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SUMMARY:Moduli Spaces\, Combinatorics and Poisson Geometry
DTSTART;VALUE=DATE-TIME:20211115T060000Z
DTEND;VALUE=DATE-TIME:20220831T150000Z
DTSTAMP;VALUE=DATE-TIME:20240725T133952Z
UID:indico-event-107@indico.eimi.ru
DESCRIPTION:Thematic Program\n"Moduli Spaces\, Combinatorics and Poisson G
eometry"\n\nNovember 2021 – August 2022\n\nModuli spaces have many non-t
rivial connections to other areas of mathematics: combinatorics\, dynamics
\, integrable systems and Poisson geometry\, to name a few. Among most cel
ebrated results over the last 30 years one can mention several proofs of W
itten’s conjecture about intersection numbers of ψ-classes (Kontsevich\
, Mirzakhani and others)\, computation of Euler’s characteristics of mod
uli spaces (Harer-Zagier)\, development of the higher Teichmüller theory
(Fock\, Goncharov) and its links with cluster algebras and associated Pois
son structures (Fomin\, Zelevinsky).\n\nThe research problems central for
the program are:\n\n\n Establishing a relationship between meandric system
s (pairs of transversal multicurves) on higher genus surfaces and square-t
iled surfaces.\n Study of the large genus asymptotics of the numbers of me
andric systems of given topological type.\n Computation of Masur-Veech vol
umes of lower dimensional strata in the moduli space of quadratic differen
tials.\n Obtaining a relation of the distribution of geodesic multicurves
to Masur-Veech volumes.\n Establishing a relation between Joyce’s struct
ures by Bridgeland to Frobenius manifolds and topological recursion formal
ism.\n Description the complete WKB expansion of the generating function o
f monodromy symplectomorphism for second order differential equations on R
iemann surfaces with second order poles and establishing the link to topol
ogical recursion formalism.\n Application of the WKB formalism to general
isomonodromic tau-function and embed it into the topological recursion fra
mework. Generalization to higher genus using the formalism of Krichever an
d Bertola-Malgrange.\n Construction of the dilogarithm line bundle over SL
(2\, R) cluster variety associated to the canonical symplectic form over t
he moduli spaces of bordered Riemann surfaces\; description of the Bohr-So
mmerfeld symplectic leaves and their quantization.\n\n\n\nThe following ac
tivities will be organised during the program:\n\n\n school "Moduli Spaces
\, Combinatorics and Integrable Systems"\, November 15 – 26\, 2021\n [CA
NCELLED] conference "Combinatorics of Moduli Spaces\, Cluster Algebras and
Topological Recursion"\, June 13 – 17\, 2022\n [CANCELLED] conference
"Geometry and Dynamics of Moduli Spaces"\, August 1 – 5\, 2022 \n a
number of minicourses given by invited visitors\n\n\n\nTentative list of m
inicourse lecturers includes:\n\n\n \n \n Amol Aggarwal\, Harvard Unive
rsity\n Nicolai Reshetikhin\, University of California\,\n \n \n An
ton Alekseev\, University of Geneva\n Berkeley Michael Shapiro\, Mich
igan State University\n \n \n Gaëtan Borot\, Max Planck Institute for
Mathematics\n Leon Takhtajan\, Stony Brook University and EIMI\n \n
\n Vladimir Fock\, University of Strasbourg\n Richard Wentworth\, Un
iversity of Maryland \n \n \n Sergey Fomin\, University of Michigan\
n Don Zagier\, Max Planck Institute for Mathematics\n \n \n Martin
Möller\, Goethe University\n Anton Zorich\, Skoltech and IMJ – PRG\n
\n \n Alexey Rosly\, Skoltech\n Dimitri Zvonkine (CNRS) (to be
confirmed)\n \n \n\n\n\nOrganizers:\n\n\n Dmitry Korotkin\, Concordia Un
iversity and Centre de Recherches Mathématiques\n Peter Zograf\, PDMI RAS
and St. Petersburg University\n\n\n\nInstitutions participating in the or
ganization of the event:\n\n\n St. Petersburg Department of Steklov Mathem
atical Institute of Russian Academy of Sciences\n Leonhard Euler Internati
onal Mathematical Institute in Saint Petersburg\n Chebyshev Laboratory at
St.Petersburg State University\n\n\nThe program is supported by a grant fr
om the Government of the Russian Federation\, agreements 075-15-2019-1619
and 075-15-2019-1620\, and by a grant from Simons Foundation.\n\nhttps:/
/indico.eimi.ru/event/107/
LOCATION: Leonhard Euler International Mathematical Institute in Saint Pet
ersburg
URL:https://indico.eimi.ru/event/107/
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