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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:20220521T102300Z
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.\nhttps://i
ndico.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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SUMMARY:New Trends in Topology
DTSTART;VALUE=DATE-TIME:20220201T060000Z
DTEND;VALUE=DATE-TIME:20220630T150000Z
DTSTAMP;VALUE=DATE-TIME:20220521T102300Z
UID:indico-event-104@indico.eimi.ru
DESCRIPTION:The program is partly suspended\nThe school “New Methods in
Enumerative Geometry” is cancelled\nThe conference “Low-Dimensional
Topology” is cancelled\nThe conference “On the Crossroad of Topology
and Enumerative Geometry” is cancelled\n\nThematic program "New Trends i
n Topology"\n\nFebruary 1 – June 30\, 2022\n\nThere were several far-re
aching conceptual developments in topology at the turn of the century. In
the late 1980’s – early 1990’s\, a spectacular progress in the theor
y of knots and 3-dimensional manifolds was made by the Fields medalists E.
Witten and V. Jones followed by the work of N. Reshetikhin\, V. Turaev\,
O. Viro and others who related this area of topology to the theory of quan
tum groups. As a result\, a new mathematical field was born\, the topologi
cal quantum field theory.\n\nIn parallel to the appearance of the topologi
cal quantum field theory\, there emerged a theory of Gromov-Witten invaria
nts\, under the influence of implantation of pseudo-holomorphic curve tech
nique into symplectic geometry by M. Gromov and the holomorphic curve coun
ting into quantum 2-dimensional gravity by E. Witten. This had led\, in pa
rticular\, to the Kontsevich-Manin theory of quantum cohomology and a brea
kthrough in enumerative geometry.\n\nThese new research areas are not only
linked by the time of their appearance and the string theory as a common
root\, but also by deep relations between the techniques and underlying al
gebraic structures. The very recent developments in Gromov-Witten theory b
rought to light direct bridges between enumerative geometry of open string
s and the theory of knot invariants. This program is devoted to a number
of the most active areas of these research fields.\n\n\nThe following acti
vities will be organized during the program:\n\n\n introductory school “
Low-dimensional Topology”\, April 25 – 29\, 2022\n [CANCELLED] introd
uctory school “New Methods in Enumerative Geometry”\n [CANCELLED] con
ference “Low-Dimensional Topology”\, June 6 – 10\, 2022\n [CANCELLED
] conference “On the Crossroad of Topology and Enumerative Geometry
”\n a weekly research seminar\n a number of lecture courses.\n\n\n\nOrga
nizers:\n\n\n Evgeny Fominykh\, St. Petersburg University\n Ilia Itenberg\
, Sorbonne University\n Viatcheslav Kharlamov\, Université de Strasbourg\
n Vladimir Turaev\, Indiana University\n Oleg Viro\, Stony Brook Universi
ty\n\n\n\nInstitutions participating in the organization of the event:\n\n
\n St. Petersburg Department of Steklov Mathematical Institute of Russian
Academy of Sciences\n Leonhard Euler International Mathematical Institute
in Saint Petersburg\n Chebyshev Laboratory at St.Petersburg State Universi
ty\n\n\nThe program is supported by a grant from the Government of the Rus
sian Federation\, agreements 075-15-2019-1619 and 075-15-2019-1620\, and
by a grant from Simons Foundation.\nhttps://indico.eimi.ru/event/104/
LOCATION:Leonhard Euler International Mathematical Institute in Saint Pete
rsburg
URL:https://indico.eimi.ru/event/104/
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