January 27, 2023

**Title:** *Recognition of objects and representability of symplectic capacities*

**Speaker:** Yann Guggisberg

In this talk, I will define symplectic capacities, which are numerical invariants of symplectic manifolds. I will then present some examples, and provide some answers to questions asked by K. Cielibak, H. Hofer, J. Latschev, and F. Schlenk.

First, I will show that for some symplectic categories, the generalized symplectic capacities recognize objects. This means that if all the capacities agree on two symplectic manifolds, then they are symplectomorphic. Hence, the generalized capacities on that category are a complete invariant.

Next, I will give some concrete examples of capacities that cannot be represented by a target-embedding capacity.

The talk is based on joint work with F. Ziltener.