Witten equation and singularity theory
主 题: Witten equation and singularity theory
报告人: 范辉军 教授 (北大数学学院)
时 间: 2006-12-15 下午 2:30 - 3:30
地 点: 理科一号楼 1114（数学所活动）
In this talk, Ｉ will introduce my recent work with my cooperators on Witten equation. Witten equation was introduced by E. Witten to generalize his famous Witten conjecture, which was solved by Konstevich more than ten years ago. Our recent work shows that Witten equation is very important to construct the right module space theory-module theory of spin curves. It turns out that the Picard-Lefschetz theory of singularities can be recovered in the level of module space. Also the construction of virtual cycle gives a rigorous foundation to the generalized Witten conjecture. This theory also occures as the A model of the Laudau_ginzeburg theory which corresponds to the B model which gives the orbifold Frobenious algebra. Recently we can calculate the G-Frobenious algebra in A model and shows the mirror symmetry proposed by Intriligator-Vafa. Another interesting part of the Witten equation is that it brings an suitable question for the study of singularities of semi-linear elliptic equations.
