Cel "The proposed research belongs to symplectic topology, a rapidly developingfield 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." Dziedzina nauki natural sciencesphysical sciencesquantum physicsnatural sciencesmathematicspure mathematicstopologysymplectic topologynatural sciencesmathematicspure mathematicsgeometrynatural sciencesphysical sciencesclassical mechanics Program(-y) 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) Temat(-y) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Zaproszenie do składania wniosków ERC-2013-ADG Zobacz inne projekty w ramach tego zaproszenia System finansowania ERC-AG - ERC Advanced Grant Instytucja przyjmująca TEL AVIV UNIVERSITY Wkład UE € 1 787 200,00 Adres RAMAT AVIV 69978 Tel Aviv Izrael Zobacz na mapie Rodzaj działalności Higher or Secondary Education Establishments Kontakt administracyjny Lea Pais (Ms.) Kierownik naukowy Leonid Polterovich (Prof.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych Beneficjenci (1) Sortuj alfabetycznie Sortuj według wkładu UE Rozwiń wszystko Zwiń wszystko TEL AVIV UNIVERSITY Izrael Wkład UE € 1 787 200,00 Adres RAMAT AVIV 69978 Tel Aviv Zobacz na mapie Rodzaj działalności Higher or Secondary Education Establishments Kontakt administracyjny Lea Pais (Ms.) Kierownik naukowy Leonid Polterovich (Prof.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych
