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
Abstract:
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.