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### Frobenius manifolds and integrable equations of KdV-type.

**Special Events**

Speaker: | Motohico Mulase, UC Davis |

Location: | 593 Kerr |

Start time: | Thu, Jan 22 2004, 3:10PM |

Last week Albert gave the definition of Frobenius algebras. A Frobenius manifold is a (differential) manifold whose tangent space at every point is a Frobenius algebra. Frobenius manifold structures arise in many different contexts in mathematics, including 1. Gromov-Witten invariants of a symplectic manifold and the quantum cohomology; 2. Deformations of complex structures of a Calabi-Yau manifold; 3. Deformations of isolated hypersurface singularities; 4. Stable manifolds of integrable hierarchies. The relation between 1 and 2 forms the mathematical foundation of now celebrated "Mirror Symmetry." In this talk, I will explain how the Frobenius manifold structures naturally arise from integrable equations of KdV-type, and observe that the structures are identical to those appearing in the singularity theory of complex algebraic geometry. I will focus on just one illustrative example to make exposition easy to understand. (I hope.)