Espaces de modules en topologie symplectique et en théorie de Gauge

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Date/heure
Date(s) - 01/06/2015 - 05/06/2015
0 h 00 min

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*Colloque

,
dans le cadre de la Chaire Jean Morlet

Moduli Spaces in Symplectic Topology and in Gauge Theory.

Symplectic topology can be considered as the mathematical versant of String theory. They were discovered independently at the same time in the 80’s. The second one is a fantastic enterprise to unify low-scale and highscale physics, while the -first one was born as a tool to resolve the extraordinarily difficult problems of closed orbits in non integrable generic Hamiltonian systems (the famous Arnold and Weinstein conjectures). Since that time, both theories have developed into a far reaching mathematical endeavour and much of today’s attention from the geometers across the world is directed towards the many conjectures of Symplectic Topology. Symplectic Topology is, together with Number Theory, the only -field that seems able to produce very simple conjectures that are notoriously hard to prove. It is also the only theory, to our knowledge, that produces deep and rich moduli spaces at such a pace! This workshop will bring together the best specialists in the world around the problems of moduli spaces in Symplectic topology and Gauge theory. These rich moduli spaces are always set up to de-fine functors or morphisms depending on pertinent non-linear elliptic PDE’s configurations-, often coupled with trees of Morse flows. Our understanding of these moduli spaces is based on (1) the appropriate setting for these moduli spaces to get the right compactifi-cation needed (of which Uhlenbeck’s and the Gromov’s compacti-fication theorems are just the very -first basic blocks), and (2) the construction of the algebraic structures that prevail in these moduli spaces and that, ultimately, govern the whole Floer-SFT-like theory.

{{Sujets :}}
– (1) Analytic foundations and applications to dynamics.
– (2) Algebraic structures and ramifi-cations.

{{Organisateurs :}}
– Helmut Hofer (Institute for Advanced Studies, Princeton)
– Ilia Itenberg (Jussieu)
– François Lalonde (Aix-Marseille & Montréal)
– Dusa McDuff (Columbia)
– Kaoru Ono (RIMS, Kyoto University)
– Leonid Polterovich (Tel Aviv University)
Andrei Teleman (Aix-Marseille)

{{Partenaires :}}
Chaire Jean-Morlet

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Olivier CHABROL
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