Shinnosuke Okawa, Moduli Space of Semiorthogonal Decompositions

Semiorthogonal decomposition (SOD) is a central notion in the study of triangulated categories. In particular, SODs of the bounded derived category of coherent sheaves of a variety (SODs of the variety, for short) have profound relations to its geometry. In this talk I discuss the moduli functor which classifies SODs of the fibers of smooth projective morphisms. The main result is that it is an algebraic space which is locally etale over the target of the morphism. I will explain the main points of the proof, various applications and open problems. This talk is based on the joint work arXiv:2002.03303 with Andrea Ricolfi and Pieter Belmans.