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BEGIN:VEVENT
SUMMARY:Alexander Buryak (HSE Moscow)
DTSTART:20210312T080000Z
DTEND:20210312T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/1
DESCRIPTION:Title: A noncommutative generalization of Witten's conjecture\nby Alexa
nder Buryak (HSE Moscow) as part of IBS-CGP Mathematical Physics Seminar\n
\n\nAbstract\nThe classical Witten conjecture says that the generating ser
ies of integrals over the moduli spaces of curves of monomials in the psi-
classes is a solution of the Korteweg - de Vries (KdV) hierarchy. Together
with Paolo Rossi\, we present the following generalization of Witten's co
njecture. On one side\, let us deform Witten's generating series by insert
ing in the integrals certain naturally defined cohomology classes\, the so
-called double ramification cycles. It turns out that the resulting genera
ting series is conjecturally a solution of a noncommutative KdV hierarchy\
, where one spatial variable is replaced by two spatial variables and the
usual multiplication of functions is replaced by the noncommutative Moyal
multiplication in the space of functions of two variables.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Chekhov (Michigan State University and Steklov Mathematical
Institute)
DTSTART:20210319T010000Z
DTEND:20210319T020000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/2
DESCRIPTION:Title: Darboux coordinates for symplectic groupoid and cluster algebras
\nby Leonid Chekhov (Michigan State University and Steklov Mathematical In
stitute) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\nTh
e talk is based on Arxiv:2003:07499\, joint work with Misha Shapiro. I wil
l start with a short elementary excursion into cluster algebras---a fascin
ating branch of modern algebra introduced by Fomin and Zelvinsky in 2000's
---and describe planar directed networks. We then concentrate on another
interesting algebraic object---the $\\mathcal A_n$ groupoid of upper-trian
gular matrices\, which has had many appearances in studies of algebras of
monodromies of $SL_2$ Fuchsian systems and in geometry\, including the cel
ebrated Goldman bracket. I will show how we can use Fock--Goncharov higher
Teichm\\"uller space variables to derive canonical (Darboux) coordinate
representation for entries of general symplectic leaves of the $\\mathcal
A_n$ groupoid and\, in a more general setting\, of higher-dimensional symp
lectic leaves for algebras governed by the quantum reflection equation wit
h the trigonometric $R$-matrix. For the groupoid of upper-triangular matri
ces\, we represent braid-group transformations via sequences of cluster mu
tations in the special $\\mathbb A_n$-quiver. Time permitting\, I will als
o describe a generalization of this construction to affine Lie-Poisson alg
ebras and to quantum loop algebras (Arxiv:2012:10982).\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kazumi Okuyama (Shinshu University)
DTSTART:20210326T010000Z
DTEND:20210326T020000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/3
DESCRIPTION:Title: Quenched free energy from spacetime D-branes\nby Kazumi Okuyama
(Shinshu University) as part of IBS-CGP Mathematical Physics Seminar\n\n\n
Abstract\nWe propose a useful integral representation of the quenched free
energy which is applicable to any random systems. Our formula involves th
e generating function of multi-boundary correlators\, which can be interpr
eted on the bulk gravity side as spacetime D-branes introduced by Marolf a
nd Maxfield in [arXiv:2002.08950]. As an example\, we apply our formalism
to the Airy limit of the random matrix model and compute its quenched free
energy under certain approximations of the generating function of correla
tors. It turns out that the resulting quenched free energy is a monotonica
lly decreasing function of the temperature\, as expected.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Di Yang (University of Science and Technology of China)
DTSTART:20210402T080000Z
DTEND:20210402T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/4
DESCRIPTION:Title: Loop equations and integrable hierarchies for special cubic Hodge in
tegrals\nby Di Yang (University of Science and Technology of China) as
part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\nBy using the
Virasoro constraints we derive the loop equations for the cubic Hodge part
ition function with three parameters p\,q\,r satisfying the Calabi-Yau con
dition pq + qr + rp = 0. We then show that the Hodge integrable hierarchy
associated to the special cubic Hodge integrals is normal Miura equivalent
to the fractional Volterra hierarchy. In the procedure of the proof\, a p
articular tau-function for the fractional Volterra hierarchy is constructe
d\, which we call the topological tau-function. Finally\, when one of the
three parameters p\,q\,r is equal to 1\, we prove a certain gap condition
for the logarithm of the topological tau-function. The talk is based on jo
int works with Si-Qi Liu\, Youjin Zhang and Chunhui Zhou.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rinat Kashaev (Université de Genève)
DTSTART:20210409T080000Z
DTEND:20210409T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/5
DESCRIPTION:Title: The Alexander polynomial as a universal invariant\nby Rinat Kash
aev (Université de Genève) as part of IBS-CGP Mathematical Physics Semin
ar\n\n\nAbstract\nI will explain how the reciprocal of the Alexander polyn
omial of a knot can be viewed as a universal (quantum) invariant associate
d to the Hopf algebra of regular functions on the group of affine linear t
ransformations of the complex plane. This provides a conceptual interpreta
tion for the Melvin--Morton--Rozansky conjecture proven by Bar-Nathan and
Garoufalidis\, and Garoufalidis and Le about the relation of the colored J
ones polynomials to the reciprocal of the Alexander polynomial in a large
color limit.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Neitzke (Yale University)
DTSTART:20210416T010000Z
DTEND:20210416T020000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/6
DESCRIPTION:Title: Abelianization\, exact WKB and link invariants\nby Andrew Neitzk
e (Yale University) as part of IBS-CGP Mathematical Physics Seminar\n\n\nA
bstract\nIt has been understood in the last decade that various\ndifferent
problems\, including\n\n1) the exact WKB method for studying monodromy of
linear ODEs\,\n\n2) the study of some link invariants\, such as the Jones
polynomial\,\n\n3) the computation of classical Chern-Simons invariants o
f flat connections\,\n\ncan all be understood as aspects of a general stra
tegy for reduction from a\nnonabelian Lie group to its maximal abelian sub
group. I will describe this\npoint of view\, emphasizing the common featur
es of the three problems. Parts of\nthe talk are a report of joint works w
ith Dan Freed\, Davide Gaiotto\, Greg\nMoore\, Lotte Hollands\, and Fei Ya
n.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Norbury (University of Melbourne)
DTSTART:20210423T010000Z
DTEND:20210423T020000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/7
DESCRIPTION:Title: Enumerative geometry via the moduli space of super Riemann surfaces<
/a>\nby Paul Norbury (University of Melbourne) as part of IBS-CGP Mathemat
ical Physics Seminar\n\n\nAbstract\nMumford initiated the calculation of m
any algebraic topological invariants over the moduli space of Riemann surf
aces in the 1980s\, and Witten related these invariants to two dimensional
gravity in the 1990s. This viewpoint led Wittento a conjecture\, proven b
y Kontsevich\, that a generating function for intersection numbers on the
moduli space of curves is a tau function of the KdV hierarchy\, now known
as the Kontsevich-Witten tau function\, which allowed their evaluation. In
2004\, Mirzakhaniproduced another proof of Witten's conjecture via the st
udy of Weil-Petersson volumes of the moduli space using hyperbolic geometr
y. In this lecture I will describe a new collection of integrals over the
moduli space of Riemann surfaces whose generating functionis a tau functio
n of the KdV hierarchy\, known as the Brezin-Gross-Witten tau function. I
will sketch a proof of this result that uses an analogue of Mirzakhani's a
rgument applied to the moduli space of super Riemann surfaces - defined by
replacing the fieldof complex numbers with a Grassman algebra - which use
s recent work of Stanford and Witten. This appearance of the moduli space
of super Riemann surfaces to solve a problem over the classical moduli spa
ce is deep and surprising.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Todor Milanov (IPMU\, University of Tokyo)
DTSTART:20210430T010000Z
DTEND:20210430T020000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/8
DESCRIPTION:Title: Topological recursion for simple singularities\nby Todor Milanov
(IPMU\, University of Tokyo) as part of IBS-CGP Mathematical Physics Semi
nar\n\n\nAbstract\nIt is known that Givental's total ancestor potential of
any semi-simple Frobenius manifold can be reconstructed via the so-called
local Eynard--Orantin recursion. For the application to integrable system
s and the representation theory of W-algebras however\, it is important to
determine whether the local recursion can be extended to a global one. In
my talk\, I would like to explain the problem of comparing local and glob
al Eynard--Orantin recursions and to explain the case of a Frobenius manif
old corresponding to a simple singularity.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Harnad (Université de Montréal)
DTSTART:20210507T010000Z
DTEND:20210507T020000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/9
DESCRIPTION:Title: Bilinear expansions of lattices of KP $\\tau$-function in BKP $\\tau
$-functions: a fermionic approach\nby John Harnad (Université de Mont
réal) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\nThe
notion of Kadomtsev-Petviashvili (KP) and BKP $\\tau$ functions will\nbe r
ecalled\, together with their representations as fermionic expectation val
ues.\nSchur-type lattices of such KP and BKP $\\tau$-functions will be def
ined\, corresponding to\na given infinite general linear or orthogonal gro
up element\, labelled by partitions\nand strict partitions respectively. A
bilinear expansion expressing elements of these lattices of KP $\\tau$-fu
nctions as sums over products of pairs of elements of associated lattices
of BKP $\\tau$-functions will be presented\, generalizing earlier results
relating determinants and Pfaffians of minors of skew symmetric matrices
\, with applications to Schur functions and Schur $Q$-functions. Further a
pplications include inhomogeneous polynomial $\\tau$-functions of KP and B
KP type\, with their determinantal and Pfaffian representations.\n\nRefs:\
n 1) F. Balogh\, J. Harnad and J. Hurtubise\, “Isotropic Grassmannians\,
Plücker and Cartan maps”\, J. Math. Phys. 62\, 021701 (2021)\n2) J. Ha
rnad and A. Yu. Orlov\, “Bilinear expansions of lattices of KP tau-funct
ions in BKP tau-functions: a fermionic approach”\, J. Math. Phys. 62\, 0
13508 (2021)\n3) J. Harnad and A. Yu. Orlov\, “Bilinear expansions of Sc
hur functions in Schur Q-functions: a fermionic approach”\, arxiv: 2008
.13734 (Proc. Amer. Math. Soc.\, in press\, 2021)\n4) J. Harnad and A. Yu.
Orlov\, “Polynomial KP and BKP τ-functions and correlators”\, arXiv
:2011.13339\, (Ann. H. Poincaré\, in press 2021).\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech)
DTSTART:20210521T010000Z
DTEND:20210521T020000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/10
DESCRIPTION:Title: New exact results for open enumerative invariants\nby Sergei Gu
kov (Caltech) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstrac
t\nProblems that involve bordered pseudoholomorphic curves with boundary o
n a Lagrangian submanifold in a Calabi-Yau 3-fold are usually called "open
enumerative invariants." The analysis involved in such problems is extrem
ely rich and interesting\, which makes the study of open enumerative invar
iants challenging and complicated. Yet\, over the past 30 years a lot of p
rogress has been made\, in part due to various "dualities" --- such as mir
ror symmetry --- that relate open enumerative problems to questions in oth
er areas of mathematics. After a short survey of past developments\, I wil
l present a new class of Calabi-Yau 3-folds with Lagrangian submanifolds w
here the problem can be solved completely thanks to a new connection with
quantum groups at generic values of the parameter q.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wolfgang Lerche (CERN)
DTSTART:20210528T080000Z
DTEND:20210528T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/11
DESCRIPTION:Title: Fluxes\, Holomorphic Anomalies and Elliptic Genera in d=4\nby W
olfgang Lerche (CERN) as part of IBS-CGP Mathematical Physics Seminar\n\n\
nAbstract\nMotivated by tests of Weak Gravity Conjectures\, we investigate
properties of elliptic genera of string theories that arise in large dist
ance limits of the moduli space of F-theory compactifications. This allows
for a non-perturbative definition of elliptic genera that goes beyond the
ordinary world-sheet description. While this construction has been known
for six-dimensional theories\, we find the four-dimensional variant to be
surprisingly complex. The essential new ingredient is background fluxes\,
and these lead to different sectors of the elliptic genus with different m
odular properties. Crucial is the appearance of derivatives which leads to
novel modular (and hence\, holomorphic) anomalies that are much worse tha
n expected. We also give a physical interpretation of these phenomena.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Walcher (Heidelberg University)
DTSTART:20210514T080000Z
DTEND:20210514T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/12
DESCRIPTION:Title: On the rationality of MUMs and 2-functions\nby Johannes Walcher
(Heidelberg University) as part of IBS-CGP Mathematical Physics Seminar\n
\n\nAbstract\nPoints of maximal unipotent monodromy in Calabi-Yau moduli s
pace play a central role in mirror symmetry\, and also harbor some interes
ting arithmetic. In the classic examples\, suitable expansion coefficients
of the (all-genus) prepotential (in polylogarithms) under the mirror map
are integers with an enumerative interpretation on the mirror manifold. Th
is correspondence should be expected to extend to periods relative to alge
braic cycles capturing the enumerative geometry relative to Lagrangian sub
manifolds. This expectation is challenged\, however\, when the mixed degen
eration is not defined over Q. After musing about compatibility with mirro
r symmetry\, I will discuss two recent results that sharpen these question
s further: The first is a theorem proven by Felipe Müller which states th
at the coefficients of rational 2-functions are necessarily contained in a
n abelian number field. (As defined in the talk\, 2-functions are formal p
ower series whose coefficients satisfy a natural Hodge theoretic supercong
ruence.) The second are examples worked out in collaboration with Bönisch
\, Klemm\, and van Straten\, of MUMs that are themselves not defined over
Q.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Alexandrov (IBS CGP)
DTSTART:20210618T010000Z
DTEND:20210618T020000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/13
DESCRIPTION:Title: KP integrability of triple Hodge integrals\nby Alexander Alexan
drov (IBS CGP) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstra
ct\nIn my talk\, I will describe a relation between the Givental group of
rank one and the Heisenberg-Virasoro symmetry group of the KP integrable h
ierarchy. It appears that only a two-parameter family of the Givental oper
ators can be identified with elements of the Heisenberg-Virasoro symmetry
group. This family describes triple Hodge integrals satisfying the Calabi-
Yau condition. Using the identification of the elements of two groups it i
s possible to prove that the generating function of triple Hodge integrals
satisfying the Calabi-Yau condition and its $\\Theta$-version are tau-fun
ctions of the KP hierarchy. This generalizes the result of Kazarian on KP
integrability in the case of linear Hodge integrals. I will also describe
the relation of this family of tau-functions with the deformation of the K
ontsevich matrix model. My talk is based on two papers\, arXiv:2009.01615
and arXiv:2009.10961.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Bouchard (University of Alberta)
DTSTART:20210924T010000Z
DTEND:20210924T020000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/14
DESCRIPTION:Title: Whittaker vectors for W-algebras from topological recursion\nby
Vincent Bouchard (University of Alberta) as part of IBS-CGP Mathematical
Physics Seminar\n\n\nAbstract\nGaiotto vectors\, describing the fundamenta
l class in the equivariant cohomology of a suitable compactification of th
e moduli space of G-bundles over P^2\, for G a complex simple Lie group\,
are Whittaker vectors for modules of W-algebras. In this work we identify
these Whittaker vectors with partition functions of quantum Airy structure
s\, which means that they can be calculated by topological recursion metho
ds. On the physics side\, it means that the Nekrasov partition function fo
r pure N=2 4d supersymmetric gauge theories can be accessed via a topologi
cal recursion à la Chekhov-Eynard-Orantin. We formulate the connection fo
r Gaiotto vectors of type A\, B\, C\, and D. For those interested in topol
ogical recursion\, the type A case at arbitrary level gives rise to a new
non-commutative formulation of topological recursion.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Bertola (Concordia University)
DTSTART:20211001T010000Z
DTEND:20211001T020000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/15
DESCRIPTION:Title: Graph connections\, (wild) character varieties and generating funct
ion in symplectic geometry\nby Marco Bertola (Concordia University) as
part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\nWe will discu
ss a natural (pre)-symplectic structure associated to an arbitrary flat gr
aph connection on a Riemann surface and its invariance properties. This al
lows to efciently parametrize (wild) character varieties using Fock-Goncha
rov coordinates and provide explicit log-canonical coordinates for several
types of Poisson structures\; Goldman on the standard character variety\,
Flaschka-Newell-Boalch on Stokes' manifolds and Ugaglia-Bondal Poisson st
ructures. \nIn the case of (wild) character varieties\, this construction
allows to define the generating functions of symplectic polarizations and
identify them with the classical notion of isomonodromic tau functions of
the Japanese school.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kazarian (HSE & Skoltech)
DTSTART:20211008T080000Z
DTEND:20211008T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/16
DESCRIPTION:Title: Topological recursion for generalized Hurwitz numbers\nby Maxim
Kazarian (HSE & Skoltech) as part of IBS-CGP Mathematical Physics Seminar
\n\n\nAbstract\nThe topological recursion or Chekhov-Eunard-Orantin recurs
ion is an inductive procedure for an explicit computation of correlator fu
nctions appearing in a large number of problems in mathematical physics\,
from matrix integrals and Gromov-Witten invariants to enumerations of maps
and meromorphic functions with prescribed singularities. In spite of exis
tence of a huge number of known cases where this procedure does work\, its
validity and universality still remains mysterious in much extend.\n \nWe
develop a new tool based on the theory of KP hierarchy that allows one no
t only formally prove it in a unified way for a wide class of problems but
also to understand its true nature and the origin. These problems include
enumeration various kinds of Hurwitz numbers: ordinary ones\, orbifold\,
double\, monotone\, r-spin Hurwitz numbers\, as well as enumeration of (hy
per) maps and extends much beyond. The talk is based on a joint work with
B.Bychkov\, P.Dunin-Barkowski\, S.Shadrin.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Harnad (CRM & Concordia University)
DTSTART:20211022T010000Z
DTEND:20211022T020000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/17
DESCRIPTION:Title: Bilinear expansions of lattices of KP $\\tau$-functions in BKP $\\t
au$-functions\, determinant and Pfaffian expressions of polynomial $\\tau$
-functions\nby John Harnad (CRM & Concordia University) as part of IBS
-CGP Mathematical Physics Seminar\n\n\nAbstract\nThe notion of Kadomtsev-P
etviashvili (KP) and BKP $\\tau$ functions will\nbe recalled\, together wi
th their representations as fermionic expectation values.\nSchur-type latt
ices of KP and BKP $\\tau$-functions will be defined\, corresponding to\na
given infinite general linear or orthogonal group element\, labelled by p
artitions\nand strict partitions respectively. A bilinear expansion expres
sing elements of these lattices of KP $\\tau$-functions\nas sums over prod
ucts of pairs of elements of associated lattices of BKP $\\tau$-functions
will be presented\,\ngeneralizing earlier results relating determinants a
nd Pfaffians of minors of skew symmetric matrices\,\nwith applications to
Schur functions and Schur $Q$-functions. Further applications include\nde
terminantal and Pfaffian representations of all inhomogeneous polynomial $
\\tau$-functions of KP and BKP type.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danilo Lewański (IHES and IPhT)
DTSTART:20211119T080000Z
DTEND:20211119T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/18
DESCRIPTION:Title: Cohomological field theories and BKP integrability: Omega classes t
imes Witten-classes\nby Danilo Lewański (IHES and IPhT) as part of IB
S-CGP Mathematical Physics Seminar\n\n\nAbstract\nThere is a deep interact
ion between Cohomological field theories (CohFTs)\, introduced by Kontsevi
ch and Manin\, and integrable hierarchies. For instance\, the celebrated W
itten-Kontsevich result shows that the trivial CohFT gives rise to a solut
ion of the KdV integrable hierarchy. As another example\, Kazarian’s the
orem shows that the Hodge CohFT gives rise to a solution of the KP hierarc
hy\, and so do Hurwitz numbers\, which by ELSV formula are descendant inte
grals of the Hodge CohFT. The change of variable which carries the partiti
on function of Hurwitz numbers into the partition function of pure descend
ant Hodge integrals is triangular and KP-preserving\, it is in fact essent
ially given by the Topological Recursion spectral curve in the sense of Ey
nard and Orantin. \n\nWe study spin-Hurwitz numbers (not to be confused wi
th completed cycles Hurwitz numbers) enumerating branches Riemann covers w
eighted by the parity of theta characteristics. They obey the BKP integrab
le hierarchy. We prove that the Topological Recursion conjecture for these
numbers is equivalent to their underlying CohFT to be an explicit product
between Witten’s class and Omega-classes computed by Chiodo. The Topolo
gical Recursion conjecture has recently been proved by Alexandrov and Shad
rin in a more general framework for BKP integrability.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bertrand Eynard (IHES and IPhT)
DTSTART:20211126T080000Z
DTEND:20211126T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/19
DESCRIPTION:Title: CFT from Topological Recursion\nby Bertrand Eynard (IHES and IP
hT) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\nConform
al Field Theories\, can be "defined" by the bootstrap axioms. The main axi
oms are that we have a set of functions (amplitudes) that should satisfy O
PE (short distance asymptotic behaviour)\, Ward identities (reflecting con
formal invariance) and crossing-symmetry (all possible ways of computing a
n amplitude should give the same answer).\nTopological Recursion is a recu
rsive recipe that associates to a spectral curve S (an algebraic plane cur
ve with some additional features)\, a sequence of n-forms\, denoted $\\ome
ga_{g\,n}(S)$\, $g=0\,\\dots\,\\infty$\, $n=0\,\\dots\,\\infty$. These n-f
orms naturally allow to define amplitudes (as formal series) that do satis
fy OPE and Ward Identities axioms. Moreover\, there is a way to adapt them
to also satisfy crossing symmetry. This last statement is presently a con
jecture\, not yet proved in all cases\, but belived to be true.\nWe shall
also discuss the link to integrable systems and algebraic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamara Grava (University of Bristol & SISSA)
DTSTART:20211112T080000Z
DTEND:20211112T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/20
DESCRIPTION:Title: Correlation functions for unitary invariant ensembles and Hurwitz n
umbers\nby Tamara Grava (University of Bristol & SISSA) as part of IBS
-CGP Mathematical Physics Seminar\n\n\nAbstract\nWe provide effective form
ulae for generating functions of multipoint correlators for unitary invari
ants ensembles. As an application we show that the multipoint correlators
of the Laguerre and the Jacobi ensembles are obtained in terms of Hahn pol
ynomials and Wilson polynomials generalising earlier formula for one-poin
t correlators. Finally we provide an enumerative interpretation of the top
ological expansion of these multipoint correlators. This is a joint work w
ith M. Gisonni and G. Ruzza.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Nekrasov (Simons Center for Geometry and Physics)
DTSTART:20211029T080000Z
DTEND:20211029T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/21
DESCRIPTION:Title: Quantum T-Q and KZ equations in gauge theory\nby Nikita Nekraso
v (Simons Center for Geometry and Physics) as part of IBS-CGP Mathematical
Physics Seminar\n\n\nAbstract\nBaxter's T-Q equation is a main instrument
in the functional and algebraic Bethe ansatz approach to quantum spin cha
ins. Knizhnik-Zamolodchikov equation is obeyed by the conformal blocks of
the two dimensional current algebra. Remarkably\, the analytic continuatio
n of the latter\, and a deformation of the former can be found in the real
m of the four dimensional supersymmetric gauge theories with matter. \n\nB
ased on the recent work with Saebyeok Jeong and Norton Lee.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaëtan Borot (Institute for Mathematics & Institute for Physics\,
Humboldt University of Berlin)
DTSTART:20220304T080000Z
DTEND:20220304T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/22
DESCRIPTION:Title: (CANCELED!) The B-model for singular spectral curves and its enumer
ative interpretation\nby Gaëtan Borot (Institute for Mathematics & In
stitute for Physics\, Humboldt University of Berlin) as part of IBS-CGP Ma
thematical Physics Seminar\n\n\nAbstract\nThe talk is canceled because of
technical problems.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Marshakov (Center for Advanced Studies\, Skoltech)
DTSTART:20220311T080000Z
DTEND:20220311T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/23
DESCRIPTION:Title: Cluster integrable systems and supersymmetric gauge theories\nb
y Andrei Marshakov (Center for Advanced Studies\, Skoltech) as part of IBS
-CGP Mathematical Physics Seminar\n\n\nAbstract\nI am going to discuss the
relation between the cluster integrable systems (or the Goncharov-Kenyon
systems and their reductions) with the supersymmetric gauge theories. I ho
pe to overview the basic definitions\, the facts around the statement that
their deautonomizations are solved by dual partition functions of supersy
mmetric gauge theories\, and some recent developements in this picture.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guillaume Chapuy (IRIF\, Université de Paris)
DTSTART:20220318T080000Z
DTEND:20220318T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/24
DESCRIPTION:Title: b-monotone Hurwitz numbers: Virasoro constraints\, BKP hierarchy\,
and O(N)-BGW integral\nby Guillaume Chapuy (IRIF\, Université de Pari
s) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\nMy talk
will be an introduction to (part of) my recent paper arXiv:2109.01499 writ
ten jointly with Valentin Bonzom and Maciej Dołęga. We study a b-deforma
tion of monotone Hurwitz numbers\, obtained by deforming Schur functions i
nto Jack symmetric functions. It is a special case of the b-deformed weigh
ted Hurwitz numbers recently introduced by Dołęga and myself and is rela
ted branched coverings of the sphere by non-oriented surfaces.\n\nWe give
an evolution (cut-and-join) equation for the model and we derive\, by a me
thod of independent interest\, explicit Virasoro constraints from it\, for
arbitrary values of the deformation parameter b. For b=1 the model is rel
ated to the (large) BKP hierarchy and an O(N) version of the BGW integral.
The talk will not assume previous knowledge\, I will try in particular to
explain where the interest of combinatorialists for these deformations co
me from\, and in particular the Goulden-Jackson b-conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Basalaev (HSE & Skoltech)
DTSTART:20220325T080000Z
DTEND:20220325T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/25
DESCRIPTION:Title: Mirror symmetry for a cusp polynomial Landau-Ginzburg orbifold\
nby Alexey Basalaev (HSE & Skoltech) as part of IBS-CGP Mathematical Physi
cs Seminar\n\n\nAbstract\nWe will establish mirror symmetry between the cu
sp polynomials considered with a nontrivial symmetry group and Geigle-Lenz
ing orbifold projective lines. In particular\, we will introduce Dubrovin-
Frobenius manifold of equivariant Saito theory of any cusp polynomial and
show that it is isomorphic to Dubrovin-Frobenius manifold of the respectiv
e Geigle-Lenzing orbifold. We will also show that in the case of simple-el
liptic singularities this mirror isomorphism is equivalent the certain rel
ations in the ring of modular forms. This is a joint work with A.Takahashi
(Osaka).\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Penka Georgieva (Institut de Mathématiques de Jussieu)
DTSTART:20220408T080000Z
DTEND:20220408T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/26
DESCRIPTION:Title: Klein TQFT and real Gromov-Witten invariants\nby Penka Georgiev
a (Institut de Mathématiques de Jussieu) as part of IBS-CGP Mathematical
Physics Seminar\n\n\nAbstract\nIn this talk I will explain how the Real Gr
omov-Witten theory of local 3-folds gives rise to an extension of a 2d Kle
in TQFT. The latter theory is furthermore semi-simple which allows for com
plete computation from the knowledge of a few basic elements which can be
calculated explicitly. As a consequence of the explicit expressions we fin
d in the Calabi-Yau case we obtain the expected GV formula and relation to
SO/Sp Chern-Simons theory.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Rossi (University of Padua)
DTSTART:20220401T080000Z
DTEND:20220401T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/27
DESCRIPTION:Title: Moduli spaces of residueless meromorphic differentials and the KP h
ierarchy\nby Paolo Rossi (University of Padua) as part of IBS-CGP Math
ematical Physics Seminar\n\n\nAbstract\nI'll present a recent joint work w
ith A. Buryak and D. Zvonkine\, where we study the moduli spaces of residu
eless meromorphic differentials\, i.e.\, the closures\, in the moduli spac
e of stable curves\, of the loci of smooth curves whose marked points are
the zeros and poles of prescribed orders of a meromorphic differential wit
h vanishing residues. Our main result is that intersection theory on these
spaces is controlled by an integrable system containing the celebrated Ka
domtsev-Petviashvili (KP) hierarchy as a reduction to the case of differen
tials with exactly two zeros and any number of poles. This fact has severa
l deep consequences and in particular it relates the aforementioned moduli
spaces with Hurwitz theory\, representation theory of sl2(C)\, integrabil
ity and a conjecture of Schmitt and Zvonkine on the r=0 limit of Witten's
r-spin classes.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaëtan Borot (Institute for Mathematics & Institute for Physics\,
Humboldt University of Berlin)
DTSTART:20220415T080000Z
DTEND:20220415T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/28
DESCRIPTION:Title: The B-model for singular spectral curves and its enumerative interp
retation\nby Gaëtan Borot (Institute for Mathematics & Institute for
Physics\, Humboldt University of Berlin) as part of IBS-CGP Mathematical P
hysics Seminar\n\n\nAbstract\nI will discuss the definition of B-model/top
ological recursion for spectral curves and explain the obstructions to the
well-posedness of this definition for arbitrary spectral curves. The ques
tion can be approached by the representation theory of W-algebras\, and I
will describe the largest known class of admissible spectral curves (inclu
ding singular cases) that has been obtained in this way. Each case is expe
cted to have an enumerative interpretation in a sense that I will specify.
In particular l will describe possible applications in open r-spin inters
ection theory.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaobo Liu (Beijing International Center for Mathematical Research
)
DTSTART:20220422T010000Z
DTEND:20220422T020000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/29
DESCRIPTION:Title: Hall-Littlewood functions and Virasoro constraints\nby Xiaobo L
iu (Beijing International Center for Mathematical Research) as part of IBS
-CGP Mathematical Physics Seminar\n\n\nAbstract\nHall-Littlewood functions
are generalizations of Schur Q-functions which have been used to study Ko
ntsevich-Witten and Brezin-Gross-Witten tau functions. Recently Mironov an
d Morozov proposed to use Hall-Littlewood functions specialized at roots o
f unity to study generalized Kontsevich matrix models. Virasoro constraint
s are powerful tools in the study of matrix models and Gromov-Witten invar
iants. In this talk\, I will describe how Virasoro operators act on Hall-L
ittlewood functions and applications of such formulas. This is based on jo
int works with Chenglang Yang.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norton Lee (IBS Center for Geometry and Physics)
DTSTART:20220916T080000Z
DTEND:20220916T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/30
DESCRIPTION:Title: Defect in gauge theory and quantum spin chains\nby Norton Lee (
IBS Center for Geometry and Physics) as part of IBS-CGP Mathematical Physi
cs Seminar\n\n\nAbstract\nThe N=2 supersymmetric gauge theories in four di
mensions have intrinsic connection to algebraic integrable systems. The ga
uge theory of interests\, the asymptotically superconformal N=2 SQCD in fo
ur dimensions\, reveals a structure which has dual descriptions. On the on
e hand it is the complex generalization of the Heisenberg XXX spin chain\,
based on the Lie algebra sl_2. On the other hand is the Gaudin model (a s
pecial type of Hitchin system)\, based on the Lie algebra sl_N. In this ta
lk I will focus on the spin chain side. I will show that by introducing BP
S surface defects\, we find observables in the gauge theory that satisfy d
ifference equations called fractional quantum T-Q equation. The observable
s represents states of the XXX Heisenberg spin chain of N Heisenberg-Weyl
modules over Y(sl_2). We also exploited to find the the explicit formula f
or the Jost function of the XXX Heisenberg spin chain from gauge theory.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reinier Kramer (University of Alberta)
DTSTART:20220923T080000Z
DTEND:20220923T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/31
DESCRIPTION:Title: The spin Gromov-Witten/Hurwitz correspondence\nby Reinier Krame
r (University of Alberta) as part of IBS-CGP Mathematical Physics Seminar\
n\n\nAbstract\nIn 2006\, Okounkov and Pandharipande established a correspo
ndence between two theories of counting maps between curves. Gromov-Witten
theory constructs a moduli space of stable maps and considers intersectio
n numbers of natural classes on this space. Hurwitz theory counts the numb
er of maps with given ramification data over all points in the target. The
Gromov-Witten theory of a surface with positive geometric genus can be lo
calised to a curve in that surface\, and this obtains a spin structure\, l
eading to spin Gromov-Witten theory of curves. The Hurwitz side also has a
natural spin analogue\, and Lee conjectured these theories correspond in
a similar manner. In this talk\, I will introduce the notions of spin Grom
ov-Witten theory and spin Hurwitz theory and give an outline of the spin G
romov-Witten/Hurwitz correspondence for the projective line. I will also e
xplain relations to the (small) 2BKP integrable hierarchy\, which is the a
nalogue of the 2D Toda lattice hierarchy in the non-spin case. This talk i
s based on joint work with Alessandro Giacchetto\, Danilo Lewański\, and
Adrien Sauvaget.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitri Zvonkine (Université de Versailles Saint-Quentin-en-Yveli
nes)
DTSTART:20220930T080000Z
DTEND:20220930T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/32
DESCRIPTION:Title: Fractional quantum Hall effect via the Grothendieck-Riemann-Roch fo
rmula\nby Dimitri Zvonkine (Université de Versailles Saint-Quentin-en
-Yvelines) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\n
We study the fractional quantum Hall effect on a Riemann surface of genus
g traversed by a magnetic field of total flux d. The wave functions of cha
rged particles have a semi-phenomenological description by Laughlin states
. These states can be studied by methods of algebraic geometry: they form
a holomorphic vector bundle over the d-th Picard group of the Riemann surf
ace. The Chern characters of this vector bundle can be computed by the Gro
thendieck-Riemann-Roch formula. In a fully filled state the Chern characte
r we obtain is compatible with the existence of a projectively flat connec
tion on the vector bundle. In a state with quasiholes our computation impl
ies that no such connection can exist. This is joint work with Semyon Klev
tsov.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jian Zhou (Tsinghua University)
DTSTART:20221014T010000Z
DTEND:20221014T020000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/33
DESCRIPTION:Title: Integrable Systems and mirror symmetry in probability theory and co
mbinatorics\nby Jian Zhou (Tsinghua University) as part of IBS-CGP Mat
hematical Physics Seminar\n\n\nAbstract\nWe will first explain how any mom
ent sequence leads to a sequence of tau-functions of the KP hierarchy\, wh
ich can be interpreted in terms of weighted counts of nonintersecting latt
ice paths. We will also explain how various lattice counting problems and
some other problems in combinatorics lead to probability measures on the
real line\, and surprising mirror symmetry among them.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Popolitov (ITEP)
DTSTART:20221028T080000Z
DTEND:20221028T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/34
DESCRIPTION:Title: Superintegrability: new and old meanings and techniques\nby Ale
xander Popolitov (ITEP) as part of IBS-CGP Mathematical Physics Seminar\n\
n\nAbstract\nThe goal of this talk is to review the topic of\nsuperintegra
bility/character expansion\nwhich recently enjoyed very rapid development
and discovery of new\ntechniques and is on the verge\nof becoming a system
atic approach to matrix models.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Lisovyy (Université de Tours)
DTSTART:20221021T080000Z
DTEND:20221021T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/35
DESCRIPTION:Title: Perturbative connection formulas for Heun equations\nby Oleg Li
sovyy (Université de Tours) as part of IBS-CGP Mathematical Physics Semin
ar\n\n\nAbstract\nConnection formulas relating Frobenius solutions of line
ar ODEs at different Fuchsian singular points can be expressed in terms of
the large order asymptotics of the corresponding power series. I will sho
w that for the Heun equation and some of its confluent versions\, the seri
es expansion of the relevant asymptotic amplitude in a suitable parameter
can be systematically computed to arbitrary order. This allows to check a
recent conjecture of Bonelli-Iossa-Panea-Tanzini expressing the Heun conne
ction matrix in terms of quasiclassical Virasoro conformal blocks.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Sułkowski (University of Warsaw)
DTSTART:20221104T080000Z
DTEND:20221104T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/36
DESCRIPTION:by Piotr Sułkowski (University of Warsaw) as part of IBS-CGP
Mathematical Physics Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ran Tessler (Weizmann Institute of Science)
DTSTART:20221118T080000Z
DTEND:20221118T090000Z
DTSTAMP:20260404T110743Z
UID:CGP-MP/37
DESCRIPTION:Title: Open r-spin theories with multiple boundary states\nby Ran Tess
ler (Weizmann Institute of Science) as part of IBS-CGP Mathematical Physic
s Seminar\n\n\nAbstract\nIn his 92' work\, Witten has defined the r-spin i
ntersection theory. This theory have found an open counterpart\, in genus
0\, in a recent joint work with Buryak and Clader. In the closed and open
setting there are (internal) marked points\, which are allowed to carry an
y twist from the set 0\,1\,...\,r-1\, and in the open setting there are al
so boundary markings whose twist is restricted to be r-2. My talk will des
cribe a new construction of genus=0 open r-spin theories\, which allows di
fferent collections of boundary states\, as well as the relations satisfie
d by the resulting intersection numbers. If time permits I will also say a
few words on higher genus. Based on a joint work with Yizhen Zhao.\n
LOCATION:https://stable.researchseminars.org/talk/CGP-MP/37/
END:VEVENT
END:VCALENDAR