EVENT DETAILS AND ABSTRACT

Title: Counting embedded curves in Calabi-Yau threefolds and Gopakumar-Vafa invariants
Speaker: Yong-Geun Oh
Speaker Info: Wisconsin
Brief Description:
Special Note:
Abstract:

The Gopakumar-Vafa BPS invariant is an integer invariant of the cohomology of D-brane moduli spaces on Calabi-Yau threefolds in string theory. By a conjectured relationship to Gromov-Witten theory, it is expected that the invariant coincides with the "number" of embedded (pseudo)holomorphic curves (the Gopakumar-Vafa conjecture). In this talk, we will explain the speaker's recent result that the latter integer invariants can be defined for a generic choice of compatible almost complex structures. We will also discuss the corresponding wall-crossing phenomenon and some open questions towards a complete solution to the Gopakumar-Vafa conjecture.