[鐗瑰埆鏁板?璁插骇绗?3鏈焆 Integrable systems and Gromov-Witten invariants
主 题: [鐗瑰埆鏁板?璁插骇绗?3鏈焆 Integrable systems and Gromov-Witten invariants
报告人: Liu Xiaobo, University of Notre Dame & Peking University
时 间: 2010-06-02 08:00 - 2010-06-30 18:00
地 点: 鍖椾含鍥介檯鏁板?鐮旂┒涓?績
Abstract: These lectures will provide an introduction to aspects of integrable systems which are related to Gromov-Witten invariants. An integrable hierarchy is a sequence of commuting flow equations. We will start from basic theories of KdV heirarchies, tau funtions and Virasoro constraints. We will then explain how these theories are applied to study intersection numbers on moduli spaces of stable curves, i.e. the Kontsevich-Witten theory. Such numbers are considered as the simplest Gromov-Witten invariants. Roughly Gromov-Witten invariants counts numbers of pseudo-holomorphic curves in symplectic manifolds. If time permits, we will also give a short introduction to Gromov-Witten invariants. No prior knowledge of integrable systems, symplectic geometry, and Gromov-Witten invariants are required. Basic knowledge of manifold theory and topology will be sufficient to follow the lectures.