Alexander Kuznetsov: Homological algebraic geometry

The idea of studying the geometry of an algebraic variety through the structure of its derived category of coherent sheaves goes back to the pioneering works of Bondal and Orlov on the verge of the millennium. One of the central concepts of this approach is that of a semiorthogonal decomposition. In my talk I will overview the (rapidly developing) story of semiorthogonal decompositions, touching on some of its most fascinating aspects:
(1) Semiorthogonal components with interesting properties and their geometric significance;
(2) Categorical extensions of classical geometric constructions (homological projective duality, categorical joins and cones, categorical resolutions of singularities); and
(3) Completely new constructions such as categorical absorptions of singularities.
Slides: www.mathunion....