| Speaker: | Tony Yue-Yu (Laboratoire de Mathematiques d'Orsay, Universite Paris-Sud) |
|---|---|
| Title: | The Frobenius structure conjecture in dimension two |
| Date (JST): | Tue, Feb 27, 2018, 15:30 - 17:00 |
| Place: | Seminar Room B |
| Abstract: | The Frobenius structure conjecture is a conjecture about the geometry of rational curves in log Calabi-Yau varieties proposed by Gross-Hacking-Keel. It was motivated by the study of mirror symmetry. It predicts that the enumeration of rational curves in a log Calabi-Yau variety gives rise naturally to a Frobenius algebra satisfying nice properties. In a joint work with S. Keel, we prove the conjecture in dimension two. Our method is based on the enumeration of non-archimedean holomorphic curves developed in my thesis. We construct the structure constants of the Frobenius algebra directly from counting non-archimedean holomorphic disks. If time permits, I will also talk about compactification and extension of the algebra. |
