SYMPTOPODYNQUANT
Symplectic topology and its interactions: from dynamics to quantization
| Coordinatore | TEL AVIV UNIVERSITY
Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie. |
| Nazionalità Coordinatore | Israel [IL] |
| Totale costo | 1˙787˙200 € |
| EC contributo | 1˙787˙200 € |
| Programma | FP7-IDEAS-ERC
Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) |
| Code Call | ERC-2013-ADG |
| Funding Scheme | ERC-AG |
| Anno di inizio | 2013 |
| Periodo (anno-mese-giorno) | 2013-10-01 - 2018-09-30 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
TEL AVIV UNIVERSITY
Organization address
address: RAMAT AVIV contact info |
IL (TEL AVIV) | hostInstitution | 1˙787˙200.00 |
| 2 |
TEL AVIV UNIVERSITY
Organization address
address: RAMAT AVIV contact info |
IL (TEL AVIV) | hostInstitution | 1˙787˙200.00 |
Mappa
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Obiettivo del progetto (Objective)
'The proposed research belongs to symplectic topology, a rapidly developing field of mathematics which originally appeared as a geometric tool for problems of classical mechanics. Since the 1980ies, new powerful methods such as theory of pseudo-holomorphic curves, Morse-Floer theory on loop spaces, symplectic field theory and mirror symmetry changed the face of the field and put it at the crossroads of several mathematical disciplines. In this proposal I develop function theory on symplectic manifolds, a recently emerged subject providing new tools and an alternative intuition in the field. With these tools, I explore footprints of symplectic rigidity in quantum mechanics, a brand new playground for applications of ``hard' symplectic methods. This enterprise should bring novel insights into both fields. Other proposed applications of function theory on symplectic manifolds include Hamiltonian dynamics and Lagrangian knots. Function theory on symplectic manifolds is fruitfully interacting with geometry and algebra of groups of symplectic and contact transformations, which form another objective of this proposal. I focus on distortion of cyclic subgroups, quasi-morphisms and restrictions on finitely generated subgroups including the symplectic and contact versions of the Zimmer program. In the contact case, this subject is making nowadays its very first steps and is essentially unexplored. The progress in this direction will shed new light on the structure of these transformation groups playing a fundamental role in geometry, topology and dynamics.'