Recording: https://disk.pku.edu.cn:443/link/30CE439C8E7E695A13394DCD1E8D74AA
Valid Until: 2024-11-30 23:59
Abstract: I will describe the following series of results, partly obtained in collaboration with A. Rosly, about derived categories of coherent sheaves on complex manifolds. For a general complex torus X, D^b(Coh-X) has a semiorthogonal decomposition, and it is not equivalent to D^b_{coh}(O_X-mod). There is a twist-closed DG-enhancement of the latter category by dbar-superconnections for any smooth compact complex manifold. This DG-enhancement allows us to define Bott-Chern cohomology for any object of D^b_{coh}(O_X-mod), in particular, for a coherent sheaf. If time permits, I will describe the extension of the enhancement theorem to the case of non-compact complex manifolds and applications to constructing the moduli space of objects in the above category.
Bio: Prof. Bondal received his Ph.D. in Steklov Mathematical Institute of RAS in Moscow in 1989. He was an associate professor at Moscow State University from 1990 to 1994. Prof. Bondal joined Steklov Institute in 1994, where he was promoted to a Leading Researcher. He was an invited speaker at the International Congress of Mathematicians in Beijing in 2002. His research interests include Algebraic and Complex Geometry, Homological Algebra and Representation Theory. Currently, he is visiting the Institute for Physics and Mathematics of the Universe, Tokyo University, Japan.
