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SUMMARY:New Trends in Topology
DTSTART;VALUE=DATE-TIME:20220201T060000Z
DTEND;VALUE=DATE-TIME:20220630T150000Z
DTSTAMP;VALUE=DATE-TIME:20220521T083551Z
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.\n\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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