Relative quantum cohomology and its application

Quantum cohomology has played an important role in the modern development of algebraic geometry and symplectic geometry. In this talk, we will begin with a quick review of quantum cohomology and its classical application: Kontsevich's formula for rational plane curves. Then we will give a construction of relative quantum cohomology ring which encodes the information of relative Gromov-Witten invariants. At last, we will talk about one enumerative application of relative quantum cohomology ring. This is based on joint work with Honglu Fan and Fenglong You.