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SUMMARY:Topological Recursion\, from Enumerative Geometry to Integrability
(1/4)
DTSTART;VALUE=DATE-TIME:20180315T090000Z
DTEND;VALUE=DATE-TIME:20180315T110000Z
DTSTAMP;VALUE=DATE-TIME:20190618T151731Z
UID:indico-event-3191@indico.math.cnrs.fr
DESCRIPTION:Topological recursion (TR) is a remarkable universal recursive
structure that has been found in many enumerative geometry problems\, fro
m combinatorics of maps (discrete surfaces)\, to random matrices\, Gromov-
Witten invariants\, knot polynomials\, conformal blocks\, integrable syste
ms... An example of topological recursion is the famous Mirzakhani recursi
on that determines recursively the hyperbolic volumes of moduli spaces. It
is a recursion on the Euler characteristic\, whence the name "topological
" recursion.\n\nA recursion needs an initial data: a "spectral curve" (whi
ch we shall define)\, and the recursion defines the sequence of "TR-invari
ants" of that spectral curve.\n\nIn this series of lectures\, we shall:\n\
n- define the topological recursion\, spectral curves and their TR-invaria
nts\, and illustrated with examples.\n\n- state and prove many important p
roperties\, in particular how TR-invariants get deformed under deformation
s of the spectral curve\, and how they are related to intersection numbers
of moduli spaces of Riemann surfaces\, for example the link to Givental f
ormalism.\n\n- introduce the new algebraic approach by Kontsevich-Soibelma
n\, in terms of quantum Airy structures.\n\n- present the relationship of
these invariants to integrable systems\, tau functions\, quantum curves.\n
\n- if time permits\, we shall present the conjectured relationship to Jon
es and Homfly polynomials of knots\, as an extension of the volume conject
ure.\n\nhttps://indico.math.cnrs.fr/event/3191/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/3191/
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