We can define a Tamarkin category for an open set in a cotangent bundle using microlocal geometry of sheaves. Then it is known that the categorical dimension, which is also called the Chiu-Tamarkin invariant, of the Tamarkin category is a symplectic invariant of the open set. We will explain some geometric applications of the categorical dimension, including symplectic capacities and a Viterbo isomorphism. Part of the talk is based on a joint work with Christopher Kuo and Vivek Shende.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/12424