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BEGIN:VEVENT
SUMMARY:Alexander Buryak (HSE Moscow)
DTSTART;VALUE=DATE-TIME:20210312T080000Z
DTEND;VALUE=DATE-TIME:20210312T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/1
DESCRIPTION:Title: A
noncommutative generalization of Witten's conjecture\nby Alexander Bu
ryak (HSE Moscow) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbs
tract\nThe classical Witten conjecture says that the generating series 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 P
aolo Rossi\, we present the following generalization of Witten's conjectur
e. On one side\, let us deform Witten's generating series by inserting in
the integrals certain naturally defined cohomology classes\, the so-called
double ramification cycles. It turns out that the resulting generating se
ries is conjecturally a solution of a noncommutative KdV hierarchy\, where
one spatial variable is replaced by two spatial variables and the usual m
ultiplication of functions is replaced by the noncommutative Moyal multipl
ication in the space of functions of two variables.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Chekhov (Michigan State University and Steklov Mathematical
Institute)
DTSTART;VALUE=DATE-TIME:20210319T010000Z
DTEND;VALUE=DATE-TIME:20210319T020000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/2
DESCRIPTION:Title: D
arboux coordinates for symplectic groupoid and cluster algebras\nby Le
onid Chekhov (Michigan State University and Steklov Mathematical Institute
) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\nThe talk
is based on Arxiv:2003:07499\, joint work with Misha Shapiro. I will start
with a short elementary excursion into cluster algebras---a fascinating b
ranch of modern algebra introduced by Fomin and Zelvinsky in 2000's---and
describe planar directed networks. We then concentrate on another interes
ting algebraic object---the $\\mathcal A_n$ groupoid of upper-triangular m
atrices\, which has had many appearances in studies of algebras of monodro
mies of $SL_2$ Fuchsian systems and in geometry\, including the celebrated
Goldman bracket. I will show how we can use Fock--Goncharov higher Teichm
\\"uller space variables to derive canonical (Darboux) coordinate represe
ntation for entries of general symplectic leaves of the $\\mathcal A_n$ gr
oupoid and\, in a more general setting\, of higher-dimensional symplectic
leaves for algebras governed by the quantum reflection equation with the t
rigonometric $R$-matrix. For the groupoid of upper-triangular matrices\, w
e represent braid-group transformations via sequences of cluster mutations
in the special $\\mathbb A_n$-quiver. Time permitting\, I will also descr
ibe a generalization of this construction to affine Lie-Poisson algebras a
nd to quantum loop algebras (Arxiv:2012:10982).\n
LOCATION:https://researchseminars.org/talk/CGP-MP/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kazumi Okuyama (Shinshu University)
DTSTART;VALUE=DATE-TIME:20210326T010000Z
DTEND;VALUE=DATE-TIME:20210326T020000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/3
DESCRIPTION:Title: Q
uenched free energy from spacetime D-branes\nby Kazumi Okuyama (Shinsh
u University) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstrac
t\nWe propose a useful integral representation of the quenched free energy
which is applicable to any random systems. Our formula involves the gener
ating function of multi-boundary correlators\, which can be interpreted on
the bulk gravity side as spacetime D-branes introduced by Marolf and Maxf
ield 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 correlators. I
t turns out that the resulting quenched free energy is a monotonically dec
reasing function of the temperature\, as expected.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Di Yang (University of Science and Technology of China)
DTSTART;VALUE=DATE-TIME:20210402T080000Z
DTEND;VALUE=DATE-TIME:20210402T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/4
DESCRIPTION:Title: L
oop equations and integrable hierarchies for special cubic Hodge integrals
\nby Di Yang (University of Science and Technology of China) as part o
f IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\nBy using the Virasor
o constraints we derive the loop equations for the cubic Hodge partition f
unction with three parameters p\,q\,r satisfying the Calabi-Yau condition
pq + qr + rp = 0. We then show that the Hodge integrable hierarchy associa
ted to the special cubic Hodge integrals is normal Miura equivalent to the
fractional Volterra hierarchy. In the procedure of the proof\, a particul
ar tau-function for the fractional Volterra hierarchy is constructed\, whi
ch we call the topological tau-function. Finally\, when one of the three p
arameters 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 joint wor
ks with Si-Qi Liu\, Youjin Zhang and Chunhui Zhou.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rinat Kashaev (Université de Genève)
DTSTART;VALUE=DATE-TIME:20210409T080000Z
DTEND;VALUE=DATE-TIME:20210409T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/5
DESCRIPTION:Title: T
he Alexander polynomial as a universal invariant\nby Rinat Kashaev (Un
iversité de Genève) as part of IBS-CGP Mathematical Physics Seminar\n\n\
nAbstract\nI will explain how the reciprocal of the Alexander polynomial o
f a knot can be viewed as a universal (quantum) invariant associated to th
e Hopf algebra of regular functions on the group of affine linear transfor
mations of the complex plane. This provides a conceptual interpretation fo
r the Melvin--Morton--Rozansky conjecture proven by Bar-Nathan and Garoufa
lidis\, and Garoufalidis and Le about the relation of the colored Jones po
lynomials to the reciprocal of the Alexander polynomial in a large color l
imit.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Neitzke (Yale University)
DTSTART;VALUE=DATE-TIME:20210416T010000Z
DTEND;VALUE=DATE-TIME:20210416T020000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/6
DESCRIPTION:Title: A
belianization\, exact WKB and link invariants\nby Andrew Neitzke (Yale
University) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstract
\nIt has been understood in the last decade that various\ndifferent proble
ms\, 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 polyno
mial\,\n\n3) the computation of classical Chern-Simons invariants of flat
connections\,\n\ncan all be understood as aspects of a general strategy fo
r reduction from a\nnonabelian Lie group to its maximal abelian subgroup.
I will describe this\npoint of view\, emphasizing the common features of t
he three problems. Parts of\nthe talk are a report of joint works with Dan
Freed\, Davide Gaiotto\, Greg\nMoore\, Lotte Hollands\, and Fei Yan.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Norbury (University of Melbourne)
DTSTART;VALUE=DATE-TIME:20210423T010000Z
DTEND;VALUE=DATE-TIME:20210423T020000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/7
DESCRIPTION:Title: E
numerative geometry via the moduli space of super Riemann surfaces\nby
Paul Norbury (University of Melbourne) as part of IBS-CGP Mathematical Ph
ysics Seminar\n\n\nAbstract\nMumford initiated the calculation of many alg
ebraic topological invariants over the moduli space of Riemann surfaces in
the 1980s\, and Witten related these invariants to two dimensional gravit
y in the 1990s. This viewpoint led Wittento a conjecture\, proven by Konts
evich\, 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 study of
Weil-Petersson volumes of the moduli space using hyperbolic geometry. In t
his lecture I will describe a new collection of integrals over the moduli
space of Riemann surfaces whose generating functionis a tau function of th
e KdV hierarchy\, known as the Brezin-Gross-Witten tau function. I will sk
etch a proof of this result that uses an analogue of Mirzakhani's argument
applied to the moduli space of super Riemann surfaces - defined by replac
ing the fieldof complex numbers with a Grassman algebra - which uses recen
t work of Stanford and Witten. This appearance of the moduli space of supe
r Riemann surfaces to solve a problem over the classical moduli space is d
eep and surprising.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Todor Milanov (IPMU\, University of Tokyo)
DTSTART;VALUE=DATE-TIME:20210430T010000Z
DTEND;VALUE=DATE-TIME:20210430T020000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/8
DESCRIPTION:Title: T
opological recursion for simple singularities\nby Todor Milanov (IPMU\
, University of Tokyo) as part of IBS-CGP Mathematical Physics Seminar\n\n
\nAbstract\nIt is known that Givental's total ancestor potential of any se
mi-simple Frobenius manifold can be reconstructed via the so-called local
Eynard--Orantin recursion. For the application to integrable systems and t
he representation theory of W-algebras however\, it is important to determ
ine whether the local recursion can be extended to a global one. In my tal
k\, I would like to explain the problem of comparing local and global Eyna
rd--Orantin recursions and to explain the case of a Frobenius manifold cor
responding to a simple singularity.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Harnad (Université de Montréal)
DTSTART;VALUE=DATE-TIME:20210507T010000Z
DTEND;VALUE=DATE-TIME:20210507T020000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/9
DESCRIPTION:Title: B
ilinear expansions of lattices of KP $\\tau$-function in BKP $\\tau$-funct
ions: a fermionic approach\nby John Harnad (Université de Montréal)
as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\nThe notion
of Kadomtsev-Petviashvili (KP) and BKP $\\tau$ functions will\nbe recalled
\, together with their representations as fermionic expectation values.\nS
chur-type lattices of such KP and BKP $\\tau$-functions will be defined\,
corresponding to\na given infinite general linear or orthogonal group elem
ent\, labelled by partitions\nand strict partitions respectively. A biline
ar expansion expressing elements of these lattices of KP $\\tau$-functions
as sums over products of pairs of elements of associated lattices of BKP
$\\tau$-functions will be presented\, generalizing earlier results relati
ng determinants and Pfaffians of minors of skew symmetric matrices\, with
applications to Schur functions and Schur $Q$-functions. Further applicat
ions include inhomogeneous polynomial $\\tau$-functions of KP and BKP type
\, with their determinantal and Pfaffian representations.\n\nRefs:\n 1) F.
Balogh\, J. Harnad and J. Hurtubise\, “Isotropic Grassmannians\, Plück
er and Cartan maps”\, J. Math. Phys. 62\, 021701 (2021)\n2) J. Harnad an
d A. Yu. Orlov\, “Bilinear expansions of lattices of KP tau-functions in
BKP tau-functions: a fermionic approach”\, J. Math. Phys. 62\, 013508 (
2021)\n3) J. Harnad and A. Yu. Orlov\, “Bilinear expansions of Schur fun
ctions 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:2011.1
3339\, (Ann. H. Poincaré\, in press 2021).\n
LOCATION:https://researchseminars.org/talk/CGP-MP/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech)
DTSTART;VALUE=DATE-TIME:20210521T010000Z
DTEND;VALUE=DATE-TIME:20210521T020000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/10
DESCRIPTION:Title:
New exact results for open enumerative invariants\nby Sergei Gukov (Ca
ltech) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\nProb
lems that involve bordered pseudoholomorphic curves with boundary on a Lag
rangian submanifold in a Calabi-Yau 3-fold are usually called "open enumer
ative invariants." The analysis involved in such problems is extremely ric
h and interesting\, which makes the study of open enumerative invariants c
hallenging and complicated. Yet\, over the past 30 years a lot of progress
has been made\, in part due to various "dualities" --- such as mirror sym
metry --- that relate open enumerative problems to questions in other area
s of mathematics. After a short survey of past developments\, I will prese
nt a new class of Calabi-Yau 3-folds with Lagrangian submanifolds where th
e problem can be solved completely thanks to a new connection with quantum
groups at generic values of the parameter q.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wolfgang Lerche (CERN)
DTSTART;VALUE=DATE-TIME:20210528T080000Z
DTEND;VALUE=DATE-TIME:20210528T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/11
DESCRIPTION:Title:
Fluxes\, Holomorphic Anomalies and Elliptic Genera in d=4\nby Wolfgang
Lerche (CERN) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstra
ct\nMotivated by tests of Weak Gravity Conjectures\, we investigate proper
ties of elliptic genera of string theories that arise in large distance li
mits of the moduli space of F-theory compactifications. This allows for a
non-perturbative definition of elliptic genera that goes beyond the ordina
ry world-sheet description. While this construction has been known for six
-dimensional theories\, we find the four-dimensional variant to be surpris
ingly complex. The essential new ingredient is background fluxes\, and the
se lead to different sectors of the elliptic genus with different modular
properties. Crucial is the appearance of derivatives which leads to novel
modular (and hence\, holomorphic) anomalies that are much worse than expec
ted. We also give a physical interpretation of these phenomena.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Walcher (Heidelberg University)
DTSTART;VALUE=DATE-TIME:20210514T080000Z
DTEND;VALUE=DATE-TIME:20210514T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/12
DESCRIPTION:Title:
On the rationality of MUMs and 2-functions\nby Johannes Walcher (Heide
lberg University) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbs
tract\nPoints of maximal unipotent monodromy in Calabi-Yau moduli space pl
ay a central role in mirror symmetry\, and also harbor some interesting ar
ithmetic. In the classic examples\, suitable expansion coefficients of the
(all-genus) prepotential (in polylogarithms) under the mirror map are int
egers with an enumerative interpretation on the mirror manifold. This corr
espondence should be expected to extend to periods relative to algebraic c
ycles capturing the enumerative geometry relative to Lagrangian submanifol
ds. This expectation is challenged\, however\, when the mixed degeneration
is not defined over Q. After musing about compatibility with mirror symme
try\, I will discuss two recent results that sharpen these questions furth
er: The first is a theorem proven by Felipe Müller which states that the
coefficients of rational 2-functions are necessarily contained in an abeli
an number field. (As defined in the talk\, 2-functions are formal power se
ries whose coefficients satisfy a natural Hodge theoretic supercongruence.
) The second are examples worked out in collaboration with Bönisch\, Klem
m\, and van Straten\, of MUMs that are themselves not defined over Q.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Alexandrov (IBS CGP)
DTSTART;VALUE=DATE-TIME:20210618T010000Z
DTEND;VALUE=DATE-TIME:20210618T020000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/13
DESCRIPTION:Title:
KP integrability of triple Hodge integrals\nby Alexander Alexandrov (I
BS CGP) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\nIn
my talk\, I will describe a relation between the Givental group of rank on
e and the Heisenberg-Virasoro symmetry group of the KP integrable hierarch
y. It appears that only a two-parameter family of the Givental operators c
an be identified with elements of the Heisenberg-Virasoro symmetry group.
This family describes triple Hodge integrals satisfying the Calabi-Yau con
dition. Using the identification of the elements of two groups it is possi
ble to prove that the generating function of triple Hodge integrals satisf
ying the Calabi-Yau condition and its $\\Theta$-version are tau-functions
of the KP hierarchy. This generalizes the result of Kazarian on KP integra
bility in the case of linear Hodge integrals. I will also describe the rel
ation of this family of tau-functions with the deformation of the Kontsevi
ch matrix model. My talk is based on two papers\, arXiv:2009.01615 and arX
iv:2009.10961.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Bouchard (University of Alberta)
DTSTART;VALUE=DATE-TIME:20210924T010000Z
DTEND;VALUE=DATE-TIME:20210924T020000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/14
DESCRIPTION:Title:
Whittaker vectors for W-algebras from topological recursion\nby Vincen
t Bouchard (University of Alberta) as part of IBS-CGP Mathematical Physics
Seminar\n\n\nAbstract\nGaiotto vectors\, describing the fundamental class
in the equivariant cohomology of a suitable compactification of the modul
i space of G-bundles over P^2\, for G a complex simple Lie group\, are Whi
ttaker vectors for modules of W-algebras. In this work we identify these W
hittaker vectors with partition functions of quantum Airy structures\, whi
ch means that they can be calculated by topological recursion methods. On
the physics side\, it means that the Nekrasov partition function for pure
N=2 4d supersymmetric gauge theories can be accessed via a topological rec
ursion à la Chekhov-Eynard-Orantin. We formulate the connection for Gaiot
to vectors of type A\, B\, C\, and D. For those interested in topological
recursion\, the type A case at arbitrary level gives rise to a new non-com
mutative formulation of topological recursion.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Bertola (Concordia University)
DTSTART;VALUE=DATE-TIME:20211001T010000Z
DTEND;VALUE=DATE-TIME:20211001T020000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/15
DESCRIPTION:Title:
Graph connections\, (wild) character varieties and generating function in
symplectic geometry\nby Marco Bertola (Concordia University) as part o
f IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\nWe will discuss a na
tural (pre)-symplectic structure associated to an arbitrary flat graph con
nection on a Riemann surface and its invariance properties. This allows to
efciently parametrize (wild) character varieties using Fock-Goncharov coo
rdinates and provide explicit log-canonical coordinates for several types
of Poisson structures\; Goldman on the standard character variety\, Flasch
ka-Newell-Boalch on Stokes' manifolds and Ugaglia-Bondal Poisson structure
s. \nIn the case of (wild) character varieties\, this construction allows
to define the generating functions of symplectic polarizations and identif
y them with the classical notion of isomonodromic tau functions of the Jap
anese school.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kazarian (HSE & Skoltech)
DTSTART;VALUE=DATE-TIME:20211008T080000Z
DTEND;VALUE=DATE-TIME:20211008T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/16
DESCRIPTION:Title:
Topological recursion for generalized Hurwitz numbers\nby Maxim Kazari
an (HSE & Skoltech) as part of IBS-CGP Mathematical Physics Seminar\n\n\nA
bstract\nThe topological recursion or Chekhov-Eunard-Orantin recursion is
an inductive procedure for an explicit computation of correlator functions
appearing in a large number of problems in mathematical physics\, from ma
trix integrals and Gromov-Witten invariants to enumerations of maps and me
romorphic functions with prescribed singularities. In spite of existence o
f a huge number of known cases where this procedure does work\, its validi
ty and universality still remains mysterious in much extend.\n \nWe develo
p a new tool based on the theory of KP hierarchy that allows one not only
formally prove it in a unified way for a wide class of problems but also t
o understand its true nature and the origin. These problems include enumer
ation various kinds of Hurwitz numbers: ordinary ones\, orbifold\, double\
, monotone\, r-spin Hurwitz numbers\, as well as enumeration of (hyper) ma
ps and extends much beyond. The talk is based on a joint work with B.Bychk
ov\, P.Dunin-Barkowski\, S.Shadrin.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Harnad (CRM & Concordia University)
DTSTART;VALUE=DATE-TIME:20211022T010000Z
DTEND;VALUE=DATE-TIME:20211022T020000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/17
DESCRIPTION:Title:
Bilinear expansions of lattices of KP $\\tau$-functions in BKP $\\tau$-fun
ctions\, determinant and Pfaffian expressions of polynomial $\\tau$-functi
ons\nby John Harnad (CRM & Concordia University) as part of IBS-CGP Ma
thematical Physics Seminar\n\n\nAbstract\nThe notion of Kadomtsev-Petviash
vili (KP) and BKP $\\tau$ functions will\nbe recalled\, together with thei
r representations as fermionic expectation values.\nSchur-type lattices of
KP and BKP $\\tau$-functions will be defined\, corresponding to\na given
infinite general linear or orthogonal group element\, labelled by partitio
ns\nand strict partitions respectively. A bilinear expansion expressing el
ements of these lattices of KP $\\tau$-functions\nas sums over products of
pairs of elements of associated lattices of BKP $\\tau$-functions will b
e presented\,\ngeneralizing earlier results relating determinants and Pfaf
fians of minors of skew symmetric matrices\,\nwith applications to Schur
functions and Schur $Q$-functions. Further applications include\ndetermina
ntal and Pfaffian representations of all inhomogeneous polynomial $\\tau$-
functions of KP and BKP type.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danilo Lewański (IHES and IPhT)
DTSTART;VALUE=DATE-TIME:20211119T080000Z
DTEND;VALUE=DATE-TIME:20211119T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/18
DESCRIPTION:Title:
Cohomological field theories and BKP integrability: Omega classes times Wi
tten-classes\nby Danilo Lewański (IHES and IPhT) as part of IBS-CGP M
athematical Physics Seminar\n\n\nAbstract\nThere is a deep interaction bet
ween Cohomological field theories (CohFTs)\, introduced by Kontsevich and
Manin\, and integrable hierarchies. For instance\, the celebrated Witten-K
ontsevich result shows that the trivial CohFT gives rise to a solution of
the KdV integrable hierarchy. As another example\, Kazarian’s theorem sh
ows that the Hodge CohFT gives rise to a solution of the KP hierarchy\, an
d so do Hurwitz numbers\, which by ELSV formula are descendant integrals o
f the Hodge CohFT. The change of variable which carries the partition func
tion of Hurwitz numbers into the partition function of pure descendant Hod
ge integrals is triangular and KP-preserving\, it is in fact essentially g
iven by the Topological Recursion spectral curve in the sense of Eynard an
d Orantin. \n\nWe study spin-Hurwitz numbers (not to be confused with comp
leted cycles Hurwitz numbers) enumerating branches Riemann covers weighted
by the parity of theta characteristics. They obey the BKP integrable hier
archy. We prove that the Topological Recursion conjecture for these number
s is equivalent to their underlying CohFT to be an explicit product betwee
n Witten’s class and Omega-classes computed by Chiodo. The Topological R
ecursion conjecture has recently been proved by Alexandrov and Shadrin in
a more general framework for BKP integrability.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bertrand Eynard (IHES and IPhT)
DTSTART;VALUE=DATE-TIME:20211126T080000Z
DTEND;VALUE=DATE-TIME:20211126T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/19
DESCRIPTION:Title:
CFT from Topological Recursion\nby Bertrand Eynard (IHES and IPhT) as
part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\nConformal Fiel
d Theories\, can be "defined" by the bootstrap axioms. The main axioms are
that we have a set of functions (amplitudes) that should satisfy OPE (sho
rt distance asymptotic behaviour)\, Ward identities (reflecting conformal
invariance) and crossing-symmetry (all possible ways of computing an ampli
tude should give the same answer).\nTopological Recursion is a recursive r
ecipe that associates to a spectral curve S (an algebraic plane curve with
some additional features)\, a sequence of n-forms\, denoted $\\omega_{g\,
n}(S)$\, $g=0\,\\dots\,\\infty$\, $n=0\,\\dots\,\\infty$. These n-forms na
turally allow to define amplitudes (as formal series) that do satisfy OPE
and Ward Identities axioms. Moreover\, there is a way to adapt them to als
o satisfy crossing symmetry. This last statement is presently a conjecture
\, not yet proved in all cases\, but belived to be true.\nWe shall also di
scuss the link to integrable systems and algebraic geometry.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamara Grava (University of Bristol & SISSA)
DTSTART;VALUE=DATE-TIME:20211112T080000Z
DTEND;VALUE=DATE-TIME:20211112T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/20
DESCRIPTION:Title:
Correlation functions for unitary invariant ensembles and Hurwitz numbers<
/a>\nby Tamara Grava (University of Bristol & SISSA) as part of IBS-CGP Ma
thematical Physics Seminar\n\n\nAbstract\nWe provide effective formulae fo
r generating functions of multipoint correlators for unitary invariants en
sembles. As an application we show that the multipoint correlators of the
Laguerre and the Jacobi ensembles are obtained in terms of Hahn polynomial
s and Wilson polynomials generalising earlier formula for one-point corre
lators. Finally we provide an enumerative interpretation of the topologica
l expansion of these multipoint correlators. This is a joint work with M.
Gisonni and G. Ruzza.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Nekrasov (Simons Center for Geometry and Physics)
DTSTART;VALUE=DATE-TIME:20211029T080000Z
DTEND;VALUE=DATE-TIME:20211029T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/21
DESCRIPTION:Title:
Quantum T-Q and KZ equations in gauge theory\nby Nikita Nekrasov (Simo
ns Center for Geometry and Physics) as part of IBS-CGP Mathematical Physic
s Seminar\n\n\nAbstract\nBaxter's T-Q equation is a main instrument in the
functional and algebraic Bethe ansatz approach to quantum spin chains. Kn
izhnik-Zamolodchikov equation is obeyed by the conformal blocks of the two
dimensional current algebra. Remarkably\, the analytic continuation of th
e latter\, and a deformation of the former can be found in the realm of th
e four dimensional supersymmetric gauge theories with matter. \n\nBased on
the recent work with Saebyeok Jeong and Norton Lee.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaëtan Borot (Institute for Mathematics & Institute for Physics\,
Humboldt University of Berlin)
DTSTART;VALUE=DATE-TIME:20220304T080000Z
DTEND;VALUE=DATE-TIME:20220304T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/22
DESCRIPTION:Title:
(CANCELED!) The B-model for singular spectral curves and its enumerative i
nterpretation\nby Gaëtan Borot (Institute for Mathematics & Institute
for Physics\, Humboldt University of Berlin) as part of IBS-CGP Mathemati
cal Physics Seminar\n\n\nAbstract\nThe talk is canceled because of technic
al problems.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Marshakov (Center for Advanced Studies\, Skoltech)
DTSTART;VALUE=DATE-TIME:20220311T080000Z
DTEND;VALUE=DATE-TIME:20220311T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/23
DESCRIPTION:Title:
Cluster integrable systems and supersymmetric gauge theories\nby Andre
i Marshakov (Center for Advanced Studies\, Skoltech) as part of IBS-CGP Ma
thematical Physics Seminar\n\n\nAbstract\nI am going to discuss the relati
on between the cluster integrable systems (or the Goncharov-Kenyon systems
and their reductions) with the supersymmetric gauge theories. I hope to o
verview the basic definitions\, the facts around the statement that their
deautonomizations are solved by dual partition functions of supersymmetric
gauge theories\, and some recent developements in this picture.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guillaume Chapuy (IRIF\, Université de Paris)
DTSTART;VALUE=DATE-TIME:20220318T080000Z
DTEND;VALUE=DATE-TIME:20220318T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
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 Paris) as p
art of IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\nMy talk will be
an introduction to (part of) my recent paper arXiv:2109.01499 written joi
ntly with Valentin Bonzom and Maciej Dołęga. We study a b-deformation of
monotone Hurwitz numbers\, obtained by deforming Schur functions into Jac
k symmetric functions. It is a special case of the b-deformed weighted Hur
witz numbers recently introduced by Dołęga and myself and is related bra
nched coverings of the sphere by non-oriented surfaces.\n\nWe give an evol
ution (cut-and-join) equation for the model and we derive\, by a method of
independent interest\, explicit Virasoro constraints from it\, for arbitr
ary values of the deformation parameter b. For b=1 the model is related to
the (large) BKP hierarchy and an O(N) version of the BGW integral. The ta
lk will not assume previous knowledge\, I will try in particular to explai
n where the interest of combinatorialists for these deformations come from
\, and in particular the Goulden-Jackson b-conjecture.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Basalaev (HSE & Skoltech)
DTSTART;VALUE=DATE-TIME:20220325T080000Z
DTEND;VALUE=DATE-TIME:20220325T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/25
DESCRIPTION:Title:
Mirror symmetry for a cusp polynomial Landau-Ginzburg orbifold\nby Ale
xey Basalaev (HSE & Skoltech) as part of IBS-CGP Mathematical Physics Semi
nar\n\n\nAbstract\nWe will establish mirror symmetry between the cusp poly
nomials considered with a nontrivial symmetry group and Geigle-Lenzing orb
ifold projective lines. In particular\, we will introduce Dubrovin-Frobeni
us manifold of equivariant Saito theory of any cusp polynomial and show th
at it is isomorphic to Dubrovin-Frobenius manifold of the respective Geigl
e-Lenzing orbifold. We will also show that in the case of simple-elliptic
singularities this mirror isomorphism is equivalent the certain relations
in the ring of modular forms. This is a joint work with A.Takahashi (Osaka
).\n
LOCATION:https://researchseminars.org/talk/CGP-MP/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Penka Georgieva (Institut de Mathématiques de Jussieu)
DTSTART;VALUE=DATE-TIME:20220408T080000Z
DTEND;VALUE=DATE-TIME:20220408T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/26
DESCRIPTION:Title:
Klein TQFT and real Gromov-Witten invariants\nby Penka Georgieva (Inst
itut de Mathématiques de Jussieu) as part of IBS-CGP Mathematical Physics
Seminar\n\n\nAbstract\nIn this talk I will explain how the Real Gromov-Wi
tten theory of local 3-folds gives rise to an extension of a 2d Klein TQFT
. The latter theory is furthermore semi-simple which allows for complete c
omputation from the knowledge of a few basic elements which can be calcula
ted explicitly. As a consequence of the explicit expressions we find in th
e Calabi-Yau case we obtain the expected GV formula and relation to SO/Sp
Chern-Simons theory.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Rossi (University of Padua)
DTSTART;VALUE=DATE-TIME:20220401T080000Z
DTEND;VALUE=DATE-TIME:20220401T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/27
DESCRIPTION:Title:
Moduli spaces of residueless meromorphic differentials and the KP hierarch
y\nby Paolo Rossi (University of Padua) as part of IBS-CGP Mathematica
l Physics Seminar\n\n\nAbstract\nI'll present a recent joint work with A.
Buryak and D. Zvonkine\, where we study the moduli spaces of residueless m
eromorphic differentials\, i.e.\, the closures\, in the moduli space of st
able curves\, of the loci of smooth curves whose marked points are the zer
os and poles of prescribed orders of a meromorphic differential with vanis
hing residues. Our main result is that intersection theory on these spaces
is controlled by an integrable system containing the celebrated Kadomtsev
-Petviashvili (KP) hierarchy as a reduction to the case of differentials w
ith exactly two zeros and any number of poles. This fact has several deep
consequences and in particular it relates the aforementioned moduli spaces
with Hurwitz theory\, representation theory of sl2(C)\, integrability and
a conjecture of Schmitt and Zvonkine on the r=0 limit of Witten's r-spin
classes.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaëtan Borot (Institute for Mathematics & Institute for Physics\,
Humboldt University of Berlin)
DTSTART;VALUE=DATE-TIME:20220415T080000Z
DTEND;VALUE=DATE-TIME:20220415T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/28
DESCRIPTION:Title:
The B-model for singular spectral curves and its enumerative interpretatio
n\nby Gaëtan Borot (Institute for Mathematics & Institute for Physics
\, Humboldt University of Berlin) as part of IBS-CGP Mathematical Physics
Seminar\n\n\nAbstract\nI will discuss the definition of B-model/topologica
l recursion for spectral curves and explain the obstructions to the well-p
osedness of this definition for arbitrary spectral curves. The question ca
n be approached by the representation theory of W-algebras\, and I will de
scribe the largest known class of admissible spectral curves (including si
ngular cases) that has been obtained in this way. Each case is expected to
have an enumerative interpretation in a sense that I will specify. In par
ticular l will describe possible applications in open r-spin intersection
theory.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaobo Liu (Beijing International Center for Mathematical Research
)
DTSTART;VALUE=DATE-TIME:20220422T010000Z
DTEND;VALUE=DATE-TIME:20220422T020000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/29
DESCRIPTION:Title:
Hall-Littlewood functions and Virasoro constraints\nby Xiaobo Liu (Bei
jing International Center for Mathematical Research) as part of IBS-CGP Ma
thematical Physics Seminar\n\n\nAbstract\nHall-Littlewood functions are ge
neralizations of Schur Q-functions which have been used to study Kontsevic
h-Witten and Brezin-Gross-Witten tau functions. Recently Mironov and Moroz
ov proposed to use Hall-Littlewood functions specialized at roots of unity
to study generalized Kontsevich matrix models. Virasoro constraints are p
owerful tools in the study of matrix models and Gromov-Witten invariants.
In this talk\, I will describe how Virasoro operators act on Hall-Littlewo
od functions and applications of such formulas. This is based on joint wor
ks with Chenglang Yang.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norton Lee (IBS Center for Geometry and Physics)
DTSTART;VALUE=DATE-TIME:20220916T080000Z
DTEND;VALUE=DATE-TIME:20220916T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/30
DESCRIPTION:Title:
Defect in gauge theory and quantum spin chains\nby Norton Lee (IBS Cen
ter for Geometry and Physics) as part of IBS-CGP Mathematical Physics Semi
nar\n\n\nAbstract\nThe N=2 supersymmetric gauge theories in four dimension
s have intrinsic connection to algebraic integrable systems. The gauge the
ory of interests\, the asymptotically superconformal N=2 SQCD in four dime
nsions\, reveals a structure which has dual descriptions. On the one 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 special
type of Hitchin system)\, based on the Lie algebra sl_N. In this talk I wi
ll focus on the spin chain side. I will show that by introducing BPS surfa
ce defects\, we find observables in the gauge theory that satisfy differen
ce equations called fractional quantum T-Q equation. The observables repre
sents 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 for the
Jost function of the XXX Heisenberg spin chain from gauge theory.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reinier Kramer (University of Alberta)
DTSTART;VALUE=DATE-TIME:20220923T080000Z
DTEND;VALUE=DATE-TIME:20220923T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/31
DESCRIPTION:Title:
The spin Gromov-Witten/Hurwitz correspondence\nby Reinier Kramer (Univ
ersity of Alberta) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAb
stract\nIn 2006\, Okounkov and Pandharipande established a correspondence
between two theories of counting maps between curves. Gromov-Witten theory
constructs a moduli space of stable maps and considers intersection numbe
rs of natural classes on this space. Hurwitz theory counts the number of m
aps with given ramification data over all points in the target. The Gromov
-Witten theory of a surface with positive geometric genus can be localised
to a curve in that surface\, and this obtains a spin structure\, leading
to spin Gromov-Witten theory of curves. The Hurwitz side also has a natura
l spin analogue\, and Lee conjectured these theories correspond in a simil
ar manner. In this talk\, I will introduce the notions of spin Gromov-Witt
en theory and spin Hurwitz theory and give an outline of the spin Gromov-W
itten/Hurwitz correspondence for the projective line. I will also explain
relations to the (small) 2BKP integrable hierarchy\, which is the analogue
of the 2D Toda lattice hierarchy in the non-spin case. This talk is based
on joint work with Alessandro Giacchetto\, Danilo Lewański\, and Adrien
Sauvaget.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitri Zvonkine (Université de Versailles Saint-Quentin-en-Yveli
nes)
DTSTART;VALUE=DATE-TIME:20220930T080000Z
DTEND;VALUE=DATE-TIME:20220930T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/32
DESCRIPTION:Title:
Fractional quantum Hall effect via the Grothendieck-Riemann-Roch formula\nby Dimitri Zvonkine (Université de Versailles Saint-Quentin-en-Yvelin
es) as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\nWe stud
y the fractional quantum Hall effect on a Riemann surface of genus g trave
rsed by a magnetic field of total flux d. The wave functions of charged pa
rticles have a semi-phenomenological description by Laughlin states. These
states can be studied by methods of algebraic geometry: they form a holom
orphic vector bundle over the d-th Picard group of the Riemann surface. Th
e Chern characters of this vector bundle can be computed by the Grothendie
ck-Riemann-Roch formula. In a fully filled state the Chern character we ob
tain is compatible with the existence of a projectively flat connection on
the vector bundle. In a state with quasiholes our computation implies tha
t no such connection can exist. This is joint work with Semyon Klevtsov.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jian Zhou (Tsinghua University)
DTSTART;VALUE=DATE-TIME:20221014T010000Z
DTEND;VALUE=DATE-TIME:20221014T020000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/33
DESCRIPTION:Title:
Integrable Systems and mirror symmetry in probability theory and combinato
rics\nby Jian Zhou (Tsinghua University) as part of IBS-CGP Mathematic
al Physics Seminar\n\n\nAbstract\nWe will first explain how any moment seq
uence leads to a sequence of tau-functions of the KP hierarchy\, which can
be interpreted in terms of weighted counts of nonintersecting lattice pat
hs. We will also explain how various lattice counting problems and some ot
her problems in combinatorics lead to probability measures on the real l
ine\, and surprising mirror symmetry among them.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Popolitov (ITEP)
DTSTART;VALUE=DATE-TIME:20221028T080000Z
DTEND;VALUE=DATE-TIME:20221028T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/34
DESCRIPTION:by Alexander Popolitov (ITEP) as part of IBS-CGP Mathematical
Physics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CGP-MP/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Lisovyy (Université de Tours)
DTSTART;VALUE=DATE-TIME:20221021T080000Z
DTEND;VALUE=DATE-TIME:20221021T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050713Z
UID:CGP-MP/35
DESCRIPTION:by Oleg Lisovyy (Université de Tours) as part of IBS-CGP Math
ematical Physics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CGP-MP/35/
END:VEVENT
END:VCALENDAR