|Speaker:||Ed Segal (London Imperial college)|
|Title:||The Calabi-Yau/Landau-Ginzburg correspondence for B-branes|
|Date (JST):||Mon, Jul 26, 2010, 14:00 - 17:00|
|Place:||Seminar Room A|
The CY/LG correspondence is a physical prediction of the equivalence between two 2d quantum field theories - the sigma model on a Calabi-Yau hypersurface, and the Landau-Ginzburg model on an affine orbifold. In
particular it predicts an equivalence between the categories of branes in the B-twist of each theory, which means that the derived category of sheaves on the hypersurface should be the same as a certain category of matrix factorizations. This equivalence was proven in a celebrated theorem of Orlov. I will discuss a new proof of this equivalence, more in line with the physical arguments, and partially based on work of Hori, Herbst and Page.
Part I: This will be an introduction to the mathematical formulation of the categories of B-branes and of the equivalence.
Part II: I'll go into more detail about the proof. In particular we'll see the equivalence as factoring into two steps, the first comes from a change of GIT quotient, and the second from Knorrer periodicity.