DESCRIPTION:Title: Macdonald polynomials and level two Demazure modules for affine $
\\mathfrak{sl}_{n+1}$\nby Rekha Biswal (University of Edinburgh) as pa
rt of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract
\nAn important result due to Sanderson and Ion says that characters of lev
el one Demazure modules are specialized Macdonald polynomials. In this tal
k\, I will introduce a new class of symmetric polynomials indexed by a pai
r of dominant weights of $\\mathfrak{sl}_{n+1}$ which is expressed as line
ar combination of specialized symmetric Macdonald polynomials with coeffic
ients defined recursively. These polynomials arose in my own work while in
vestigating the characters of higher level Demazure modules. Using represe
ntation theory\, we will see that these new family of polynomials interpol
ate between characters of level one and level two Demazure modules for aff
ine $\\mathfrak{sl}_{n+1}$ and give rise to new results in the representat
ion theory of current algebras as a corollary. This is based on joint work
with Vyjayanthi Chari\, Peri Shereen and Jeffrey Wand.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Yu (University of Chicago)
DTSTART:20201203T195000Z
DTEND:20201203T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/13
DESCRIPTION:Title: Wonderful compactification of a Cartan subalgebra of a semisimple
Lie algebra\nby Li Yu (University of Chicago) as part of Geometry\, P
hysics\, and Representation Theory Seminar\n\n\nAbstract\nLet $H$ be a Car
tan subgroup of a semisimple algebraic group $G$ over the complex numbers.
The wonderful compactification $\\overline{H}$ of $H$ was introduced and
studied by De Concini and Procesi. For the Lie algebra $\\mathfrak{h}$ of
$H$\, we define an analogous compactification $\\overline{\\mathfrak{h}}$
of $\\mathfrak{h}$\, to be referred to as the wonderful compactification o
f $\\mathfrak{h}$. The wonderful compactification of $\\mathfrak{h}$ is an
example of an "additive toric variety". We establish a bijection between
the set of irreducible components of the boundary $\\overline{\\mathfrak{h
}} - \\mathfrak{h}$ of $\\mathfrak{h}$ and the set of maximal closed root
subsystems of the root system for $(G\, H)$ of rank $r - 1\,$ where $r$ is
the dimension of $\\mathfrak{h}$. An algorithm based on Borel-de Siebenth
al theory that constructs all such root subsystems is given. We prove that
each irreducible component of $\\overline{\\mathfrak{h}}- \\mathfrak{h}$
is isomorphic to the wonderful compactification of a Lie subalgebra of $\\
mathfrak{h}$ and is of dimension $r - 1$. In particular\, the boundary $\
\overline{\\mathfrak{h}} - \\mathfrak{h}$ is equidimensional. We describe
a large subset of the regular locus of $\\overline{\\mathfrak{h}}$. As a c
onsequence\, we prove that $\\overline{\\mathfrak{h}}$ is a normal variety
.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Wen (Northeastern University)
DTSTART:20210128T195000Z
DTEND:20210128T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/14
DESCRIPTION:Title: Towards wreath Macdonald theory\nby Joshua Wen (Northeastern
University) as part of Geometry\, Physics\, and Representation Theory Semi
nar\n\n\nAbstract\nWreath Macdonald polynomials are generalizations of Mac
donald polynomials wherein the symmetric groups are replaced with their wr
eath products with a cyclic group of order $\\ell$. They were defined by H
aiman\, and mirroring the usual Macdonald theory\, it is not obvious that
they exist. Haiman also conjectured for them a generalization of his celeb
rated proof of Macdonald positivity where the Hilbert scheme of points on
the plane is replaced with certain cyclic Nakajima quiver varieties. This
conjecture was proven by Bezrukavnikov and Finkelberg\, which also implies
the existence of the polynomials. Analogues of standard formulas and resu
lts of usual Macdonald theory remain to be explored. I will present an app
roach to the study of the wreath variants via the quantum toroidal algebra
of $\\mathfrak{sl}_\\ell$\, generalizing the fruitful interactions betwee
n the usual Macdonald theory and the quantum toroidal algebra of $\\mathfr
ak{gl}_1$. As applications\, I'll present an analogue of the norm formula
and a conjectural path towards "wreath Macdonald operators" that makes con
tact with the spin Ruijsenaars-Schneider integrable system.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martha Precup (Washington University at St. Louis)
DTSTART:20210204T195000Z
DTEND:20210204T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/15
DESCRIPTION:Title: The cohomology of nilpotent Hessenberg varieties and the dot acti
on representation\nby Martha Precup (Washington University at St. Loui
s) as part of Geometry\, Physics\, and Representation Theory Seminar\n\n\n
Abstract\nIn 2015\, Brosnan and Chow\, and independently Guay-Paquet\, pro
ved the Shareshian--Wachs conjecture\, which links the combinatorics of ch
romatic symmetric functions to the geometry of Hessenberg varieties via a
permutation group action on the cohomology ring of regular semisimple Hess
enberg varieties. This talk will give a brief overview of that story and
discuss how the dot action can be computed in all Lie types using the Bett
i numbers of certain nilpotent Hessenberg varieties. As an application\, w
e obtain new geometric insight into certain linear relations satisfied by
chromatic symmetric functions\, known as the modular law. This is joint w
ork with Eric Sommers.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Cliff (University of Sydney)
DTSTART:20210211T195000Z
DTEND:20210211T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/16
DESCRIPTION:Title: Moduli of principal bundles for 2-groups\nby Emily Cliff (Uni
versity of Sydney) as part of Geometry\, Physics\, and Representation Theo
ry Seminar\n\n\nAbstract\nA 2-group is a categorified version of a group.
In this talk\, we will study the structure of moduli stacks and spaces of
principal bundles for 2-groups. In a special case where the isomorphism cl
asses of objects in our 2-group form a finite (ordinary) group $G$\, we sh
ow that the moduli stack provides a higher-categorical enhancement of the
Freed--Quinn line bundle appearing in Chern--Simons theory for the finite
group $G$. This is joint work with Eric Berry\, Dan Berwick-Evans\, Laura
Murray\, Apurva Nakade\, and Emma Phillips.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabell Hellmann (HCM Bonn)
DTSTART:20210218T195000Z
DTEND:20210218T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/17
DESCRIPTION:Title: The nilpotent cone in the Mukai system of rank two and genus two<
/a>\nby Isabell Hellmann (HCM Bonn) as part of Geometry\, Physics\, and Re
presentation Theory Seminar\n\n\nAbstract\nLet $S$ be a K3 surface and $C$
a smooth curve in $S$. We consider the moduli space $M$ of coherent sheav
es on $S$ which are supported on a curve rational equivalent to $nC$ and h
ave fixed Euler characteristic (coprime to $n$). Then $M$ is an irreducibl
e holomorphic symplectic manifold equipped with a Lagrangian fibration giv
en by taking supports. This is the beautiful Mukai system.\n\nOne source o
f interest in the Mukai system is\, that it deforms to the Hitchin system
on $C$. And there is a notion of the nilpotent cone in the Mukai system de
forming to the nilpotent cone in the Hitchin system. In my talk\, I presen
t some results about the nilpotent cone on the Mukai side (in the lowest d
imensional case)\, which can then be transferred to the Hitchin side.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oksana Yakimova (University of Jena)
DTSTART:20210304T195000Z
DTEND:20210304T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/18
DESCRIPTION:Title: Symmetrisation and the Feigin-Frenkel centre\nby Oksana Yakim
ova (University of Jena) as part of Geometry\, Physics\, and Representatio
n Theory Seminar\n\n\nAbstract\nLet $G$ be a complex reductive group\, set
$\\mathfrak g={\\mathrm{Lie\\\,}}G$. The algebra ${\\mathcal S}(\\mathfra
k g)^{\\mathfrak g}$ of symmetric $\\mathfrak g$-invariants and the centre
${\\mathcal Z}(\\mathfrak g)$ of the enveloping algebra ${\\mathcal U}(\\
mathfrak g)$ are polynomial rings in ${\\mathrm{rk\\\,}}\\mathfrak g$ gene
rators. There are several isomorphisms between them\, including the symmet
risation map $\\varpi$\, which exists also for the Lie algebras $\\mathfra
k q$ with $\\dim\\mathfrak q=\\infty$.\n\nHowever\, in the infinite dimens
ional case\, one may need to complete ${\\mathcal U}(\\mathfrak q)$ in ord
er to replace ${\\mathcal Z}(\\mathfrak q)$ with an interesting related ob
ject. Roughly speaking\, the Feigin-Frenkel centre arises as a result of s
uch completion in case of an affine Kac-Moody algebra. From 1982 until 200
6\, this algebra existed as an intriguing black box with many applications
. Then explicit formulas for its elements appeared first in type ${\\sf A}
$\, later in all other classical types\, and it was discovered that the FF
-centre is the centraliser of the quadratic Casimir element.\n\nWe will di
scuss the type-free role of the symmetrisation map in the description of t
he FF-centre and present new explicit formulas for its generators in types
${\\sf B}$\, ${\\sf C}$\, ${\\sf D}$\, and ${\\sf G}_2$. One of our main
technical tools is a certain map from ${\\mathcal S}^{k}(\\mathfrak g)$ to
$\\Lambda^2\\mathfrak g \\otimes {\\mathcal S}^{k-3}(\\mathfrak g)$.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Dinkins (UNC Chapel Hill)
DTSTART:20210225T195000Z
DTEND:20210225T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/19
DESCRIPTION:Title: Combinatorics of 3d Mirror Symmetry\nby Hunter Dinkins (UNC C
hapel Hill) as part of Geometry\, Physics\, and Representation Theory Semi
nar\n\n\nAbstract\n3d mirror symmetry is a conjectured duality among sympl
ectic varieties that expects deep relationships between enumerative invari
ants of varieties that may appear to be unrelated. In this talk\, I will d
escribe the general setup of 3d mirror symmetry and will then explain its
nontrivial combinatorial implications in the example of the cotangent bund
le of the Grassmannian and its mirror variety. In this case\, the 3d mirro
r relationship is governed by a new family of difference operators which c
haracterize the Macdonald polynomials.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tina Kanstrup (UMass Amherst)
DTSTART:20210311T195000Z
DTEND:20210311T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/20
DESCRIPTION:Title: Link homologies and Hilbert schemes via representation theory
\nby Tina Kanstrup (UMass Amherst) as part of Geometry\, Physics\, and Rep
resentation Theory Seminar\n\n\nAbstract\nThe aim of this joint work in pr
ogress with Roman Bezrukavnikov is to unite different approaches to Khovan
ov-Rozansky triply graded link homology. The original definition is comple
tely algebraic in terms of Soergel bimodules. It has been conjectured by G
orsky\, Negut and Rasmussen that it can also be calculated geometrically i
n terms of cohomolgy of sheaves on Hilbert schemes. Motivated by string th
eory Oblomkov and Rozansky constructed a link invariant in terms of matrix
factorizations on related spaces and later proved that it coincides with
Khovanov-Rozansky homology. In this talk I’ll discuss a direct relation
between the different constructions and how one might invent these spaces
starting directly from definitions.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Zhao (MIT)
DTSTART:20210318T185000Z
DTEND:20210318T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/21
DESCRIPTION:by Yu Zhao (MIT) as part of Geometry\, Physics\, and Represent
ation Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Shapiro (Notre Dame)
DTSTART:20210325T185000Z
DTEND:20210325T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/22
DESCRIPTION:Title: Cluster realization of spherical DAHA\nby Alexander Shapiro (
Notre Dame) as part of Geometry\, Physics\, and Representation Theory Semi
nar\n\n\nAbstract\nSpherical subalgebra of Cherednik's double affine Hecke
algebra of type A admits a polynomial representation in which its generat
ors act via elementary symmetric functions and Macdonald operators. Recogn
izing the elementary symmetric functions as eigenfunctions of quantum Toda
Hamiltonians\, and applying (the inverse of) the Toda spectral transform\
, one obtains a new representation of spherical DAHA. In this talk\, I wil
l discuss how this new representation gives rise to an injective homomorph
ism from the spherical DAHA into a quantum cluster algebra in such a way t
hat the action of the modular group on the former is realized via cluster
transformations. The talk is based on a joint work in progress with Philip
pe Di Francesco\, Rinat Kedem\, and Gus Schrader.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kristin DeVleming (UC San Diego)
DTSTART:20210415T185000Z
DTEND:20210415T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/23
DESCRIPTION:Title: Wall crossing for K-moduli spaces\nby Kristin DeVleming (UC S
an Diego) as part of Geometry\, Physics\, and Representation Theory Semina
r\n\n\nAbstract\nThere are many different methods to compactly moduli spac
es of varieties with a rich source of examples from compactifying moduli s
paces of curves. In this talk\, I will explain a relatively new compactif
ication coming from K-stability and how it connects to serval other compac
tifications\, focusing on the case of plane curves of degree $d$. In parti
cular\, we regard a plane curve as a log Fano pair $(\\mathbb{P}^2\, aC)$
and study the K-moduli compactifications and establish a wall crossing fra
mework as a varies. We will describe all wall crossings for low degree pla
ne curves and discuss the picture for general $\\mathbb{Q}$-Gorenstein smo
othable log Fano pairs. This is joint work with Kenneth Ascher and Yuchen
Liu.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harm Derksen (Northeastern University)
DTSTART:20210422T185000Z
DTEND:20210422T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/24
DESCRIPTION:Title: The G-Stable Rank for Tensors\nby Harm Derksen (Northeastern
University) as part of Geometry\, Physics\, and Representation Theory Semi
nar\n\n\nAbstract\nThe rank of a matrix can be generalized to tensors. In
fact\, there are many different rank notions for tensors that all coincide
for matrices\, such as the tensor rank\, border rank\, subrank and slice
rank (and asymptotic versions of each of these). In this talk I will discu
ss two notions of rank that are closely related to Geometric Invariant The
ory\, the non-commutative rank and the G-stable rank. The non-commutative
rank can be used for giving lower bounds for tensor rank and border rank.
The G-stable rank was recently used by my graduate student Zhi Jiang to im
prove the asymptotic upper bounds of Ellenberg and Gijswijt for the Cap Se
t Problem.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milen Yakimov (Northeastern University)
DTSTART:20210408T185000Z
DTEND:20210408T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/25
DESCRIPTION:Title: Root of unity quantum cluster algebras\nby Milen Yakimov (Nor
theastern University) as part of Geometry\, Physics\, and Representation T
heory Seminar\n\n\nAbstract\nWe will describe a theory of root of unity qu
antum cluster algebras\, which cover as special cases the big quantum grou
ps of De Concini\, Kac and Process. All such algebras will be shown to be
polynomial identity (PI) algebras. Inside each of them\, we will construct
a canonical central subalgebra which is proved to be isomorphic to the un
derlying cluster algebra. It is a far-reaching generalization of the De Co
ncini-Kac-Procesi central subalgebras in big quantum groups and presents a
general framework for studying the representation theory of quantum algeb
ras at roots of unity by means of cluster algebras as the relevant data be
comes (PI algebra\, canonical central subalgebra)=(root of unity quantum c
luster algebra\, underlying cluster algebra). We will also present an expl
icit formula for the corresponding discriminants in this general setting t
hat can be applied in many concrete situations of interest\, such as the d
iscriminants of all root of unity quantum unipotent cells for symmetrizabl
e Kac-Moody algebras. This is a joint work with Bach Nguyen (Xavier Univ)
and Kurt Trampel (Notre Dame Univ).\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inês Rodrigues (University of Lisbon)
DTSTART:20210401T185000Z
DTEND:20210401T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/26
DESCRIPTION:Title: A cactus group action on shifted tableau crystals and a shifted B
erenstein-Kirillov group\nby Inês Rodrigues (University of Lisbon) as
part of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstr
act\nGillespie\, Levinson and Purbhoo introduced a crystal-like structure
for shifted tableaux\, called the shifted tableau crystal. Following a sim
ilar approach as Halacheva\, we exhibit a natural internal action of the c
actus group on this structure\, realized by the restrictions of the shifte
d Schützenberger involution to all primed intervals of the underlying cry
stal alphabet. This includes the shifted crystal reflection operators\, wh
ich agree with the restrictions of the shifted Schützenberger involution
to single-coloured connected components\, but unlike the case for type A c
rystals\, these do not need to satisfy the braid relations of the symmetri
c group.\n\nIn addition\, we define a shifted version of the Berenstein-Ki
rillov group\, by considering shifted Bender-Knuth involutions. Parallelin
g the works of Halacheva and Chmutov\, Glick and Pylyavskyy for type A sem
istandard tableaux of straight shape\, we exhibit another occurrence of th
e cactus group action on shifted tableau crystals of straight shape via th
e action of the shifted Berenstein-Kirillov group. We conclude that the sh
ifted Berenstein-Kirillov group is isomorphic to a quotient of the cactus
group. Not all known relations that hold in the classic Berenstein-Kirillo
v group need to be satisfied by the shifted Bender-Knuth involutions\, nam
ely the one equivalent to the braid relations of the type A crystal reflec
tion operators\, but the ones implying the relations of the cactus group a
re verified\, thus we have another presentation for the cactus group in te
rms of shifted Bender-Knuth involutions.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matan Harel (Northeastern University)
DTSTART:20210422T201000Z
DTEND:20210422T211000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/27
DESCRIPTION:Title: The loop O(n) model and the XOR trick\nby Matan Harel (Northe
astern University) as part of Geometry\, Physics\, and Representation Theo
ry Seminar\n\n\nAbstract\nThe loop O(n) model is a model for random config
urations of non-overlapping loops on the hexagonal lattice\, which contain
s many models of interest (such as the Ising model\, self-avoiding walks\,
and random Lipshitz functions) as special cases. The physics literature c
onjectures that the model undergoes several different phase transitions\,
leading to a dazzling phase diagram\; over the last several years\, severa
l features of the phase diagram have been proven rigorously. In this talk\
, I will describe the predicted behavior of the model and show some recent
progress towards proving that typical samples of perturbations of the uni
form measure on loop configurations have long loops. This is joint work wi
th Nick Crawford\, Alexander Glazman\, and Ron Peled.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Jin (Boston College)
DTSTART:20210909T185000Z
DTEND:20210909T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/28
DESCRIPTION:Title: Homological mirror symmetry for the universal centralizers\nb
y Xin Jin (Boston College) as part of Geometry\, Physics\, and Representat
ion Theory Seminar\n\n\nAbstract\nI will present my recent result on homol
ogical mirror symmetry for the universal centralizer (a.k.a Toda space) as
sociated to a complex semisimple Lie group.\n\nThe A-side is a partially w
rapped Fukaya category on the universal centralizer\, and the B-side is th
e category of coherent sheaves on the categorical quotient of the dual max
imal torus by the Weyl group (with some modifications if the group has non
trivial center). I will illustrate many of the geometry and ideas of the p
roof using the example of SL_2 or PGL_2.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Ruehle (Northeastern University)
DTSTART:20210916T185000Z
DTEND:20210916T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/29
DESCRIPTION:Title: Geodesics and topological transitions in Calabi-Yau manifolds of
Picard rank two\nby Fabian Ruehle (Northeastern University) as part of
Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nWe
discuss the structure of the Kähler moduli space of Picard rank two Calab
i-Yau threefolds\, which are given in terms of complete intersections in p
rojective ambient spaces\, or as hypersurfaces in toric ambient spaces. As
it turns out\, flop transitions are ubiquitous in such setups. The triple
intersection form of the Kähler cone generators can be brought into four
different normal forms\, and we use this to solve the geodesic equations
in the moduli space for each one of them. Moreover\, we will discuss that
flops can lead to isomorphic or non-isomorphic Calabi-Yau manifolds. We fi
nd that there exist infinite flop chains of isomorphic geometries\, but on
ly a finite number of flops to inequivalent manifolds. Physically\, the la
tter result is expected based on the swampland distance conjecture\, and m
athematically fits to a conjecture due to Kawamata and Morrison for Calabi
-Yau threefolds.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ignacio Barros-Reyes (Paris-Saclay University)
DTSTART:20210923T185000Z
DTEND:20210923T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/30
DESCRIPTION:Title: Irrationality of moduli spaces\nby Ignacio Barros-Reyes (Pari
s-Saclay University) as part of Geometry\, Physics\, and Representation Th
eory Seminar\n\n\nAbstract\nI will talk about the problem of determining t
he birational complexity of moduli spaces of curves and K3 surfaces. I wil
l recall some recently introduced invariants that measure irrationality an
d talk about what is known for these moduli spaces. In the second half I w
ill report on joint work with D. Agostini and K.-W. Lai\, where we study h
ow the degrees of irrationality of the moduli spaces of polarized K3 surfa
ces grow with respect to the genus g. We provide polynomial bounds. The pr
oof relies on Kudla's modularity conjecture for Shimura varieties of ortho
gonal type. For special genera we exploit the deep Hodge theoretic relatio
n between K3 surfaces and special hyperkähler fourfolds to obtain much sh
arper bounds.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (University of Toronto)
DTSTART:20210930T185000Z
DTEND:20210930T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/31
DESCRIPTION:Title: Monodromy of eigenvectors for trigonometric Gaudin algebras\n
by Joel Kamnitzer (University of Toronto) as part of Geometry\, Physics\,
and Representation Theory Seminar\n\n\nAbstract\nConsider a tensor product
of representations of a semisimple Lie algebra g. The Gaudin algebra is a
commutative algebra which acts on this tensor product\, commuting with th
e action of g. This algebra depends on a parameter which lives in the modu
li space of marked genus 0 curves. In previous work\, we studied the monod
romy of eigenvectors for this algebra as the parameter varies in the real
locus of this space. In new work in-progress\, we consider trigonometric G
audin algebras\, which act on the same vector space (but do not commute wi
th the g-action). We see that this leads to the action of the affine cactu
s group\, and we describe the action of this group combinatorially using c
rystals. I will also describe the (conjectural) relation between trigonome
tric Gaudin algebras and the quantum cohomology of affine Grassmannian sli
ces.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renzo Cavalieri (Colorado State University)
DTSTART:20211202T195000Z
DTEND:20211202T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/32
DESCRIPTION:Title: The integral Chow ring of $M_0(\\mathbb{P}^r\,d)$\nby Renzo C
avalieri (Colorado State University) as part of Geometry\, Physics\, and R
epresentation Theory Seminar\n\n\nAbstract\nWe give an efficient presentat
ion of the Chow ring with integral coefficients of the open part of the \n
moduli space of rational maps of odd degree to projective space. A
less fancy description of this space \n has its closed points corres
pond to equivalence classes of $(r+1)$-tuples of degree $d$ polynomials in
one \n variable with no common positive degree factor. We identify
this space as a $GL(2)$ quotient of an open \n set in a projective s
pace\, and then obtain a (highly redundant) presentation by considering an
envelope \n of the complement. A combinatorial analysis then leads
us to eliminating a large number of relations\, \n and to express th
e remaining ones in generating function form for all dimensions. The upsho
t of this \n work is to observe the rich combinatorial structure con
tained in the Chow rings of these moduli spaces \n as the degree and
the target dimension vary. This is joint work with Damiano Fulghesu.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julianna Tymoczko (Smith College)
DTSTART:20211104T185000Z
DTEND:20211104T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/34
DESCRIPTION:Title: Comparing different bases for irreducible symmetric group represe
ntations\nby Julianna Tymoczko (Smith College) as part of Geometry\, P
hysics\, and Representation Theory Seminar\n\n\nAbstract\nWe describe two
different bases for irreducible symmetric group representations: the table
aux basis from combinatorics (and from the geometry of a class of varietie
s called Springer fibers)\; and the web basis from knot theory (and from t
he quantum representations of Lie algebras). We then describe new results
comparing the bases\, e.g. showing that the change-of-basis matrix is upp
er-triangular\, and sketch some applications to geometry and representatio
n theory. This work is joint with H. Russell\, as well as with T. Goldwas
ser and G. Sun.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karina Batistelli (University of Chile)
DTSTART:20211118T195000Z
DTEND:20211118T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/35
DESCRIPTION:Title: Kazhdan-Lusztig polynomials for $\\tilde{B}_2$\nby Karina Bat
istelli (University of Chile) as part of Geometry\, Physics\, and Represen
tation Theory Seminar\n\n\nAbstract\nKazhdan-Lusztig polynomials lie at th
e intersection of representation theory\, geometry and algebraic combinato
rics. Despite their relevance and elementary definition (through a recursi
ve algorithm involving only elementary operations)\, the explicit computat
ion of these polynomials is still one of the hardest open problems in alge
braic combinatorics. In this talk we will present the explicit formulas of
the Kazhdan-Lusztig polynomials for a Coxeter system of type $\\tilde{B}_
2$.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Kang (California Institute of Technology)
DTSTART:20211209T195000Z
DTEND:20211209T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/36
DESCRIPTION:Title: Characteristic numbers of elliptic fourfolds\nby Monica Kang
(California Institute of Technology) as part of Geometry\, Physics\, and R
epresentation Theory Seminar\n\n\nAbstract\nI will first consider crepant
resolutions of Weierstrass models corresponding to elliptically-fibered fo
urfolds with simple Lie algebras. I will further discuss the fibrations wi
th multisections or nontrivial Mordell-Weil groups. In contrast to the ca
se of fivefolds\, Chern and Pontryagin numbers of fourfolds are invariant
under crepant birational maps. This fact enables us to be able to compute
Chern and Pontryagin numbers\, independently from a choice of a crepant re
solution\, along with various other characteristic numbers such as the Eul
er characteristic\, the holomorphic genera\, the Todd-genus\, the L-genus\
, the A-genus\, and the eight-form curvature invariant from M-theory. For
the case of Calabi-Yau fourfolds\, F-theory compactification provides the
resulting 4d N=1 gauge theories.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Gammage (Harvard University)
DTSTART:20211014T185000Z
DTEND:20211014T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/37
DESCRIPTION:Title: Abelian 3d mirror symmetry\nby Ben Gammage (Harvard Universit
y) as part of Geometry\, Physics\, and Representation Theory Seminar\n\n\n
Abstract\n3d mirror symmetry is a proposed physical duality relating a pai
r of 3d N=4 field theories. Various mathematical shadows of this result ha
ve been studied\, but ultimately (after a topological twisting)\, 3dMS sho
uld entail an equivalence between a pair of 2-categories associated to the
algebraic (respectively\, symplectic) geometry of a pair of holomorphic s
ymplectic stacks. In general\, the definitions of these 2-categories are n
ot known\, but in this talk we explain how one can define the relevant 2-c
ategories and construct an equivalence between them in the case where the
spaces involved are linear quotients by a torus. Potential applications in
clude a Betti geometric version of Tate's thesis and a recovery of earlier
results on Koszul duality for hypertoric categories O. This is joint work
with Justin Hilburn and Aaron Mazel-Gee.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mandy Cheung (Harvard University)
DTSTART:20211021T185000Z
DTEND:20211021T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/38
DESCRIPTION:Title: Family Floer mirror and mirror symmetry for rank 2 cluster variet
ies\nby Mandy Cheung (Harvard University) as part of Geometry\, Physic
s\, and Representation Theory Seminar\n\n\nAbstract\nThe Gross-Hacking-Kee
l mirror is constructed in terms of scattering diagrams and theta function
s. The ground of the construction is that scattering diagrams inherit the
algebro-geometric analogue of the holomorphic disks counting. With Yu-shen
Lin\, we made use this idea and gave first non-trivial examples of family
Floer mirror. Then with Sam Bardwell-Evans\, Hansol Hong\, and Yu-shen LI
n\, we construct a special Lagrangian fibration on the non-toric blowups o
f toric surfaces that contains nodal fibres\, and prove that the fibres bo
unding Maslov 0 discs reproduce the scattering diagrams. As a consequence\
, we can then illustrate the mirror duality between the A and X cluster va
rieties.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Payman Eskandari (University of Toronto)
DTSTART:20211028T185000Z
DTEND:20211028T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/39
DESCRIPTION:Title: The unipotent radical of the Mumford-Tate group of a very general
mixed Hodge structure with a fixed associated graded\nby Payman Eskan
dari (University of Toronto) as part of Geometry\, Physics\, and Represent
ation Theory Seminar\n\n\nAbstract\nThe Mumford-Tate group $G(M)$ of a mix
ed Hodge structure $M$ is a subgroup of $GL(M)$ which satisfies the follow
ing property: any rational subspace of any tensor power of $M$ underlies a
mixed Hodge substructure if and only if it is invariant under the natural
action of $G(M)$. Assuming $M$ is graded-polarizable\, the unipotent radi
cal $U(M)$ of $G(M)$ is a subgroup of the unipotent radical $U_0(M)$ of th
e parabolic subgroup of $GL(M)$ associated to the weight filtration on $M$
. Let us say $U(M)$ is large if it is equal to $U_0(M)$.\n\nThis talk is a
report on a recent joint work with Kumar Murty\, where we consider the se
t of all mixed Hodge structures on a given rational vector space\, with a
fixed weight filtration and a fixed polarizable associated graded Hodge st
ructure. It is easy to see that this set is in a canonical bijection with
the set of complex points of an affine complex variety $S$. The main resul
t is that assuming some conditions on the (fixed) associated graded hold\,
outside a union of countably many proper Zariski closed subsets of $S$ th
e unipotent radical of the Mumford-Tate group is large.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter McNamara (University of Melbourne)
DTSTART:20220120T195000Z
DTEND:20220120T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/40
DESCRIPTION:Title: Sheaves behaving badly\nby Peter McNamara (University of Melb
ourne) as part of Geometry\, Physics\, and Representation Theory Seminar\n
\n\nAbstract\nThis talk is about singularities of Schubert varieties\,\nst
udied via sheaf-theoretic invariants like intersection cohomology\nand par
ity sheaves. The motivation comes from the use of these sheaves\nin repres
entation theory\, which began with the celebrated proof of the\nKazhdan-Lu
sztig conjectures by Beilinson-Bernstein localisation. We\nwill present ex
amples of poor behaviour (in particular exhibit\nnon-perverse parity sheav
es)\, which thwart historic overly-optimistic\nconjectures on the singular
ities of Schubert varieties.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Souheila Hassoun (Northeastern University)
DTSTART:20220127T195000Z
DTEND:20220127T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/41
DESCRIPTION:Title: The admissible sub-objects\nby Souheila Hassoun (Northeastern
University) as part of Geometry\, Physics\, and Representation Theory Sem
inar\n\n\nAbstract\nThe study of admissible sub-objects of a certain objec
t in an additive category relatively to a Quillen exact structure is an ex
citing subject that leads to some unaccepted characterizations. We propose
new general notions of intersections and some of sub-objects to study the
Jordan-Holder property of an exact category. We then generalize the lengt
h function and the Gabriel-Roiter measure to the realm of exact categories
. \nWe also initiate the study of weakly exact structures\, a generalizati
on of both Quillen exact structures and the important and widely used noti
on of Abelian categories. We investigate when these structures form lattic
es.\nThis talk is based on several joint works: arxiv numbers 2009.10024\,
2006.03505\, and 1809.01282.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Loizides (Cornell University)
DTSTART:20220203T195000Z
DTEND:20220203T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/42
DESCRIPTION:Title: Moduli of flat connections on a surface and the Atiyah-Bott class
es\nby Yiannis Loizides (Cornell University) as part of Geometry\, Phy
sics\, and Representation Theory Seminar\n\n\nAbstract\nLet $\\Sigma$ be a
compact oriented surface (possibly with boundary)\, and let $G$ be a comp
act connected simply connected Lie group. I will describe classes in the K
-theory of a moduli space of flat $G$-connections on $\\Sigma$. In the cas
e of a closed surface\, these classes were introduced by Atiyah and Bott.
When the boundary of the surface is non-empty\, further investigation lead
s to a gauge theoretic version of a theorem of Teleman and Woodward.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Megumi Harada (McMaster University)
DTSTART:20220428T185000Z
DTEND:20220428T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/43
DESCRIPTION:Title: Hessenberg patch ideals\, geometric vertex decomposition\, and Gr
obner bases\nby Megumi Harada (McMaster University) as part of Geometr
y\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nHessenberg
varieties are subvarieties of the flag variety $Flags(\\mathbb{C}^n)$\, th
e study of which have rich interactions with symplectic geometry\, represe
ntation theory\, and equivariant topology\, among other research areas\, w
ith particular recent attention arising from its connections to the famous
Stanley-Stembridge conjecture in combinatorics. The special case of regul
ar nilpotent Hessenberg varieties has been much studied\, and in this talk
I will describe some work in progress analyzing the local defining ideals
of these varieties. In particular\, using some techniques relating liason
theory\, geometric vertex decomposition\, and the theory of Grobner bases
(following work of Klein and Rajchgot)\, we are able to show that\, for t
he coordinate patch corresponding to the longest word $w_0$\, the local de
fining ideal for any indecomposable Hessenberg variety is geometrically ve
rtex decomposable\, and we find an explicit Grobner basis for a certain mo
nomial order. This is a report on joint work in progress with Sergio Da Si
lva.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marianna Russkikh (MIT)
DTSTART:20220210T195000Z
DTEND:20220210T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/44
DESCRIPTION:Title: Dimers and embeddings\nby Marianna Russkikh (MIT) as part of
Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nWe i
ntroduce a concept of ‘t-embeddings’ of weighted bipartite planar grap
hs. We believe that these t-embeddings always exist and that they are good
candidates to recover the complex structure of big bipartite planar graph
s carrying a dimer model. We also develop a relevant theory of discrete ho
lomorphic functions on t-embeddings\; this theory unifies Kenyon’s holom
orphic functions on T-graphs and s-holomorphic functions coming from the I
sing model. We provide a meta-theorem on convergence of the height fluctua
tions to the Gaussian Free Field.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Cannizzo (Stony Brook)
DTSTART:20220310T195000Z
DTEND:20220310T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/45
DESCRIPTION:Title: Global homological mirror symmetry for genus 2 curves\nby Cat
herine Cannizzo (Stony Brook) as part of Geometry\, Physics\, and Represen
tation Theory Seminar\n\n\nAbstract\nA smooth genus 2 curve has a 6 dimens
ional family of possible complex structures\, parametrized by the genus-2
Siegel space. We describe a generalized SYZ mirror family of symplectic ma
nifolds\, and the mirror correspondence of Kähler cones with the Siegel s
pace. We also describe the Fukaya category of the symplectic manifold (a L
andau-Ginzburg model)\, with structure maps deformed by the B-field. This
involves adapting Guillemin’s Kähler potential to a toric variety of in
finite type and computing monodromy of a symplectic fibration with critica
l locus given by the “banana manifold” of three P^1’s attached at tw
o points. Finally\, we end with a homological mirror symmetry result betwe
en the genus 2 curves and their mirrors. This is joint work with H. Azam\,
C-C. M. Liu\, and H. Lee.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Arbesfeld (Imperial College London)
DTSTART:20220303T195000Z
DTEND:20220303T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/46
DESCRIPTION:Title: Descendent series for Hilbert schemes of points on surfaces\n
by Noah Arbesfeld (Imperial College London) as part of Geometry\, Physics\
, and Representation Theory Seminar\n\n\nAbstract\nStructure often emerges
from Hilbert schemes of points on surfaces when the underlying surface is
fixed but the number of points parametrized is allowed to vary. One examp
le of such structure comes from integrals of tautological bundles\, which
appear in physical and geometric computations. When compiled into generati
ng series\, these integrals display interesting functional properties. \n\
nI will focus on the example of K-theoretic descendent series\, certain se
ries formed from holomorphic Euler characteristics of tautological bundles
. Namely\, I will explain how to use a Macdonald polynomial symmetry of Me
llit to deduce that the K-theoretic descendent series are expansions of ra
tional functions.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Weinstein (Berkeley/Stanford)
DTSTART:20220421T185000Z
DTEND:20220421T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/47
DESCRIPTION:Title: A Lie-Rinehart algebra in general relativity\nby Alan Weinste
in (Berkeley/Stanford) as part of Geometry\, Physics\, and Representation
Theory Seminar\n\n\nAbstract\nBlohmann\, Schiavina\, and I have found a Li
e-Rinehart algebra on a graded extension of the space of initial values fo
r the Einstein equations whose bracket relations match those of the constr
aints on the initial values.\n\nThis will be a follow-up to last year's ta
lk\, but I will not assume that anyone has heard it.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asilata Bapat (ANU)
DTSTART:20220224T195000Z
DTEND:20220224T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/48
DESCRIPTION:by Asilata Bapat (ANU) as part of Geometry\, Physics\, and Rep
resentation Theory Seminar\n\n\nAbstract\nConsider the space of Bridgeland
stability conditions of a suitably nice triangulated category. Autoequiva
lences of the triangulated category act on the space of stability conditio
ns. Fixing a stability condition imposes extra combinatorial structure on
the category that can be used to study the group of autoequivalences in va
rious different ways. This talk will showcase some of the fascinating stru
cture that emerges via this idea\, particularly for 2-Calabi-Yau categorie
s associated to quivers. This is based on joint work with Anand Deopurkar
and Anthony Licata.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Cristofaro-Gardiner (Maryland)
DTSTART:20220407T185000Z
DTEND:20220407T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/49
DESCRIPTION:Title: The simplicity conjecture\nby Dan Cristofaro-Gardiner (Maryla
nd) as part of Geometry\, Physics\, and Representation Theory Seminar\n\n\
nAbstract\nIn the 60s and 70s\, there was a flurry of activity concerning
the question of whether or not various subgroups of homeomorphism groups o
f manifolds are simple\, with beautiful contributions by Fathi\, Kirby\, M
ather\, Thurston\, and many others. A funnily stubborn case that remained
open was the case of area-preserving homeomorphisms of surfaces. For examp
le\, for balls of dimension at least 3\, the relevant group was shown to b
e simple by work of Fathi from the 1970s\, but the answer in the two-dimen
sional case was not known. I will explain recent joint work proving that
the group of compactly supported area preserving homeomorphisms of the two
-disc is in fact not a simple group\, which answers the ``Simplicity Conje
cture” in the affirmative. Our proof uses a new tool for studying area-
preserving surface homeomorphisms\, called periodic Floer homology (PFH) s
pectral invariants\; these recover the classical Calabi invariant via a ki
nd of Weyl law. I will also briefly mention a generalization of our resu
lt to compact surfaces of any genus.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oded Yacobi (Sydney)
DTSTART:20220324T185000Z
DTEND:20220324T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/50
DESCRIPTION:Title: On the action of Weyl groups on canonical bases and categorical b
raid group actions\nby Oded Yacobi (Sydney) as part of Geometry\, Phys
ics\, and Representation Theory Seminar\n\n\nAbstract\nIn this talk we'll
be considering the following situation: suppose we have a representation $
(V\,\\pi)$ of a Weyl group equipped with a canonical basis. Given an elem
ent $g$ of the group\, can we extract interesting information about the ma
trix of $\\pi(g)$ with respect to the basis? In general this is extremely
difficult but in some situations there are beautiful answers to this ques
tion. The first results in this direction are due to Berenstein-Zelevinsk
y and Stembridge\, who proved that the long element of the symmetric group
acts on the Kazhdan-Lusztig basis by the Schutzenberger involution on tab
leau. I will explain vast generalizations of this theorem. The underlyin
g ideas driving these results come from braid group actions on derived cat
egories. This is based on joint work with Martin Gossow.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Filip Dul (UMass Amherst)
DTSTART:20220217T195000Z
DTEND:20220217T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/51
DESCRIPTION:Title: General Covariance with Stacks\nby Filip Dul (UMass Amherst)
as part of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbs
tract\nGeneral covariance is a crucial notion in the study of field theori
es on curved spacetimes. In our context\, a generally covariant field theo
ry is one whose dependence on a Riemannian (or Lorentzian) metric is equiv
ariant with respect to the diffeomorphism group of the underlying manifold
/spacetime. In this talk\, we will make these notions precise by using sta
cks and the Batalin-Vilkovisky formalism\, and will moreover recover the a
ssociated equivariant classical observables in the perturbative case.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Utiralova (MIT)
DTSTART:20220414T185000Z
DTEND:20220414T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/52
DESCRIPTION:Title: Harish-Chandra bimodules in complex rank\nby Alexandra Utiral
ova (MIT) as part of Geometry\, Physics\, and Representation Theory Semina
r\n\n\nAbstract\nThe Deligne tensor categories are defined as an interpola
tion of the categories of representations of groups $GL_n$\, $O_n$\, $Sp_{
2n}$\, or $S_n$ to the complex values of the parameter $n$. One can extend
many classical representation-theoretic notions and constructions to this
context. These complex rank analogs of classical objects provide insights
into their stable behavior patterns as n goes to infinity.\n\nI will talk
about some of my results on Harish-Chandra bimodules in the Deligne cateo
gories. It is known that in the classical case simple Harish-Chandra bimod
ules admit a classification in terms of W-orbits of certain pairs of weigh
ts. However\, the notion of weight is not well-defined in the setting of t
he Deligne categories. I will explain how in complex rank the above-mentio
ned classification translates to a condition on the corresponding (left an
d right) central characters.\n\nAnother interesting phenomenon arising in
complex rank is that there are two ways to define harish-Chandra bimodules
. That is\, one can either require that the center acts locally finitely o
n a bimodule $M$ or that $M$ has a finite K-type. The two conditions are k
nown to be equivalent for a semi-simple Lie algebra in the classical setti
ng\, however in the Deligne categories\, it is no longer the case. I will
talk about a way to construct examples of Harish-Chandra bimodules of fini
te K-type using the ultraproduct realization of the Deligne categories.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Kirchhoff-Lukat (MIT)
DTSTART:20220331T185000Z
DTEND:20220331T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/53
DESCRIPTION:Title: Lagrangian intersection Floer cohomology for log symplectic surfa
ces\nby Charlotte Kirchhoff-Lukat (MIT) as part of Geometry\, Physics\
, and Representation Theory Seminar\n\n\nAbstract\nI will begin by giving
an introduction to a special and widely studied class of Poisson manifolds
: log symplectic manifolds. While these have degeneracies\, they are suffi
ciently close to being symplectic that many properties and techniques from
symplectic geometry extend. The main result I will present is my recent g
eneralization of Lagrangian intersection Floer cohomology to log symplecti
c surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Webster (Waterloo)
DTSTART:20220428T200000Z
DTEND:20220428T210000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/54
DESCRIPTION:Title: Representation theory and a little bit of quantum field theory\nby Ben Webster (Waterloo) as part of Geometry\, Physics\, and Represent
ation Theory Seminar\n\n\nAbstract\nOne of the central foci of representat
ion theory in the 20th century was the representation theory of Lie algebr
as\, starting with finite dimensional algebras and expanding to a rich\, b
ut still mysterious infinite dimensional theory. In this century\, we real
ized that this was only one special case of a bigger theory\, with new sou
rces of interesting non-commutative algebras whose representations we'd li
ke to study\, such as Cherednik algebras. In mathematical terms\, we could
connect these to symplectic resolutions of singularities\, but a more int
riguing explanation is that they arise from 3d quantum field theories. I'l
l try to provide an overview about what's known about this topic and what
we're still confused about.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Jeishing Wen (Northeastern)
DTSTART:20220908T185000Z
DTEND:20220908T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/55
DESCRIPTION:Title: Wreath Macdonald operators\nby Joshua Jeishing Wen (Northeast
ern) as part of Geometry\, Physics\, and Representation Theory Seminar\n\n
\nAbstract\nDefined by Haiman\, wreath Macdonald polynomials are generaliz
ations of Macdonald polynomials to wreath products of symmetric groups wit
h a fixed cyclic group. Using a wreath analogue of the Frobenius character
istic\, they can be viewed as partially-symmetric functions. Relatively li
ttle is known about them. In this talk\, we present novel difference opera
tors that are diagonalized on the wreath Macdonald polynomials. Their form
ulas are quite complicated\, but they give strong evidence that bispectral
duality holds in the wreath case. This is joint work with Daniel Orr and
Mark Shimozono.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minh-Tâm Trinh (MIT)
DTSTART:20221006T185000Z
DTEND:20221006T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/56
DESCRIPTION:Title: Catalan combinatorics versus nonabelian Hodge theory\nby Minh
-Tâm Trinh (MIT) as part of Geometry\, Physics\, and Representation Theor
y Seminar\n\n\nAbstract\nThe Oblomkov–Rasmussen–Shende conjecture rela
tes the homologies of the Hilbert schemes of a plane curve singularity to
the triply-graded Khovanov–Rozansky (i.e.\, HOMFLYPT) homology of its li
nk\, via an identity in variables a\, q\, t. Two major cases are known: (1
) the t = -1 limit\, settled a decade ago by Maulik\; (2) the lowest-a-deg
ree\, q = 1 limit of the "torus link" case\, settled jointly by Elias–Ho
gancamp\, Mellit\, and Gorsky–Mazin\, using (q\, t)-Catalan combinatoric
s as an essential bridge. An unpublished research statement of Shende spec
ulated that the ORS conjecture could be proved in a third\, totally differ
ent way\, via a wild analogue of the P = W phenomenon in nonabelian Hodge
theory. He and his coauthors carried out most of this approach for the "to
rus-knot" subcase of case (1). We extend their work\, and also refine it e
nough to handle the (more difficult) torus-knot subcase of case (2). The k
ey is our new geometric model for Khovanov–Rozansky homology\, which rea
lizes the t variable as cohomological degree. If there is time\, we will e
xplain how this flavor of nonabelian Hodge theory is related to the noncro
ssing-nonnesting dichotomy in Catalan combinatorics.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elie Casbi (Northeastern)
DTSTART:20220915T185000Z
DTEND:20220915T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/57
DESCRIPTION:Title: Hall algebras and quantum cluster algebras\nby Elie Casbi (No
rtheastern) as part of Geometry\, Physics\, and Representation Theory Semi
nar\n\n\nAbstract\nThe theory of Hall algebras has known many spectacular
developments and applications since the discovery by Ringel of their conne
ction with quantum groups. One important object arising naturally in the s
tudy of Hall algebras is the integration map defined by Reineke\, which al
lows to produce certain celebrated wall-crossing identities. In this talk
I will first focus on the Dynkin case and show how the integration map can
be interpreted in a natural way via the representation theory of quantum
affine algebras. I will then explain how this opens perspectives towards a
n analogous interpretation for more general quivers\, relying on the frame
work of quantum cluster algebras. This is ongoing joint work with Lang Mou
.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Neguţ (MIT)
DTSTART:20220929T173000Z
DTEND:20220929T183000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/58
DESCRIPTION:Title: Quantum loop groups for generalized Cartan matrices\nby Andre
i Neguţ (MIT) as part of Geometry\, Physics\, and Representation Theory S
eminar\n\n\nAbstract\nWe construct a quantum loop group associated to an a
rbitrary symmetric generalized Cartan matrix by defining appropriate versi
ons of the Drinfeld-Serre relations. Explaining the meaning of the word "a
ppropriate" and specifying the relations will be the main purpose of the t
alk.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Sherman-Bennett (MIT)
DTSTART:20221020T185000Z
DTEND:20221020T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/59
DESCRIPTION:Title: Cluster structures on type A braid varieties and 3D plabic graphs
\nby Melissa Sherman-Bennett (MIT) as part of Geometry\, Physics\, and
Representation Theory Seminar\n\n\nAbstract\nBraid varieties are smooth a
ffine varieties associated to any positive braid. Special cases of braid v
arieties include Richardson varieties\, double Bruhat cells\, and double B
ott-Samelson cells. Cluster algebras are a class of commutative rings with
a rich combinatorial structure\, introduced by Fomin and Zelevinsky. I'll
discuss joint work with P. Galashin\, T. Lam and D. Speyer in which we sh
ow the coordinate rings of braid varieties are cluster algebras\, proving
and generalizing a conjecture of Leclerc in the case of Richardson varieti
es. Seeds for these cluster algebras come from "3D plabic graphs"\, which
are bicolored graphs embedded in a 3-dimensional ball that generalize Post
nikov's plabic graphs for positroid varieties.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Dinkins (Northeastern)
DTSTART:20220922T185000Z
DTEND:20220922T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/60
DESCRIPTION:Title: Curve counts\, representation theory\, and 3d mirror symmetry
\nby Hunter Dinkins (Northeastern) as part of Geometry\, Physics\, and Rep
resentation Theory Seminar\n\n\nAbstract\nThe last two decades have seen g
reat success in studying representation theoretic objects through geometri
c techniques. One small part of this story involves Nakajima quiver variet
ies\, curve counting\, and a mysterious string-theoretic duality. More spe
cifically\, curve counting in Nakajima varieties turns out to be governed
by certain q-difference equations that\, after a nontrivial amount of work
\, can be seen to coincide with the some well-known equations from represe
ntation theory. Moreover\, these curve counts are expected to possess deep
nontrivial symmetries that have only been understood in very specific exa
mples. I will provide an overview of the main concepts and results related
to these ideas\, discuss my own contributions\, and mention some future d
irections.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davesh Maulik (MIT)
DTSTART:20221013T185000Z
DTEND:20221013T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/61
DESCRIPTION:Title: P=W conjecture for GL_n\nby Davesh Maulik (MIT) as part of Ge
ometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nThe P=
W conjecture\, first proposed by de Cataldo-Hausel-Migliorini in 2010\, gi
ves a link between the topology of the moduli space of Higgs bundles on a
curve and the Hodge theory of the corresponding character variety\, using
non-abelian Hodge theory. In this talk\, I will explain this circle of id
eas and discuss a recent proof of the conjecture for GL_n (joint with Junl
iang Shen).\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Smirnov (UNC Chapel Hill)
DTSTART:20221027T185000Z
DTEND:20221027T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/62
DESCRIPTION:Title: Vertex functions modulo p\nby Andrey Smirnov (UNC Chapel Hill
) as part of Geometry\, Physics\, and Representation Theory Seminar\n\n\nA
bstract\nThe vertex functions are generating functions counting rational c
urves in a quiver variety.\nThey also give a basis of solutions to quantum
differential equation associated with the quiver variety. \nIn my talk I
discuss a construction of certain polynomial solutions of quantum differen
tial equation modulo a prime p.\nI also describe a number of conjectures r
elating the p-adic limit of these solutions to the vertex functions. \nThe
talk is based on a joint investigation in progress with A. Varchenko.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolás Andruskiewitsch (Universidad Nacional de Córdoba)
DTSTART:20221117T195000Z
DTEND:20221117T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/63
DESCRIPTION:Title: Nichols algebras over abelian groups\nby Nicolás Andruskiewi
tsch (Universidad Nacional de Córdoba) as part of Geometry\, Physics\, an
d Representation Theory Seminar\n\n\nAbstract\nNichols algebras are fundam
ental invariants of large classes of Hopf algebras. I will survey from sc
ratch those arising from abelian groups\, focusing on the methods of comp
utation.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Mautner (UC Riverside)
DTSTART:20221208T195000Z
DTEND:20221208T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/64
DESCRIPTION:Title: Perverse sheaves on symmetric products of the plane\nby Carl
Mautner (UC Riverside) as part of Geometry\, Physics\, and Representation
Theory Seminar\n\n\nAbstract\nIn joint work with Tom Braden we give a pure
ly algebraic description of the category of perverse sheaves (with coeffic
ients in any field) on $S^n(C^2)$\, the n-fold symmetric product of the pl
ane. In particular\, using the geometry of the Hilbert scheme of points\,
we relate this category to the symmetric group and its representation rin
g. Our work is motivated by analogous structure appearing in the Springer
resolution and Hilbert-Chow morphism.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yan Zhou (Northeastern)
DTSTART:20221103T185000Z
DTEND:20221103T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/65
DESCRIPTION:Title: Irregular opers\, Stokes geometry and WKB analysis\nby Yan Zh
ou (Northeastern) as part of Geometry\, Physics\, and Representation Theor
y Seminar\n\n\nAbstract\nWe study\, using the extended isomonodromy deform
ation\, the WKB approximation of Stokes matrices of a class of meromorphic
linear ODE systems of Poincare rank 1 on the projective line that appear
in various contexts of geometry. We show that\, via the degenerate Riemann
-Hilbert map\, the WKB approximation of Stokes matrices recovers the Gelfa
nd-Tsetlin integrable systems whose action variables match with period on
spectral curves. If time permits\, we will also briefly discuss the potent
ial ramifications to cluster theory\, spectral networks and gl(n)-crystal
s (in the quantum setting). The talk is based on joint work with Anton Ale
kseev and Xiaomeng Xu and ongoing discussions with Andrew Neitzke.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abigail Ward (MIT)
DTSTART:20221201T195000Z
DTEND:20221201T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/66
DESCRIPTION:Title: Symplectomorphisms mirror to birational transformations of the pr
ojective plane\nby Abigail Ward (MIT) as part of Geometry\, Physics\,
and Representation Theory Seminar\n\n\nAbstract\nWe construct a non-finite
type four-dimensional Weinstein domain $M_{univ}$ and describe a HMS corr
espondence between distinguished birational transformations of the project
ive plane preserving a standard holomorphic volume form and symplectomorph
isms of $M_{univ}$. The space $M_{univ}$ is universal in the sense that it
contains every Liouville manifold mirror to a log Calabi-Yau surface as a
Weinstein subdomain\; after restricting to these subdomains\, we recover
a mirror correspondence between the automorphism group of any open log Cal
abi-Yau surface and the symplectomorphism group of its mirror. This is joi
nt work with Ailsa Keating.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ahmad Reza Haj Saeedi Sadegh (Northeastern)
DTSTART:20221110T195000Z
DTEND:20221110T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/67
DESCRIPTION:Title: Deformation spaces\, rescaled bundles\, and their applications in
geometry and analysis\nby Ahmad Reza Haj Saeedi Sadegh (Northeastern)
as part of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAb
stract\nWe construct an algebraic vector bundle over the deformation to th
e normal cone for an embedding of manifolds through a rescaling of a vecto
r bundle over the ambient space. This method generalizes the construction
of the spinor rescaled bundle over the tangent groupoid by Nigel Higson an
d Zelin Yi. Applications of this construction include local index formula\
, equivariant index formula\, Kirillov formula and Witten and Novikov defo
rmation of de Rham operator.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weiqiang Wang (UVA)
DTSTART:20230302T195000Z
DTEND:20230302T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/68
DESCRIPTION:Title: Quantum Schur dualities ABC\nby Weiqiang Wang (UVA) as part o
f Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nTh
e classical Schur duality admits a q-deformation due to Jimbo\, which is a
duality between a quantum group and Hecke algebra of type A. A new quantu
m Schur duality between an i-quantum group (arising from quantum symmetric
pairs) and Hecke algebra of type B was formulated by Huanchen Bao and mys
elf. In this talk\, I will explain these dualities\, their geometric incar
nation\, and applications to super Kazhdan-Lusztig theories of type ABC.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu-Shen Lin (BU)
DTSTART:20230316T185000Z
DTEND:20230316T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/69
DESCRIPTION:Title: Symplectic scattering diagrams for Log Calabi-Yau Surfaces\nb
y Yu-Shen Lin (BU) as part of Geometry\, Physics\, and Representation Theo
ry Seminar\n\n\nAbstract\nThe pioneering work of Gross-Hacking-Keel studie
d the mirror symmetry for log Calabi-Yau surfaces proved that there exists
a natural superpotential defined on the mirrors. The key intermediate pro
duct of the mirror construction are some combinatorial data called scatter
ing diagrams. In this talk\, I will explain the symplectic heuristic of th
e construction and mathematically how we retrieve the superpotentials and
the scattering diagram from Lagrangian Floer theory. As corollaries\, we p
rove a version of cluster mirror symmetry of rank two\, a real analogue of
27 lines on cubic surfaces and a folklore conjecture "open Gromov-Witten
invariants=log Gromov-Witten invariants. This is a joint work with Bardwel
l-Evans\, Cheung and Hong.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Larson (Harvard)
DTSTART:20230126T195000Z
DTEND:20230126T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/70
DESCRIPTION:Title: Cohomology of moduli spaces of stable curves\nby Hannah Larso
n (Harvard) as part of Geometry\, Physics\, and Representation Theory Semi
nar\n\n\nAbstract\nThe cohomology rings of moduli spaces often have distin
guished classes called tautological classes. This talk is about the specia
l situation when all cohomology classes on a moduli space are tautological
. I will start with the example of projective space. Then I'll introduce t
he moduli spaces M_{g\,n}-bar of n-poined\, stable genus g curves\, using
the example M_{2\,0}-bar as a guide. At the end\, I'll present several new
small values (g\, n) where we have proven that all classes on M_{g\,n}-ba
r are tautological. This is joint work with Samir Canning.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Frechette (BC)
DTSTART:20230406T185000Z
DTEND:20230406T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/71
DESCRIPTION:Title: Metaplectic ice: using statistical mechanics in representation th
eory\nby Claire Frechette (BC) as part of Geometry\, Physics\, and Rep
resentation Theory Seminar\n\n\nAbstract\nLocal Whittaker functions for re
ductive groups play an integral role in number theory and representation t
heory\, and many of their applications extend to the metaplectic case\, wh
ere reductive groups are replaced by their metaplectic covering groups. We
will examine these functions for covers of $GL_r$ through the lens of a s
olvable lattice model\, or ice model: a construction from statistical mech
anics that provides a surprising bridge between spaces of Whittaker functi
ons and representations of quantum groups. This story has been well studie
d before for the case of one particularly nice cover of $GL_r$\, which eli
minates all complications arising from the center of the group. In this ta
lk\, we will see that the same types of connections hold for any metaplect
ic cover of $GL_r$\, as well as examine how different choices of covering
group interact with the center of $GL_r$ to change the story.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Rybnikov (Harvard)
DTSTART:20230202T195000Z
DTEND:20230202T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/73
DESCRIPTION:Title: Kashiwara crystals from maximal commutative subalgebras\nby L
eonid Rybnikov (Harvard) as part of Geometry\, Physics\, and Representatio
n Theory Seminar\n\n\nAbstract\nShift of argument subalgebras is a family
of maximal commutative subalgebras in the universal enveloping algebra U(g
) parametrized by regular elements of the Cartan subalgebra of a reductive
Lie algebra g. According to Vinberg\, the Gelfand-Tsetlin subalgebra in U
(gl_n) is a limit case of such family\, so one can regard the eigenbases f
or such commutative subalgebras in finite-dimensional g-modules as a defor
mation of the Gelfand-Tsetlin basis (which is more general than Gelfand-Ts
etlin bases themselves because exists for arbitrary semisimple Lie algebra
g). I will define a natural structure of a Kashiwara crystal on the spect
ra of the shift of argument subalgebras of U(g) in finite-dimensional g-mo
dules. This gives a topological description of the inner cactus group acti
on on a g-crystal\, as a monodromy of an appropriate covering of the De Co
ncini-Procesi closure of the complement of the root hyperplane arrangement
in the Cartan subalgebra. In particular\, this gives a topological descri
ption of the Berenstein-Kirillov group (generated by Bender-Knuth involuti
ons on the Gelfand-Tsetlin polytope) and of its relation to the cactus gro
up due to Chmutov\, Glick and Pylyavskyy.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Hogancamp (Northeastern)
DTSTART:20230330T185000Z
DTEND:20230330T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/74
DESCRIPTION:Title: The nilpotent cone for sl2 and annular link homology\nby Matt
Hogancamp (Northeastern) as part of Geometry\, Physics\, and Representati
on Theory Seminar\n\n\nAbstract\nIn this talk I will discuss an equivalenc
e of categories relating SL(2)-equivariant vector bundles on the nilpotent
cone for sl(2) and the annular Bar-Natan category (this latter category a
ppears in the context of Khovanov homology for links in a thickened annulu
s). Indeed\, both categories admit a diagrammatic description in terms of
the same "dotted" Temperley-Lieb diagrammatics\, as I will explain. Unde
r this equivalence\, Bezrukavnikov's quasi-exceptional collection on the n
ilcone (in the SL2 case) has an elegant description in terms of some speci
al annular links. In recent joint work with Dave Rose and Paul Wedrich\,
we constructed a very special Ind-object in the annular Bar-Natan category
which is a categorical analogue of a "Kirby element" from quantum topolog
y\; I will conclude by sketching a neat "BGG resolution" afforded by our
categorified Kirby element. This is based on joint work with Rose and Wed
rich.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Travis Mandel (OU)
DTSTART:20230223T195000Z
DTEND:20230223T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/75
DESCRIPTION:Title: Bracelet bases are theta bases\nby Travis Mandel (OU) as part
of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\n
Cluster algebras from marked surfaces can be interpreted as skein algebras
\, as functions on decorated Teichmüller space\, or as functions on certa
in moduli of SL2-local systems. These algebras and their quantizations ha
ve well-known collections of special elements called "bracelets" (due to F
ock-Goncharov and Musiker-Schiffler-Williams\, and due to D. Thurston in t
he quantum setting). On the other hand\, Gross-Hacking-Keel-Kontsevich us
ed ideas from mirror symmetry to construct canonical bases of "theta funct
ions" for cluster algebras\, and this was extended to the quantum setting
in my work with Ben Davison. I will review these constructions and descri
be recent work with Fan Qin in which we prove that the (quantum) bracelets
bases coincide with the corresponding (quantum) theta bases.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pham Tiep (Rutgers/MIT/Princeton)
DTSTART:20230216T195000Z
DTEND:20230216T205000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/76
DESCRIPTION:Title: Character bounds for finite simple groups\nby Pham Tiep (Rutg
ers/MIT/Princeton) as part of Geometry\, Physics\, and Representation Theo
ry Seminar\n\n\nAbstract\nGiven the current knowledge of complex represent
ations of finite simple groups\, obtaining good upper bounds for their cha
racters values is still a difficult problem\, a satisfactory solution of w
hich would have significant implications in a number of applications. We w
ill report on recent results that produce such character bounds\, and disc
uss some applications of them\, in and outside of group theory.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cesar Cuenca (Harvard)
DTSTART:20230420T185000Z
DTEND:20230420T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/77
DESCRIPTION:Title: Invariant measures of infinite-dimensional groups over finite fie
lds\nby Cesar Cuenca (Harvard) as part of Geometry\, Physics\, and Rep
resentation Theory Seminar\n\n\nAbstract\nIn this talk\, we study the prob
lem of characterizing the set of G-invariant measures on a space of infini
te-dimensional matrices over a finite field. The groups G being considered
are inductive limits of the finite general linear groups GL(n\, q) and th
e finite even unitary groups $U(2n\, q^2)$ over a finite field\; our propo
sed problem is still open in the latter even unitary case and the talk foc
uses on it. One partial result translates the problem to the classificatio
n of positive harmonic functions on branching graphs that are Hall-Littlew
ood versions of the Young graph. A second partial result is the constructi
on of a large class of invariant measures by means of the Hopf-algebra str
ucture on the ring of symmetric functions. The talk is based on joint work
with Grigori Olshanski.\n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (McGill)
DTSTART:20230427T185000Z
DTEND:20230427T195000Z
DTSTAMP:20260404T094701Z
UID:GPRTatNU/78
DESCRIPTION:Title: Virtual cactus group: combinatorics and topology\nby Joel Kam
nitzer (McGill) as part of Geometry\, Physics\, and Representation Theory
Seminar\n\n\nAbstract\nThe cactus group is a finitely presented group anal
ogous to the braid group. It acts on combinatorial objects\, especially te
nsor products of crystals. It is also the fundamental group of the moduli
space of marked real genus 0 stable curves. The virtual cactus group conta
ins both the cactus group and the symmetric group with some natural relati
ons (here "virtual" is in the sense of virtual knot theory). I will explai
n how the virtual cactus group appears combinatorially and topologically.\
n
LOCATION:https://stable.researchseminars.org/talk/GPRTatNU/78/
END:VEVENT
END:VCALENDAR