Marcello Bernardara - Semiorthogonal Decompositions as Markings and Autoequivalences

Explore the concept of markings in triangulated categories and their role in lifting autoequivalences in this hour-long lecture. Delve into the definition of a marking as a choice of semiorthogonal decompositions and examine how this notion, combined with spherical CY functors, can be applied to transfer autoequivalences between triangulated categories. Discover the categorical framework underlying Macmullen's construction of special automorphisms of rational surfaces and learn about its potential extension to non-commutative examples. Gain insights into this ongoing research, conducted in collaboration with E. Macrì, as presented by Marcello Bernardara at the Hausdorff Center for Mathematics.