Title: Virasoro Constraints for Topological Recursion

Abstract: Topological recursion on spectral curves provides a powerful framework connecting enumerative geometry and integrable hierarchies. In this talk, we study this connection through the Virasoro constraints. Specifically, we derive the ancestor Virasoro constraints satisfied by the topological recursion. Under certain conditions, we also investigate the corresponding descendent Virasoro constraints. As an application, we present the Virasoro constraints for the deformed negative r-spin theory. This talk is based on joint work with Shuai Guo.