Geometry and Physics Seminar: Andrei Caldararu

I shall present results of work with Arinkin and Hablicsek which allow us to understand the Frobenius push-forward of the de Rham complex as the structure sheaf of a twisted derived intersection. Similar considerations also apply for twisted de Rham complexes, yielding results which have applications in singularity theory and in the study of matrix factorizations. Using our theorems we recover and strengthen earlier results of Deligne-Illusie, Barannikov-Kontsevich, and Sabbah. Our approach gives a new point of view on recent works of Joyce et al, generalizing results of Behrend, on understanding the holomorphic Fukaya-Floer homology.