Geometry of 2d topological field theories and integrable hierarchies

In this talk, I will explain a mathematical formulation of 2d topological field theories making use of integrable hierarchies, which is a framework initiated by B. Dubrovin and developed by many other mathematicians. The talk is divided into two parts. The first 45 minutes is a gentle introduction on how the mathematical structure called Frobenius manifolds naturally appears from topological field theories. The remaining part of the talk is devoted to explaining relationships between Frobenius manifolds and integrable hierarchies via the example of the KdV hierarchy.