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BEGIN:VEVENT
SUMMARY:Pietro Longhi (ETH Zurich)
DTSTART;VALUE=DATE-TIME:20201007T140000Z
DTEND;VALUE=DATE-TIME:20201007T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/1
DESCRIPTION:Title: BPS States and Geometry\nby Pietro Longhi (ETH Zurich) as part of
SISSA's Integrable Systems and Mathematical Physics seminar\n\n\nAbstract\
nThe study of BPS states in string theory and supersymmetric gauge theorie
s prompted the development of new mathematical tools to analyze geometric
properties of manifolds of various dimensions. In this talk I will introdu
ce the framework of exponential networks\, a novel approach to computing v
arious types of enumerative invariants of toric Calabi-Yau threefolds from
the geometry of Riemann surfaces. The structure behind this framework hin
ges on wall-crossing phenomena involving different kinds of BPS spectra\,
described by a synthesis of the wall-crossing formulae of Cecotti-Vafa and
Kontsevich-Soibelman inspired by work of Gaiotto-Moore-Neitzke. While pro
viding an effective way to study Donaldson-Thomas invariants\, an interest
ing byproduct of exponential networks is the prediction of unexpected rela
tions between the latter and new `3d-5d’ invariants\, as well as (for sp
ecific geometries) knot invariants.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giordano Cotti (Lisbon)
DTSTART;VALUE=DATE-TIME:20201013T140000Z
DTEND;VALUE=DATE-TIME:20201013T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/2
DESCRIPTION:Title: Quantum differential equations\, isomonodromic deformations\, and deri
ved categories\nby Giordano Cotti (Lisbon) as part of SISSA's Integrab
le Systems and Mathematical Physics seminar\n\n\nAbstract\nThe quantum dif
ferential equation (qDE) is a rich object attached to a smooth projective
variety X. It is an ordinary differential equation in the complex domain w
hich encodes information of the enumerative geometry of X\, more precisely
its Gromov-Witten theory. Furthermore\, the asymptotic and monodromy of i
ts solutions conjecturally rules also the topology and complex geometry of
X. These differential equations were introduced in the middle of the crea
tive impetus for mathematically rigorous foundations of Topological Field
Theories\, Supersymmetric Quantum Field Theories and related Mirror Symmet
ry phenomena. Special mention has to be given to the relation between qDE'
s and Dubrovin-Frobenius manifolds\, the latter being identifiable with th
e space of isomonodromic deformation parameters of the former. The study o
f qDE's represents a challenging active area in both contemporary geometr
y and mathematical physics: it is continuously inspiring the introduction
of new mathematical tools\, ranging from algebraic geometry\, the realm of
integrable systems\, the analysis of ODE's\, to the theory of integral tr
ansforms and special functions. This talk will be a gentle introduction to
the analytical study of qDE's\, their relationship with derived categorie
s of coherent sheaves (in both non-equivariant and equivariant settings)\,
and a theory of integral representations for its solutions. The talk will
be a survey of the results of the speaker in this research area.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Rossi (Università degli Studi di Padova)
DTSTART;VALUE=DATE-TIME:20201021T140000Z
DTEND;VALUE=DATE-TIME:20201021T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/3
DESCRIPTION:Title: (2+1)-dimensional integrable systems and moduli spaces of curves\n
by Paolo Rossi (Università degli Studi di Padova) as part of SISSA's Inte
grable Systems and Mathematical Physics seminar\n\n\nAbstract\nIntegrable
systems of (1+1)-dimensional PDEs lurk in the intersection theory of modul
i spaces of stable algebraic curves\, describing the intricate relations a
mong intersection numbers. There are at least two methods to uncover them:
the Dubrovin-Zhang method and the double ramification hierarchy construct
ion\, the latter due to Buryak and myself. The power of our approach consi
sts in requiring weaker assumptions and in leading to a quantum integrable
system\, whose classical limit conjecturally recovers the Dubrovin-Zhang
result (we have proven this conjecture in a wide class of examples). In th
is talk\, after a brief general introduction\, I will use a third advantag
e of the DR construction (that\, at the classical level\, it works for inf
inite rank CohFTs as well) to apply it to the intersection theory of the m
oduli space meromorphic functions and of meromorphic differentials\, produ
cing two (2+1)-dimensional integrable systems: a version of the KdV equati
on on the Moyal torus and the celebrated KP equation.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yankı Lekili (KCL)
DTSTART;VALUE=DATE-TIME:20201028T150000Z
DTEND;VALUE=DATE-TIME:20201028T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/4
DESCRIPTION:Title: A biased view of mirror symmetry\nby Yankı Lekili (KCL) as part o
f SISSA's Integrable Systems and Mathematical Physics seminar\n\n\nAbstrac
t\nMirror symmetry is one of the most striking developments in modern math
ematics whose scope extends to very different\nﬁelds of pure mathematics
. It predicts a broad correspondence between two sub-ﬁelds of geometry
- symplectic geometry\nand algebraic geometry. Homological mirror symmetry
uses the language of triangulated categories to give a mathematically\npr
ecise meaning to this correspondence. Since its announcement\, by Kontsevi
ch in ICM (1994)\, it has attracted huge attention and\nover the years sev
eral important cases of it have been established. Despite signiﬁcant pr
ogress\, many central problems in\nthe ﬁeld remain open. After reviewin
g the general theory\, I will survey some of my own results on mirror symm
etry.\n\nThe seminar will be hold on line but not via ZOOM\nPlease connec
t to the following address\n\nhttps://bbb.freemath.xyz/b/yan-udr-zvu\n\nwi
th access code 155936\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Miller (University of Michigan)
DTSTART;VALUE=DATE-TIME:20201216T150000Z
DTEND;VALUE=DATE-TIME:20201216T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/5
DESCRIPTION:Title: Universal Wave Breaking in the Semiclassical Sine-Gordon Equation\
nby Peter Miller (University of Michigan) as part of SISSA's Integrable Sy
stems and Mathematical Physics seminar\n\n\nAbstract\nThe sine-Gordon equa
tion has slowly-modulated librational wave solutions that are approximated
at leading-order by a Whitham averaging formalism. The Whitham modulation
equations are an elliptic quasilinear system whose solutions develop sing
ularities in finite time. We show that when the solution of the Whitham sy
stem develops a generic type of gradient catastrophe singularity\, the sol
ution of the sine-Gordon equation locally takes on a universal form\, inde
pendent of initial data and described in terms of the real tritronquée so
lution of the Painlevé-I equation and a two-parameter family of exact sol
utions of sine-Gordon that represent space-time localized defects on an ot
herwise periodic background wave. This is joint work with Bing-Ying Lu.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaultier Lambert
DTSTART;VALUE=DATE-TIME:20201211T160000Z
DTEND;VALUE=DATE-TIME:20201211T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/6
DESCRIPTION:Title: On the characteristic polynomial of the Gaussian β-ensemble\nby G
aultier Lambert as part of SISSA's Integrable Systems and Mathematical Phy
sics seminar\n\n\nAbstract\nThe Gaussian β-ensemble is one of the central
model in random matrix theory. Because of its integrable structure\, it a
llows to describe several universal limiting laws of the eigenvalues of ra
ndom matrices. For instance\, in a seminal work\, Ramirez-Rider-Virag cons
tructed the Airy-β process\, the scaling limit of the eigenvalues near th
e spectral edge of the Gaussian β-ensemble and gave a new representation
for the Tracy-Widom distributions.\nIn this talk\, I intend to review this
construction and present recent results on the asymptotics for the charac
teristic polynomial of the Gaussian β-ensemble obtained jointly with Elli
ot Paquette (McGill University). Our results rely on a new approach to stu
dy the characteristic polynomial based on its recurrence.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Bufetov (Bonn)
DTSTART;VALUE=DATE-TIME:20201104T150000Z
DTEND;VALUE=DATE-TIME:20201104T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/7
DESCRIPTION:Title: Random tilings and representations of classical Lie groups\nby Ale
xey Bufetov (Bonn) as part of SISSA's Integrable Systems and Mathematical
Physics seminar\n\n\nAbstract\nI will speak about a new way to analyze the
global limit behavior of stochastic particle systems. It can be viewed as
a certain version of a non-commutative Fourier analysis related to unitar
y groups of growing size. As applications\, several models from integrable
probability will be discussed: models of random tilings of planar domains
\, random matrices\, and probabilistic models coming from representation t
heory.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Du Pei (Harvard)
DTSTART;VALUE=DATE-TIME:20201110T150000Z
DTEND;VALUE=DATE-TIME:20201110T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/8
DESCRIPTION:Title: Integrability from Fivebranes\nby Du Pei (Harvard) as part of SISS
A's Integrable Systems and Mathematical Physics seminar\n\n\nAbstract\nThe
existence of quantum field theories in higher dimensions leads to many in
teresting predictions in mathematics. In this talk\, I will survey some re
cent developments in this area\, centered on the theme of integrability an
d its interplay with geometry and topology.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kohei Iwaki (Tokyo)
DTSTART;VALUE=DATE-TIME:20201125T120000Z
DTEND;VALUE=DATE-TIME:20201125T130000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/9
DESCRIPTION:Title: Topological recursion and uncoupled BPS structure arising from spectra
l curves of hypergeometric type\nby Kohei Iwaki (Tokyo) as part of SIS
SA's Integrable Systems and Mathematical Physics seminar\n\n\nAbstract\nI'
ll discuss a relationship between the following two objects arising from t
he spectral curves of hypergeometric differential equation and its conflue
nt degenerations: The free energy compute by Eynard-Orantin's topological
recursion\, and BPS spectrum (degeneration of spectral networks) for the c
orresponding quadratic differentials computed by the algorithm of Gaiotto-
Moore-Neitzke / Bridgeland-Smith. In particular\, I’ll show a simple for
mula expressing the topological recursion free energies as a sum over BPS
states. My talk is based on a joint work with O. Kidwai.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Valeri (Glasgow)
DTSTART;VALUE=DATE-TIME:20201111T150000Z
DTEND;VALUE=DATE-TIME:20201111T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/10
DESCRIPTION:Title: Vertex algebras in representation theory\, geometry and mathematical
physics\nby Daniele Valeri (Glasgow) as part of SISSA's Integrable Sys
tems and Mathematical Physics seminar\n\n\nAbstract\nIn this talk we will
review some applications of vertex algebras and Poisson vertex algebras to
representation theory\, geometry and mathematical physics. An emphasis wi
ll be given on the notion of W-algebra which plays an important role in cl
assical and quantum integrable systems and in the representation theory of
Yangians.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Govind Menon (Brown)
DTSTART;VALUE=DATE-TIME:20210113T150000Z
DTEND;VALUE=DATE-TIME:20210113T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/11
DESCRIPTION:Title: Conformal processes with branching and the Dyson superprocess\nby
Govind Menon (Brown) as part of SISSA's Integrable Systems and Mathematic
al Physics seminar\n\n\nAbstract\nVarious growth processes for conformal m
aps with branching\, such as Diffusion Limited Aggregation (DLA) were sugg
ested by physicists in the 1980s. Despite spectacular numerical simulation
s\, there are few rigorous mathematical results in the area.\n\nI will dis
cuss a new form of stochastic Loewner evolution that is designed for the s
tudy of such processes. The main new idea is to use Dyson Brownian motion\
, coupled with natural branching rules\, as the driving measure of a Loewn
er evolution. The main advantage of this method is that yields new stochas
tic PDE as a scaling limit.\n\nThis is joint work with Vivian Olsiewski-He
aley.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nobutaka Nakazono (Tokyo University of Agriculture and Technology)
DTSTART;VALUE=DATE-TIME:20210210T120000Z
DTEND;VALUE=DATE-TIME:20210210T130000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/12
DESCRIPTION:Title: Special solutions to the multiplicative type discrete KdV equation\nby Nobutaka Nakazono (Tokyo University of Agriculture and Technology) a
s part of SISSA's Integrable Systems and Mathematical Physics seminar\n\n\
nAbstract\nIn 1977\, Hirota found the autonomous 2-dimensional difference
-difference equation\, which is a discrete analogue of the KdV equation.
Then\, in 1991 Capel\, Nijhoff and Papageorgiou found its deautonomized v
esrion. The solutions of both versions have been investigated.\nIn this t
alk\, we show that special solutions of its multiplicative (q-difference)
version are given by\n(1) solution to the q-Painleve equation of A5-type\
;\n(2) Casorati determinants whose entries are given by basic hypergeomet
ric functions.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danilo Lewanski (Paris)
DTSTART;VALUE=DATE-TIME:20210127T150000Z
DTEND;VALUE=DATE-TIME:20210127T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/14
DESCRIPTION:Title: Topological recursion\, matrix models\, and moduli spaces of curves.<
/a>\nby Danilo Lewanski (Paris) as part of SISSA's Integrable Systems and
Mathematical Physics seminar\n\n\nAbstract\nTopological recursion can be t
hought as an algorithm that generates recursively solutions of certain enu
merative geometric problems. It does arise from matrix models\, although i
t does not necessarily need one to be run. On the other hand\, it provides
a system of cohomology classes on the moduli spaces of curves (often a co
homological field theory). It certainly connects with integrable hierarchi
es although\, despite several results and conjectures\, the general theory
remains open. We will review and connect some recent results in the field
\, especially about Hurwitz theory and Masur-Veech volumes.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xavier Blot (Weizmann Institute of Sciences)
DTSTART;VALUE=DATE-TIME:20210217T150000Z
DTEND;VALUE=DATE-TIME:20210217T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/15
DESCRIPTION:Title: The quantum Witten-Kontsevich series.\nby Xavier Blot (Weizmann I
nstitute of Sciences) as part of SISSA's Integrable Systems and Mathematic
al Physics seminar\n\n\nAbstract\nThe Witten-Kontsevich series is a genera
ting series of intersection numbers on the moduli space of curves. In 2016
\, Buryak\, Dubrovin\, Guéré and Rossi defined an extension of this se
ries using a quantization of the KdV hierarchy based on the geometry of do
uble ramification cycle in M_{g\,n}. This series\, the quantum Witten-Kons
tevich series\, depends on a quantum parameter. When this quantum paramete
r vanishes\, the quantum Witten-Kontsevich series restricts to the Witten-
Kontsevich series. In this talk\, we will first construct the quantum Witt
en-Kontsevich series and then present all the known results about its coef
ficients. Surprisingly\, a part of these coefficients are expressed in ter
ms of Hurwitz numbers.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Shepelsky (Institute for Low Temperature Physics and Engine
ering)
DTSTART;VALUE=DATE-TIME:20210224T150000Z
DTEND;VALUE=DATE-TIME:20210224T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/16
DESCRIPTION:Title: Long-time asymptotics for the integrable nonlocal nonlinear Schrödin
ger equation\nby Dmitry Shepelsky (Institute for Low Temperature Physi
cs and Engineering) as part of SISSA's Integrable Systems and Mathematical
Physics seminar\n\n\nAbstract\nWe study the initial value problem for th
e integrable nonlocal nonlinear Schrödinger (NNLS) equation\nwith the ini
tial conditions of two types: \n(i) decaying at infinity initial conditi
ons\;\n(ii) step-like initial data: \n Our main tool is the adaptation of
the nonlinear steepest-decent method to \nthe study of Riemann-Hilbert p
roblems associated with the NNLS equation\nwith the specified boundary co
nditions.\nIn case (i)\, our main result is that\, in contrast to the conv
entional (local) NLS equation\, the power decay rate as t goes to infinit
y depends on the ratio x/t.\nFor case (ii)\, since our equation is not tr
anslation invariant\, we \nexplore the dependence of the asymptotic scenar
ios on shifts of the step-like initial data.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Tovbis (University of Central Florida)
DTSTART;VALUE=DATE-TIME:20210303T150000Z
DTEND;VALUE=DATE-TIME:20210303T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/17
DESCRIPTION:Title: Soliton and breather gases for integrable equations\nby Alexander
Tovbis (University of Central Florida) as part of SISSA's Integrable Syst
ems and Mathematical Physics seminar\n\n\nAbstract\nIn the talk we introdu
ce the idea of an "integrable gas" as a collection\nof large random ensemb
les of special localized solutions (solitons\, \nbreathers) of a given int
egrable system. These special solutions can\nbe treated as "particles". In
this talk we consider soliton and breather\ngases for the focusing Nonli
near Schroedinger Equation (fNLS) as\nspecial thermodynamic limits of fini
te gap (nonlinear multi phase wave) \nfNLS solutions. In this limit the ra
te of growth of the number of bands\nis linked with the rate of (simultane
ous) shrinkage of the size of individual\nbands. This approach leads to th
e derivation of the equation of state\nfor the gas and its certain limitin
g regimes (condensate\, ideal gas limits)\,\nas well as construction of v
arious interesting examples.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harini Desiraju (University of Birmingham)
DTSTART;VALUE=DATE-TIME:20210415T140000Z
DTEND;VALUE=DATE-TIME:20210415T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/18
DESCRIPTION:Title: Isomonodromic tau-functions on a torus as Fredholm determinants and c
harged partitions\nby Harini Desiraju (University of Birmingham) as pa
rt of SISSA's Integrable Systems and Mathematical Physics seminar\n\n\nAbs
tract\nIn the past five years\, a surge of new techniques from different a
reas of mathematics and physics led to a rigorous study of the tau-functio
ns of isomonodromic systems on a Riemann sphere and in particular\, the Pa
inlevé equations. We know that the tau-functions of Painlevé VI\, V\, I
II can be described as a Fredholm determinant of a combination of Toeplitz
operators called Widom constants and as a series of Conformal blocks or N
ekrasov functions\, the tau-function of Painlevé II can be written as a F
redholm determinant of an integrable operator\, and the tau-function of Pa
inlevé I is described by the discrete Fourier transform of the topologica
l recursion partition function for a family of elliptic curves.\n\n\nIn th
is talk I will show that the isomonodromic tau-function on a torus with Fu
chsian singularities and generic monodromies can be written as a Fredholm
determinant of Cauchy-Plemelj operators\, and its minor expansion is a com
binatorial series labeled by charged tuples of Young diagrams. The simples
t example in this setting is a torus with one puncture associated to the f
ormulation of the Painlevé VI equation as a time-dependent Hamiltonian sy
stem with an elliptic potential\, the time being the modular parameter of
the torus. I will show that the isomonodromic tau-function of such a syste
m is a Fredholm determinant described solely by hypergeometric functions\,
and its combinatorial expression takes the form of a dual Nekrasov-Okounk
ov partition function with a non-zero total charge.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Alexandrov (IBS Center for Geometry and Physics)
DTSTART;VALUE=DATE-TIME:20210505T090000Z
DTEND;VALUE=DATE-TIME:20210505T100000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/19
DESCRIPTION:Title: KP integrability of triple Hodge integrals\nby Alexander Alexandr
ov (IBS Center for Geometry and Physics) as part of SISSA's Integrable Sys
tems and Mathematical Physics seminar\n\n\nAbstract\nIn my talk\, I will d
escribe a relation between the Givental group of rank one and the Heisenbe
rg-Virasoro symmetry group of the KP integrable hierarchy. It appears that
only a two-parameter family of the Givental operators can be identified w
ith elements of the Heisenberg-Virasoro symmetry group. This family descri
bes triple Hodge integrals satisfying the Calabi-Yau condition. Using the
identification of the elements of two groups it is possible to prove that
the generating function of triple Hodge integrals satisfying the Calabi-Ya
u condition and its $\\Theta$-version are tau-functions of the KP hierarch
y. This generalizes the result of Kazarian on KP integrability in the case
of linear Hodge integrals. I will also describe the relation of this fami
ly of tau-functions with the generalized Kontsevich matrix model. My talk
is based on two papers\, arXiv:2009.01615 and arXiv:2009.10961.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gennady El (University of Northumbria)
DTSTART;VALUE=DATE-TIME:20210519T140000Z
DTEND;VALUE=DATE-TIME:20210519T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/20
DESCRIPTION:Title: Riemann problem for the Benjamin-Bona-Mahony equation\nby Gennady
El (University of Northumbria) as part of SISSA's Integrable Systems and
Mathematical Physics seminar\n\n\nAbstract\nI present recent analytical a
nd numerical results on the long time dynamics \nof the smoothed step init
ial value problem or dispersive Riemann problem \nfor the Benjamin-Bona-Ma
hony (BBM) equation $u_t + uu_x = u_{xxt}$. \nThe catalog of solutions of
the dispersive Riemann problem for the BBM equation is much richer than\n
for the related\, integrable\, Korteweg-de Vries equation and includes\, a
long with dispersive shock waves (DSWs)\nand rarefaction waves\, the rich
variety of nonclassical dispersive hydrodynamic solutions such as dispersi
ve Lax shocks\, \nexpansion shocks\, DSW implosion regimes and incoherent
solitary wave trains.\nThis is joint work with T. Congy\, M. Hoefer and M
. Shearer\, arXiv:2012.14579\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Norbury (Melbourne)
DTSTART;VALUE=DATE-TIME:20210512T100000Z
DTEND;VALUE=DATE-TIME:20210512T110000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/21
DESCRIPTION:Title: A new cohomology class on the moduli space of curves\nby Paul Nor
bury (Melbourne) as part of SISSA's Integrable Systems and Mathematical Ph
ysics seminar\n\n\nAbstract\nI will define a collection of cohomology clas
ses over the moduli space of stable Riemann surfaces which pull back natur
ally under the forgetful map and the inclusion of lower strata. These cla
sses have beautiful properties with conjectural relations to the KdV hiera
rchy\, the moduli space of super Riemann surfaces and to polynomial relati
ons among the kappa classes over the moduli space of stable Riemann surfac
es.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neil O'Connel (University College\, Dublin)
DTSTART;VALUE=DATE-TIME:20210518T140000Z
DTEND;VALUE=DATE-TIME:20210518T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/22
DESCRIPTION:Title: Colloquium: From longest increasing subsequences to Whittaker functio
ns and random polymers\nby Neil O'Connel (University College\, Dublin)
as part of SISSA's Integrable Systems and Mathematical Physics seminar\n\
n\nAbstract\nThe Robinson-Schensted-Knuth (RSK) correspondence is a combin
atorial bijection which plays an important role in the theory of Young tab
leaux and provides a natural framework for the study of longest increasing
subsequences in random permutations and related percolation problems. In
this talk I will give some background on this and then explain how a birat
ional version of the RSK mapping provides a similar framework for the stud
y of Whittaker functions and random polymers. Based on joint works with I
van Corwin\, Timo Seppalainen and Nikos Zygouras.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Youjin Zhang (Tsinghua University)
DTSTART;VALUE=DATE-TIME:20210527T090000Z
DTEND;VALUE=DATE-TIME:20210527T100000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/23
DESCRIPTION:Title: Virasoro constraints for Drinfeld-Sokolov hierarchies and equations o
f Painleve type\nby Youjin Zhang (Tsinghua University) as part of SISS
A's Integrable Systems and Mathematical Physics seminar\n\n\nAbstract\nWe
construct a tau cover of the generalized Drinfeld-Sokolov hierarchy associ
ated to an arbitrary affine Kac-Moody algebra \nwith gradations $s\\le 1$
and derive its Virasoro symmetries. By imposing the Virasoro constraints w
e obtain solutions of the Drinfeld-Sokolov \nhierarchy of Witten-Kontsevic
h and of Brezin-Gross-Witten types\, and of those characterized by certain
ordinary differential equations of \nPainleve type. We also show the exis
tence of affine Weyl group actions on solutions of such ordinary different
ial equations\, which generalizes \nthe theory of Noumi and Yamada on affi
ne Weyl group symmetries of the Painlev\\'e type equations.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonatan Lenells (KTH)
DTSTART;VALUE=DATE-TIME:20220117T150000Z
DTEND;VALUE=DATE-TIME:20220117T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/24
DESCRIPTION:Title: The focusing nonlinear Schrödinger equation with step-like oscillati
ng background\nby Jonatan Lenells (KTH) as part of SISSA's Integrable
Systems and Mathematical Physics seminar\n\n\nAbstract\nI will discuss joi
nt work with Anne Boutet de Monvel and Dmitry Shepelsky where we study the
asymptotic behavior of solutions of the nonlinear Schrödinger equation.
More precisely\, we consider the Cauchy problem for the focusing nonlinear
Schrödinger equation with initial data approaching different plane waves
at plus and minus infinity. Using Riemann–Hilbert techniques and Deift-
Zhou steepest descent arguments\, we study the long-time behavior of the s
olution. We show that there is a wide range of possible asymptotic scenari
os. We propose a method for rigorously establishing the existence of certa
in higher-genus asymptotic sectors\, and we compute detailed asymptotic fo
rmulas in a genus three sector\, i.e.\, in a sector where the leading term
of the asymptotics is given in terms of hyperelliptic functions attached
to a Riemann surface of genus three.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Doliwa (University of Warmia and Mazury)
DTSTART;VALUE=DATE-TIME:20220124T150000Z
DTEND;VALUE=DATE-TIME:20220124T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/25
DESCRIPTION:Title: On Hirota's discrete KP equation - old and new\nby Adam Doliwa (U
niversity of Warmia and Mazury) as part of SISSA's Integrable Systems and
Mathematical Physics seminar\n\n\nAbstract\nIn the first part of the talk
I would like to recall basic information on the non-abelian Hirota-Miwa eq
uation and on the corresponding map satisfying Zamolodchikov's tetrahedron
condition. This includes the projective geometric interpretation of the H
irota map and of its multidimensional consistency\, which points out towar
ds a generalization of the map allowing for the quantum reduction. In the
second part I will show that the Hermite-Pad\\'e type I approximation prob
lem leads in a natural way to Hirota's discrete KP system subject to an in
tegrable constraint. Our result explains the appearence of various ingredi
ents of the integrable systems theory in application to multiple orthogona
l polynomials\, numerical algorithms\, random matrices\, and in other bran
ches of mathematical physics and applied mathematics where the Hermite-Pad
\\'e approximation problem is relevant. If time permits I will show how ge
neralize this connection to the non-commutative level.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leslie Molag (Bielefeld University)
DTSTART;VALUE=DATE-TIME:20220131T150000Z
DTEND;VALUE=DATE-TIME:20220131T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/26
DESCRIPTION:Title: On the complex elliptic Ginibre ensemble and some generalizations
\nby Leslie Molag (Bielefeld University) as part of SISSA's Integrable Sys
tems and Mathematical Physics seminar\n\n\nAbstract\nThe complex elliptic
Ginibre ensemble allows one to interpolate between the Ginibre ensemble an
d the Gaussian Unitary ensemble. It represents a determinantal point proce
ss in the complex plane with corresponding kernel\, constructed with plana
r Hermite polynomials. Our main tool is a saddle point analysis of a singl
e contour integral representation of this kernel. It provides a unifying a
pproach to rigorously derive several known and new results of local and gl
obal spectral statistics. In particular\, we prove rigorously some global
statistics in the elliptic Ginibre ensemble first derived by Forrester and
Jancovici. The limiting kernel receives its main contribution from the bo
undary of the limiting elliptic droplet of support.\nWe introduce a d-comp
lex dimensional generalization of the elliptic Ginibre ensemble\, which in
terpolates between d-real and d-complex dimensions. In the Hermitian limit
\, this new ensemble is related to non-interacting Fermions in a trap in d
-real dimensions with d-dimensional harmonic oscillator. We provide new lo
cal bulk and edge statistics at weak and strong non-Hermiticity for this n
ew ensemble.\n\nThis is joint work with Gernot Akemann and Maurice Duits.\
n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Glesner (UCLouvain)
DTSTART;VALUE=DATE-TIME:20220131T160000Z
DTEND;VALUE=DATE-TIME:20220131T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/27
DESCRIPTION:Title: Determinantal point processes conditioned on randomly incomplete conf
igurations\nby Gabriel Glesner (UCLouvain) as part of SISSA's Integrab
le Systems and Mathematical Physics seminar\n\n\nAbstract\nWe consider a m
arked point process with independent binomial marks 0 and 1. In our contex
t of randomly incomplete configuration\, we interpret the mark 1 points as
detected while the mark 0 ones are unobserved. We then define the point p
rocess consisting of the undetected particles conditioned on a finite obse
rvation\, i.e a finite configuration of mark 1 points.\n\nWhen the ground
process is determinantal\, so is every one of the aforementioned point pro
cesses. Furthermore\, important subclasses of determinantal point processe
s\, namely the ones induced by projections and k-integrable kernels\, are
also preserved under this conditioning. In the latter case\, the transform
ation can be characterised using a Riemann-Hilbert problem which can be se
en as a combination of the celebrated method of Its\, Izergin Korepin and
Slavnov\, with a discrete version of this method.\n\nThis is based on join
t work with Tom Claeys (UCLouvain) [https://arxiv.org/abs/2112.10642]\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavlos Kassotakis
DTSTART;VALUE=DATE-TIME:20220207T150000Z
DTEND;VALUE=DATE-TIME:20220207T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/28
DESCRIPTION:Title: Integrable two-component systems of difference equations\nby Pavl
os Kassotakis as part of SISSA's Integrable Systems and Mathematical Physi
cs seminar\n\n\nAbstract\nWe will present two lists of two-component syste
ms of integrable difference equations defined on the edges of the $\\mathb
b{Z}^2$ graph. The integrability of these systems is manifested by their L
ax formulation which is a consequence of the multi-dimensional compatibili
ty of these systems. Imposing constraints consistent with the systems of d
ifference equations\, we recover known integrable quad-equations including
the discrete version of the Krichever-Novikov equation. The systems of di
fference equations give us\, in turn\, Yang-Baxter maps. Some of these map
s can be considered as particular reductions of non-abelian Yang-Baxter ma
ps.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balázs Pozsgay (Eötvös Loránd University)
DTSTART;VALUE=DATE-TIME:20220307T150000Z
DTEND;VALUE=DATE-TIME:20220307T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/29
DESCRIPTION:Title: Integrable cellular automata: A review of recent developments\nby
Balázs Pozsgay (Eötvös Loránd University) as part of SISSA's Integrab
le Systems and Mathematical Physics seminar\n\n\nAbstract\nWe consider cel
lular automata on 1 dimensional lattices. These are dynamical systems wher
e both the space and time coordinate\, and also the configuration space ar
e discrete. Recently there has been considerable activity devoted to the s
olvable cases\, which show various signs of integrability. Despite the lon
g history of the subject\, it appears that new results were found in recen
t years\, which motivates further studies. We will focus on cellular autom
ata constructed from Yang-Baxter maps\, and also on the so-called dual uni
tary circuits.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Caudrelier (University of Leeds)
DTSTART;VALUE=DATE-TIME:20220404T140000Z
DTEND;VALUE=DATE-TIME:20220404T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/30
DESCRIPTION:Title: Classical Yang-Baxter equation\, Lagrangian multiforms and ultralocal
integrable hierarchies\nby Vincent Caudrelier (University of Leeds) a
s part of SISSA's Integrable Systems and Mathematical Physics seminar\n\n\
nAbstract\nThe notion of integrability for classical (field) theories has
been almost entirely studied from the Hamiltonian point of view since the
early days of the modern theory of integrable systems. In 2009\, the notio
n of Lagrangian multiform was first put forward by Lobb and Nijhoff\nas a
purely Lagrangian framework to capture integrability. The main idea is to
formulate a generalised variational principle for an action involving a ce
rtain differential form whose coefficients are interpreted as Lagrangians
for a hierarchy. Since its proposal\, this idea has flourished in various
directions and I will review the main developments for classical field the
ories in 1+1 dimensions.\n\nTwo key ingredients are the multiform Euler-La
grange equations and the so-called closure relation\, both of which derive
from the generalised variational principle. In this talk\, I will present
the connection between Lagrangian multiform theory and the well-establish
ed theory of the classical r-matrix which had a purely Hamiltonian interpr
etation so far. I will explain how the classical Yang-Baxter equation unde
rpins the fundamental properties of a certain Lagrangian multiform and the
corresponding zero curvature equations. A large variety of known hierarch
ies are contained as special cases\, such as the Ablowitz-Kaup-Newell-Segu
r hierarchy\, the sine-Gordon (sG) hierarchy and various hierarchies relat
ed to Zakharov-Mikhailov type models which contain the Faddeev-Reshetikhin
(FR) model and recently introduced deformed sigma/Gross-Neveu models as p
articular cases.\n\nTime permitting\, I will also illustrate the versatili
ty of our method by showing how to construct new examples of integrable fi
eld theories and their hierarchies by coupling integrable hierarchies toge
ther. We provide two examples: the coupling of the nonlinear Schrödinger
system to the FR model and the coupling of sG with the anisotropic FR mode
l.\n\nThis most recent results are based on the joint work arXiv:2201.0828
6 with M. Stoppato and B. Vicedo.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giorgio Gubbiotti (University of Milan)
DTSTART;VALUE=DATE-TIME:20220214T150000Z
DTEND;VALUE=DATE-TIME:20220214T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/31
DESCRIPTION:Title: Co-algebra symmetry for discrete systems\nby Giorgio Gubbiotti (U
niversity of Milan) as part of SISSA's Integrable Systems and Mathematical
Physics seminar\n\n\nAbstract\nWe introduce the concept of coalgebra symm
etry for discrete systems. Then\, we use this powerful tool to prove Liovi
lle integrability\, superintegrability\, and quasi-integrability of the ve
ctor versions of some well-known one-dimensional difference equations.\n\n
Joint work with Danilo Latini and Benjamin Tapley\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Doliwa (University of Warmia and Mazury)
DTSTART;VALUE=DATE-TIME:20220221T150000Z
DTEND;VALUE=DATE-TIME:20220221T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/32
DESCRIPTION:Title: On Hirota's discrete KP equation - old and new (cont.)\nby Adam D
oliwa (University of Warmia and Mazury) as part of SISSA's Integrable Syst
ems and Mathematical Physics seminar\n\n\nAbstract\nIn the first part of t
he talk I would like to recall basic information on the non-abelian Hirota
-Miwa equation and on the corresponding map satisfying Zamolodchikov's tet
rahedron condition. This includes the projective geometric interpretation
of the Hirota map and of its multidimensional consistency\, which points o
ut towards a generalization of the map allowing for the quantum reduction.
In the second part I will show that the Hermite-Pad\\'e type I approximat
ion problem leads in a natural way to Hirota's discrete KP system subject
to an integrable constraint. Our result explains the appearence of various
ingredients of the integrable systems theory in application to multiple o
rthogonal polynomials\, numerical algorithms\, random matrices\, and in ot
her branches of mathematical physics and applied mathematics where the Her
mite-Pad\\'e approximation problem is relevant. If time permits I will sho
w how generalize this connection to the non-commutative level.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaetan Borot (Humboldt University)
DTSTART;VALUE=DATE-TIME:20220314T150000Z
DTEND;VALUE=DATE-TIME:20220314T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/33
DESCRIPTION:Title: Free probability\, Hurwitz numbers and symplectic invariance\nby
Gaetan Borot (Humboldt University) as part of SISSA's Integrable Systems a
nd Mathematical Physics seminar\n\n\nAbstract\nI will survey the relations
between 1) free probability\, the theory of free cumulants and their appl
ication in random matrices \; 2) combinatorics of maps with fully-simple b
oundaries\; 3) monotone Hurwitz numbers and the Fock space formalism\; 4)
topological recursion and symplectic exchange (x\,y) -> (y\,x). In particu
lar\, I will discuss generalisation of free probability to all topologies\
, and two recent results: a) all topology free cumulants of the 1-hermitia
n matrix model are computed by topological recursion for the matrix model
spectral curve after exchange of x and y\; b) functional relations between
generating series of free cumulants and moments (in all topology)\, which
resolve a problem posed fifteen years ago by Collins\, Mingo\, Sniady and
Speicher. Based on joint works with Severin Charbonnier\, Elba Garcia-Fai
lde\, Felix Leid and Sergey Shadrin.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Masoero
DTSTART;VALUE=DATE-TIME:20220228T150000Z
DTEND;VALUE=DATE-TIME:20220228T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/34
DESCRIPTION:Title: A "proof" of the ODE/IM correspondence for the Quantum KdV model.
\nby Davide Masoero as part of SISSA's Integrable Systems and Mathematical
Physics seminar\n\n\nAbstract\nThe Quantum KdV model is a conformal field
theory\, whose hamiltonian structure is a deformation of the second KdV h
amiltonian structure. It is also the conformal (or scaling) limit of the X
XZ chain and it is integrable by the Bethe Ansatz Equations.\nIn 1998 Dor
ey and Tateo discovered that the Bethe roots for the ground state of such
a model coincide with the eigenvalues of certain anharmonic oscillators (O
DE/IM correspondence). In 2004 Bazhanov-Lukyanov-Zamolodhchikov conjecture
d that each state of the model corresponds to a "monster potential" (a gen
eralization of an anharmonic oscillator) whose eigenvalues coincide with t
he Bethe roots.\nIn this talk I provide an outline of the proof -- conditi
onal on the existence of a certain Puiseux series -- of the BLZ conjecture
that I have recently obtained in collaboration with Riccardo Conti.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton M. Zeitlin
DTSTART;VALUE=DATE-TIME:20220228T160000Z
DTEND;VALUE=DATE-TIME:20220228T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/35
DESCRIPTION:Title: Spin chains and geometric structures\nby Anton M. Zeitlin as part
of SISSA's Integrable Systems and Mathematical Physics seminar\n\n\nAbstr
act\nI will talk about the geometric aspects of integrable systems\, based
on Yangians and quantum groups\, known as XXX and XXZ spin chain models.\
nTheir "classical" limits\, the so-called Gaudin models\, are related to o
pers\, special classes of connections with regular singularities on the pr
ojective line. The key objects in this relation are the Bethe equations: a
lgebraic equations\, which on one side describe the spectrum of Gaudin mod
els\, and at the other side put constraints on the oper connections.\nThis
relation between seemingly unrelated classes of objects emerged around 20
years ago as one of the interesting examples of the geometric Langlands c
orrespondence.\nIn this presentation\, I will focus on recent developments
\, allowing to extend this correspondence to XXX and XXZ models\, by intro
ducing the necessary geometric objects\, generalizing oper connection. We
will start from the geometric setup\, leading to the notion of the q-oper.
After that\, I explain their relation to the spectrum of the XXX and XXZ
models\, generalizing the Gaudin-oper correspondence. In the end\, I will
highlight some of the applications of q-opers.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Lazag (SISSA)
DTSTART;VALUE=DATE-TIME:20220321T150000Z
DTEND;VALUE=DATE-TIME:20220321T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/36
DESCRIPTION:Title: Giambelli compatibility and characteristic polynomials of determinant
al point processes\nby Pierre Lazag (SISSA) as part of SISSA's Integra
ble Systems and Mathematical Physics seminar\n\n\nAbstract\nThe Giambelli
Formula is the equality between a Schur function indexed by a partition an
d the determinant of the Schur functions indexed by the hooks composing th
e partition. Borodin-Olshanski-Strahov define Giambelli compatible point p
rocesses to be point processes for which the Giambelli formula is stable u
nder averaging. Under suitable convergence condition\, this property is eq
uivalent to the validity of an explicit formula for averages of products o
f ratios of characteristic polynomials. Fyodorov and Strahov proved in the
90's that such a formula is satisfied for characteristic polynomials of r
andom matrices from the GUE or CUE. In a joint work with A.I. Bufetov (htt
ps://arxiv.org/abs/2111.05606)\, we prove that every determinantal point p
rocess on the real line possessing an integrable kernel is Giambelli compa
tible and that\, equivalently\, its characteristic polynomials satisfy the
formula of Fyodorov-Strahov. I will present this result in my talk and ex
plain in some details the notion of Giambelli compatibility and its connec
tion with characteristic polynomials.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Promit Ghosal (MIT)
DTSTART;VALUE=DATE-TIME:20220328T150000Z
DTEND;VALUE=DATE-TIME:20220328T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/38
DESCRIPTION:Title: Probabilistic Conformal Block and Its Properties\nby Promit Ghosa
l (MIT) as part of SISSA's Integrable Systems and Mathematical Physics sem
inar\n\n\nAbstract\nConformal blocks are fundamental ingredients of the co
nformal field theory and are closely related to supersymmetric gauge theor
y. They also have intimate connections with Painleve tau functions and lim
its of spiked random matrices.\n \nIn this talk\, I will demonstrate a pro
babilistic construction of the 1-point torus conformal block using Gaussia
n multiplicative chaos and discuss some of its properties and connections.
This talk will be based on joint works with Guillaume Remy\, Xin Sun and
Yi Sun. \n \nIf time permits\, I will mention about two ongoing works: one
on showing modular symmetry of the conformal blocks and the other on show
ing the semiclassical limit of the conformal block.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitrii Rachenkov (SISSA)
DTSTART;VALUE=DATE-TIME:20220411T140000Z
DTEND;VALUE=DATE-TIME:20220411T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/39
DESCRIPTION:Title: Dimer models and q-difference Painlevè equations\nby Dmitrii Rac
henkov (SISSA) as part of SISSA's Integrable Systems and Mathematical Phys
ics seminar\n\n\nAbstract\nDifference Painlevè equations are famous discr
ete integrable systems\, according to H. Sakai’s classification (2001) t
hey are divided into three series: $d$\, $p$ and $q$. In 2018 M. Bershtein
\, P. Gavrylenko\, and A. Marshakov have discovered cluster nature of $q$-
series equations\, i.e. it is possible to get all these equations as autom
orphisms of cluster manifolds in appropriate coordinates (= automorphisms
of quivers under mutations and permutations of vertices). Moreover\, they
noticed that almost all this quivers come from admissible dimer models. In
my talk I will speak about the categorification of this equations: dynami
cs of equations correspond to functors of autoequivalence derived categori
es of representations of these quivers with relations. These categories ar
e equivalent to derived categories of coherent sheaves over canonical bund
les of del Pezzo surfaces. The presentation is based on my graduate work u
nder the supervision of M. Bershtein.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Giacchetto (IPhT)
DTSTART;VALUE=DATE-TIME:20220502T140000Z
DTEND;VALUE=DATE-TIME:20220502T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/40
DESCRIPTION:Title: The negative side of Witten’s conjecture\nby Alessandro Giacche
tto (IPhT) as part of SISSA's Integrable Systems and Mathematical Physics
seminar\n\n\nAbstract\nIn 2017\, Norbury introduced a collection of cohomo
logy classes on the moduli space of curves\, and predicted that their inte
rsection with psi classes solves the KdV hierarchy. In a joint work in pro
gress with N. Chidambaram and E. Garcia-Failde\, we consider a deformation
of Norbury’s class and\, via the Givental–Teleman reconstruction theo
rem\, we express such deformation in terms of kappa classes establishing n
ew tautological relations. The recursive construction of these classes red
uces in the limit to certain Virasoro constraints satisfied by Norbury’s
class\, whose unique solution coincide with the Brézin–Gross–Witten
tau function of the KdV hierarchy. Time permitting\, I will explain the hi
gher spin generalisation of these results.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Suris (TU Berlin)
DTSTART;VALUE=DATE-TIME:20220516T140000Z
DTEND;VALUE=DATE-TIME:20220516T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/41
DESCRIPTION:Title: New results on geometry of bilinear discretizations of quadratic vect
or fields\nby Yuri Suris (TU Berlin) as part of SISSA's Integrable Sys
tems and Mathematical Physics seminar\n\n\nAbstract\nWe discuss dynamics o
f birational maps which appear as bilinear discretizations of quadratic ve
ctor fields. Various aspects of integrability of birational dynamical syst
ems will be discussed\, along\nwith remarkable geometric structures and co
nstructions behind some of the particular examples.\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hjalmar Rosengren (Chalmers Univeristy of Technology and Universit
y of Gothenburg)
DTSTART;VALUE=DATE-TIME:20220509T140000Z
DTEND;VALUE=DATE-TIME:20220509T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115354Z
UID:ISAMP-SISSA/42
DESCRIPTION:Title: XYZ correlations and Painlevé VI\nby Hjalmar Rosengren (Chalmers
Univeristy of Technology and University of Gothenburg) as part of SISSA's
Integrable Systems and Mathematical Physics seminar\n\n\nAbstract\nThe XX
Z spin chain is solvable in the sense that some physical quantities can be
computed exactly in the infinite lattice limit. For a special value of t
he so called crossing parameter the chain is supersymmetric. In this case
exact results can be obtained even for finite system size\, and there are
remarkable connections to combinatorics (e.g. the alternating-sign-matrix
and Razumov-Stroganov ex-conjectures). For the more general XYZ spin chain
\, less is known. We will describe how nearest neighbour correlations for
finite length supersymmetric XYZ spin chains can be computed explicitly in
terms of tau functions of Painlevé VI. This is joint work in progress wi
th Christian Hagendorf (Louvain-la-Neuve).\n
LOCATION:https://researchseminars.org/talk/ISAMP-SISSA/42/
END:VEVENT
END:VCALENDAR