Introduction and prospects of topological recursion

Topological recursion is a universal recursive formalism that connects many branches in mathematical physics, such as enumerative geometry, algebraic geometry, integrable hierarchy, matrix models, 2d gravity, and more. In the first half of this talk, I will give a pedagogical overview of topological recursion and present simple examples from which we learn how topological recursion works. Then in the second half, I will present some ongoing research projects as well as a few future directions in topological recursion.