Program
Recent progress in cohomological field theories and mirror symmetry
Student No.:80
Time:Fri 16:30-17:30, Sep.21
Instructor:范辉军 Fan Huijun  
Place:Lecture Hall, Jin Chun Yuan West Bldg.
Starting Date:2018-9-21
Ending Date:2018-9-22

Abstract:
The Gromov-Witten (GW) theory, as the first cohomological field theory founded rigorously in mathematics, has been always the main research topic in symplectic geometry and mathematical physics since 90's of last centuary. In the first part of the lecture, I will give a simple description of GW theory and its role in numerical mirror symmetry conjecture and its application to the enumerate geometry. In the first 10 years of this centuary, people have found more interesting quantum invariants and intrinsic relations among them, for instance, the quantum singularity (FJRW) theory, LG/CY correspondence, wall-crosing phenomena, and their relation to various integrable systems. In recent time, there are more exciting breakthroughs in this field, including the computation of genus 2 GW invariants, GW-FJRW correspondence, and the algebraic geometry definition of the FJRW invariants. In the second half of the talk, I will report the recent exciting progress in this field.


About Professor Yuval Flicker:
Professor Fan is now working at Institute of Mathematical Sciences of Peking University, also the winner of the National Outstanding Youth fund.
His research interests include geometric analysis, symplectic geometry and mathematical physics related to quantum field theory and superstring theory.
Professor Fan and his cooperators made important progress on the quantum singularity theory of hypercurved singularities, solving the self-duality mirror-symmetry conjecture of ADE singularities and the generalized Witten conjecture of DE condition.


摘要:
格罗莫夫-威腾(Gromov-Witten)理论,作为第一个数学中被严格建立的上同调场论,自上世纪90年代一直是辛几何和数学物理中的主要研究课题。在讲座第一部分,我将简单描述GW理论和它在数值镜对称猜想中的角色以及它在计数几何中的应用。在本世纪头10年,人们在其中找到了更多的量子不变量和内蕴关系,比如,量子奇点(FJRW)理论,LG/CY对应,穿墙现象,和它们与诸多可积系统的关系。在近期,本领域中有更多突破,包括亏格2的GW不变量的计算,GW-FJRW对应,和FJRW不变量的代数几何定义。在讲座第二部分,我会报告这个领域中激动人心的进展。


主讲人简介:
范辉军,北京大学数学科学学院教授,北京大学国际数学中心博士生导师,国家杰出青年基金获得者。范辉军教授的研究方向为几何分析、辛几何以及与量子场论、超弦理论有关的数学物理。范辉军教授与合作者在超曲面奇点的量子奇点理论方面作出过重要工作,解决了关于ADE 奇点的自对偶镜像对称猜测以及DE 情形的广义Witten 猜测。