NCTS(South)/ NCKU Math Colloquium | |
| DATE | 2011-12-07¡@15:00-17:00 |
| PLACE | R204, 2F, NCTS, NCKU |
| SPEAKER | ±iÃh¨} ±Ð±Â¡]Assistant Professor, Department of Mathematics, HKUST¡^ |
| TITLE | On higher genus Gromov-Witten invariants and Fan-Jarvis-Ruan-Witten invariants |
| ABSTRACT |
Gromov-Witten (GW) theory enumerates numbers of Riemann surfaces in a complex manifold. Counting positive-genus curves in a compact Calabi-Yau manifold is a difficult problem. Recently we use the Guffin & Sharpe's idea to produce an equivalent but much linear theory for all positive genera. This gives an algebraic geometric determination of g=1 GW invariants of quintic threefold, simplifying Aleksey Zinger's analytic approach.
Our technique, ``Kiem-Li cosection localization", can also be applied to give an algebraic geometric construction of Fan-Jarvis-Ruan-Witten invariants, which are symplectic invariants of singularities and are defined analytically. It is joint work with Jun Li and Weiping Li. |