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SUMMARY:2015 Summer School on Moduli Problems in Symplectic Geometry
DTSTART;VALUE=DATE-TIME:20150706T063000Z
DTEND;VALUE=DATE-TIME:20150717T160000Z
DTSTAMP;VALUE=DATE-TIME:20210117T095503Z
UID:indico-event-585@indico.math.cnrs.fr
DESCRIPTION:\n \n Organized as part of the IHÉS Lectures\, this
Summer School aims to provide PhD students\, post-docs\, and young resear
chers with an overview of recent developments in the theory of moduli spac
es of pseudoholomorphic curves in symplectic and contact geometry.\n
\n Moduli spaces of pseudoholomorphic curves arise as the zero se
t of a Fredholm section of a suitable bundle. Provided this section can be
appropriately perturbed\, these moduli spaces yield powerful contact and
symplectic invariants such as Gromov-Witten theory\, contact homology\, sy
mplectic homology\, and Symplectic Field Theory. Constructions and applica
tions of these invariants will be addressed in detail during the workshop.
There are two main perturbative techniques\, geometric and functional ana
lytic.\n \n The geometric perturbation methods are powerful
for applications and practical from a computational point of view but typi
cally require many restrictive assumptions and fail to generalize broadly.
We will introduce researchers to the polyfold machinery of Hofer\, Wysock
i\, and Zehnder\, a new analytic framework designed to resolve the issue o
f transversality systematically. As computations are integral in applicati
ons of the aforementioned invariants\, we will also explore how geometric
perturbation schemes can be incorporated into the polyfold package.\n
\n We will supplement 7 mini courses with moderated discussions
and related talks by senior faculty on current and future directions for t
he field.\n\n\n \n Confirmed speakers:\n\n M. Abouzaid\, Columbia
University *\n P. Biran\, ETH Zürich\n N. Bottman\, Massachusetts
Institute of Technology\n F. Bourgeois\, Université Paris-Sud Orsay\n
D. Cristofaro-Gardiner\, Harvard University\n T. Ekholm\, Uppsala Un
iversity *\n Y. Eliashberg\, Stanford\n J. Fish\, Institute for Adva
nced Study *\n H. Hofer\, Institute for Advanced Study *\n M. Hutchi
ngs\, UC Berkeley *\n D. McDuff\, Barnard College\, Columbia University
\n J. Nelson\, Columbia University and the Institute for Advanced Study
\n I. Smith\, University of Cambridge\n J. Solomon\, Hebrew Universi
ty\n C. Viterbo\, Ecole Normale Supérieure\n K. Wehrheim\, UC Berke
ley *\n C. Wendl\, University College London *\n \n * Mini course
speakers\n\n \n Organizing Committee\n\n Chair: J. Nelson (Colum
bia University and the Institute for Advanced Study)\n D. Cristofaro-Ga
rdiner (Harvard University)\n J. Fish (Institute for Advanced Study and
UMass Boston)\n\n Scientific Advisory Committee\n\n H. Hofer (Insti
tute for Advanced Study)\n M. Hutchings (UC Berkeley)\n D. McDuff (B
arnard College\, Columbia University)\n\n \n \n\n With the suppor
t of La Société Générale\n\n \n\nhttps://indico.math.cnrs.fr/even
t/585/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/585/
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