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Tuesday Seminar on Topology
Seminar information archive ～04/26｜Next seminar｜Future seminars 04/27～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2019/12/17
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Kei Irie (The University of Tokyo)
Symplectic homology of fiberwise convex sets and homology of loop spaces (JAPANESE)
Kei Irie (The University of Tokyo)
Symplectic homology of fiberwise convex sets and homology of loop spaces (JAPANESE)
[ Abstract ]
For any (compact) subset in the symplectic vector space, one can define its symplectic capacity by using symplectic homology, which is a version of Floer homology.
In general, it is very difficult to compute or estimate this capacity directly from its definition, since the definition of Floer homology involves counting solutions of nonlinear PDEs (so called Floer equations). In this talk, we consider the symplectic vector space as the cotangent bundle of the Euclidean space, and show a formula which computes symplectic homology and capacity of fiberwise convex sets from homology of loop spaces. We also explain two applications of this formula.
For any (compact) subset in the symplectic vector space, one can define its symplectic capacity by using symplectic homology, which is a version of Floer homology.
In general, it is very difficult to compute or estimate this capacity directly from its definition, since the definition of Floer homology involves counting solutions of nonlinear PDEs (so called Floer equations). In this talk, we consider the symplectic vector space as the cotangent bundle of the Euclidean space, and show a formula which computes symplectic homology and capacity of fiberwise convex sets from homology of loop spaces. We also explain two applications of this formula.
