糖心原创

Project description

Mirror symmetry is a duality which equates two completely different types of geometries, called the A-model and the B-model, of two different spaces. Mirror symmetry predicts that the A-model (resp. the B-model) of a given space is equivalent to the B-model (resp. the A-model) of its mirror space in a highly non-trivial way. Mirror symmetry has made numerous surprising predictions that turn out to be true. The A-model object that we study in this project is Gromov--Witten theory, which is one of the first modern curve counting theories in enumerative geometry.

In this project, we will use the degeneration technique in algebraic geometry to study Gromov--Witten theory and mirror symmetry. It includes questions like structures of relative Gromov--Witten theory, relative mirror symmetry and applications and connections to other aspects of mirror symmetry and enumerative geometry.