Frobenius structures on Hurwitz spaces and confluent KZ equations

The Hurwitz space is the moduli space of meromorphic functions on the Riemann surface. Dubrovin constructed Frobenius structures on Hurwitz spaces by using the theory of K. Saito. In this talk, we give the equivalence between $\mathcal{D}$-modules of Frobenius structures on Hurwitz spaces and confluent KZ equations. We also discuss the representation of framed braid groups which comes from the monodromy representation of confluent KZ equations.