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:2018-9-21

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.


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。