Non-commutative abelian surfaces I: constructions

Location: 11th Floor Lecture Hall Speaker Xiaolei Zhao, UC Santa Barbara Session Chair Anthony Várilly-Alvarado, Rice University Abstract Examples of non-commutative K3 surfaces arise from semiorthogonal decompositions of the bounded derived category of certain Fano varieties. The most interesting cases are those of cubic fourfolds and Gushel-Mukai varieties of even dimension. In this talk we will construct non-commutative abelian surfaces as equivariant categories of the derived category of K3 surfaces which specialize to Kummer K3 surfaces. This is joint work in preparation with Arend Bayer, Alex Perry and Laura Pertusi.