Algebra/Topology Seminar by Anthony Blanc

Abstract: I will report on a joint work with Katzarkov and Pandit about the deformation theory of k-linear dg-categories for a field k. In general, the Hochschild cohomology complex parametrizes curved A_infty deformations. After the work of Lurie, we show that under boundedness and the existence of a compact generator, every formal deformation is uncurved and possesses a compact generator. The proof uses a new description of the space of deformations in terms of !-group actions on the category.