Speaker: Sergey Galkin

Title: Towards the unified symmetry

Date: Dec 13, 2011, 16:00 - 19:00

Place: SFB647 Seminar "Raum - Zeit - Materie" at Freie Universitaet, Berlin

Consider a finite group G of symplectic automorphisms of K3 surface S. Mukai have shown that representation of this group on cohomology of the surface is a pullback of the standard 24-dimensional representation of Mathieu group, and unfortunately group G should have 5-dimensional invariant subspace. On this example I am going to tackle the following question: how to redefine the notions of "symmetry" and "homology" in order to make the natural representation of symmetry on homology more irreducible? This is a joint with Ludmil Katzarkov. We consider two mathematical extensions of the symmetry - to moduli spaces of sheaves and to derived categories. Some of our answers look arguably similar to the recent work of Gaberdiel, Hohenegger and Volpato that characterizes symmetries of super-conformal field theories.