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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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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:20211209T074622Z
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/
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