学术报告三

报告题目：A finite dimensional proof of the Verlinde formula

报 告 人：孙笑涛  教授 

报告时间：2021年6月11日（星期五）14:40-15:20

报告地点：育才校区国教中心2号楼211会议室

报告人简介：孙笑涛，天津大学数学学院院长，教授、博士生导师，教育部高等沐鸣数学专业教学指导委员会委员。主要从事代数几何的研究，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。

报告摘要：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 establishs 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.

                                    数学与统计学院       

计算机科学与工程学院/软件学院

                                    2021年6月10日