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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 |
Description
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.)