15:30
Gopakumar-Vafa invariants of local curves
Abstract
In the 1990s, physicists introduced an ideal way to count curves inside a Calabi-Yau 3-fold, called the Gopakumar-Vafa (GV) theory. Building on several previous attempts, Maulik-Toda recently gave a mathematical rigorous definition of the GV invariants. We expect that the GV invariants and the Gromov-Witten (GW) invariants are related by an explicit formula, but this stands as a challenging open problem. In this talk, I will explain recent mathematical developments on the GV theory, especially for local curves, including the cohomological chi-independence theorem and the GV/GW correspondence in a special case.
15:30
How to make log structures
Abstract
I will speak about my work with Helge Ruddat on how to construct explicitly log structures and morphisms. I will also discuss some motivation. I will try to stay informal and assume no prior knowledge of log structures.
Sometimes artists become better known for their lifestyle or fashion tastes than the work without which we wouldn't know or care about them - Van Gogh, Bowie, even Taylor Swift. Jim Morrison of the Doors fits that bill, in his case for his death and grave as much as his life. But he and the band wrote some songs. That's where it all starts and ends.