Analytical foundations for moduli spaces arising from geometric elliptic PDEs

Abstract:

The Moduli spaces that parametrise the finite energy solution to elliptic partial differential equations from physics provide deep information  for geometry and physics at both small and  large scales. In this talk, I will explain some of my recent work with Bohui Chen and Anmin Li  on foundation of Gromov -Witten theory. The virtual technique developed can be applied to more general  geometric elliptic PDEs to  extract geometric invariants. I will give a brief and accessible overview of this virtual technique.