The concept of a matrix factorization was originally introduced by
Eisenbud to study syzygies over local rings of singular hypersurfaces.
More recently, interactions with mathematical physics, where matrix
factorizations appear in quantum field theory, have provided various new
insights. I will explain how matrix factorizations can be studied in
the context of noncommutative algebraic geometry based on differential
graded categories. We will see the relevance of the noncommutative
analogue of de Rham cohomology in terms of classical singularity theory.
Finally, I will outline how the Kapustin-Li formula for the
noncommutative Serre duality pairing (originally computed via path
integral methods) can be mathematically explained using a combination of
homological perturbation theory and local duality. This talk is partly
based on joint work with Daniel Murfet. ## Talk:Download video. |

Yale 2013 >