You are cordially invited to the seminar organized by the Department of Mathematics.
Speaker: Umut Varolgüneş (Boğaziçi University)
“From classical mechanics to symplectic rigidity (and back?)”
Abstract: Consider a particle moving in Euclidean space under the influence of a Hamiltonian energy function. All possible trajectories of this particle define a flow on the phase space R2 x …x R2, where we paired each position coordinate with its corresponding momentum coordinate. One can assign to each (oriented) patch of surface in the phase space its symplectic area: add up the signed areas of the projections to each R2 factor. The birth of symplectic geometry is the observation that any Hamiltonian flow preserves these symplectic areas. A symplectic manifold is a generalization of this phase space structure to spaces with more interesting topology, e.g. on a three holed torus a symplectic structure is equivalent to an area form. I will outline some recent results (including some of mine) in symplectic geometry, restricting myself to phase spaces and surfaces.
Date: Wednesday, 16 November 2022
Time: 15:40 GMT+3
Place: SA141 Mathematics Seminar Room