Colloquium Schedule for 1999-2000 |

Frobenius manifolds and quantum cohomology


Professor Alexander Kabanov
ETH - Zurich




A Frobenius manifold is a complex manifold with a flat metric and a compatible fiberwise multiplication on the tangent bundle. Frobenius manifolds appear in very different situations: for example, in ''counting'' curves on smooth projective varieties, and in connection with integrable hierarchies. They produce a framework for studying the mirror phenomenon. In my talk I will introduce Frobenius manifolds, and explain their connection with the quantum cohomology. I will also describe the classification of one-dimensional formal Frobenius manifolds, and a change of coordinates formula on the space parameterizing certain Frobenius manifolds.