Functoriality in Gromov-Witten Theory and Beyond

University Of Utah, Salt Lake City UT

Investigators

Abstract

The proposed research lies on the interaction between algebraic geometry and mathematical physics. Specifically, it concerns the Gromov-Witten (GW) theory and variation of Hodge structures (VHS) on one side and birational geometry, algebraic cobordism, and mirror symmetry on the other. The main themes of the proposal are the functoriality of GW theory under crepant transformations and the extended functoriality of GW and VHS under extremal transitions (also known as space-time topology change in the physics literature). Gromov-Witten theory lies in the intersection of many exciting research areas in mathematics and physics. On the one hand, the theory itself has remarkable structures, both established and conjectural. Investigating these structures requires some new insights and technical tools and input from other areas. This provides a lot of interesting problems for classical subjects in mathematics. On the other hand, these new insights and technical tools help to discover deep relations and connections between existing mathematics and theoretical physics, especially the topological string theory.