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Infinite ECH capacities and obstructing Anosov flows
Geometry/Topology| Speaker: | Gabriel Beiner, UC Berkeley |
| Related Webpage: | https://math.berkeley.edu/~gbeiner/ |
| Location: | 2112 MSB |
| Start time: | Tue, Oct 13 2026, 2:10PM |
Description
The ECH capacities are a collection of invariants of symplectic 4-manifolds, defined using the theory of embedded contact homology. While these capacities have many applications to symplectic embeddings of convex domains, they remain poorly understood for more complicated symplectic manifolds. We will discuss recent work which shows the ECH capacities are infinite for many examples of interest, including all closed symplectic 4-manifolds and cotangent disk bundles of surfaces of genus at least two. The proof of the latter result passes through the theory of Anosov flows, and has applications to obstructing Anosov dynamics, which we will also discuss.