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Seminar
FIELD Math:Topology
DATE November 05 (Fri), 2021
TIME 16:00-17:30
PLACE Online
SPEAKER  
HOST Choa, Dongwook
INSTITUTE University of Augsburg
TITLE [GS_M_Topo] A comparison of two symplectic capacities.
ABSTRACT This talk is about work in progress. A symplectic manifold is a manifold $M$ equipped with a two form $\omega$ which is closed and nondegenerate. A symplectic capacity is a map from the class of symplectic manifolds to $[0,\infty]$, which satisfies some assumptions. A key idea is that symplectic capacities can obstruct the existence of symplectic embeddings between manifolds. Examples of such capacities are the Lagrangian capacity $c_L$ and the capacities $c_k$ coming from $S 1 $-equivariant symplectic homology. It is conjectured that for a Liouville domain $(X,\lambda)$ (a special type of symplectic manifold) we have the inequality $c_L(X,\lambda) \leq \inf_{k \in \N} c_k(X,\lambda)/k$. Our goal with this talk is to present the necessary definitions to understand this statement, a sketch of how the proof should be and if time allows some implications of this statement.
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