Forschungsseminar: Komplexe Geometrie

13.12.2013 Özgür Ceyhan (University of Luxembourg)

Quantum cohomology of real varieties

Abstract: It has long been suspected that there should be an algebraic structure in open-closed string theory arising from the enumeration of real rational curves/discs with Lagrangian boundary condition, that is analogous to quantum cohomology in complex geometry. By contrast with the spectacular achievements of closed string theory in complex geometry, the effects of open-closed string theory in real algebraic geometry remained deficient.
This talk is devoted to a plausible approach to this gap: Gromov-Witten-Welschinger (GWW) classes and their applications. In particular, Horava's definition of quantum cohomology of real algebraic varieties and a recursive formula for GWW-classes proposed by Jake Solomon will be discussed.