Gromov-Witten theory under extremal transitions and birational transformations

University Of Utah, Salt Lake City UT

Investigators

Abstract

Gromov-Witten (GW) theory lies in the intersection of many exciting research areas in mathematics and physics. Roughly speaking it counts the number of curves meeting prescribed conditions in a geometric object called a variety. On the one hand, the theory itself has remarkable structures, both established and conjectural. Investigating these structures requires some new insights and technical tools 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. This project will advance understanding in this active area of research. The project includes training of graduate students and postdocs, as well as international collaborations. This research project lies on the intersection of algebraic geometry and mathematical physics. Specifically, it concerns the Gromov-Witten theory and variation of Hodge structures (VHS) on one side and birational geometry and mirror symmetry on the other. The main themes of the project are the study of GW theory of bundles and blowing-ups and the extended functoriality of GW and VHS under extremal transitions (also known as space-time topology change in the physics literature). The relations between the crepant transformation conjecture in GW theory and the Landau-Ginzburg / Calabi-Yau correspondence will also be studied.