Representation Theory and Mathematical Physics Seminar: Matrix Factorisation for Morse-Bott functions

Seminar | November 28 | 4-5 p.m. | 891 Evans Hall

 Constantin Teleman, UC Berkeley

 Department of Mathematics

Matrix Factorizations were introduced by Eisenbud to study minimal resolutions of Cohen-Macaulay modules. The notion was rediscovered from a physics perspective, where such factorizations appeared as boundary conditions for topological quantum field theory, and led to the (curved) deformation theory of the category of coherent sheaves on complex manifolds. An important stability result here is the Knoerrer periodicity theorem, the invariance of the MF category under Cartesian crossings with non degenerate quadratic functions. I will describe a generalization of this to Morse-Bott functions. The answer involves the full Gerstenhaber structure on the Hochschild complex of a manifold, instead of the more commonly used Lie structure.