万博体育max手机登陆app-手机版下载

设为首页| 加入收藏| English|

学术讲座

学术讲座 当前位置: 首页 学术讲座

首师代数论坛系列报告(十二)

发布日期:2020-12-01点击量:


报告人:孙笑涛 教授(天津大学)

题目:A finite dimensional proof of the Verlinde formula

时间:2020年12月9日(周三)14:00-15:00

腾讯会议ID:572 9813 7220

会议链接:https://meeting.tencent.com/s/ai2R9IurQ07o

摘要

A formula of dimensions for the spaces of generalized theta functions on moduli spaces of parabolic bundles on a curve of genus g, the so called Verlinde formula, was predicted by Rational Conformal Field Theories. The proof of Verlinde formula by identifying the spaces of generalized theta functions with the spaces of conformal blocks from physics was given in last century mainly by Beauville and Faltings (so called infinite dimensional proof). Under various conditions, many mathematicians tried to give proofs of Verlinde formula without using of conformal blocks, which are called finite dimensional proofs by Beauville. In this talk, we give unconditionally a purely algebro-geometric proof of Verlinde formula.

Our proof is based on two recurrence relations, one of which establishes an inductive procedure for the genus of curves, another one provides an inductive procedure for the number of parabolic points. This is a joint work with Mingshuo Zhou.

报告人简介

孙笑涛,天津大学数学学院院长,主要从事代数几何的研究,主要研究方向为模空间理论,包括曲线上向量丛模空间的退化等。2000年获得国家杰出青年基金资助,2012年获国家自然科学二等奖,2013年获第十四届陈省身数学奖。主要学术成绩包括:发现并证明Frobenius同态与稳定向量丛之间的重要联系;证明任意秩广义theta函数的分解定理和Seshadri-Nagaraj猜想;证明模空间极小有理曲线与Hecke曲线的等价性;与人合作证明Gieseker关于平展基本群与D-模关系的猜想等。


论坛组织者

童纪龙 唐 舜 陈红星

举办单位

首都师范大学 数学科学学院 交叉科学研究院