Categorical dimension in microlocal geometry of cotangent bundles

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.