学术报告：A finite dimensional proof of the Verlinde formula
发布时间：2021-06-09 浏览次数：253
报告人：孙笑涛
报告时间：2021年6月11日下午14:00-14:40
报告地点：广西师范大学雁山图书馆204第一会议室
报告题目：A finite dimensional proof of the Verlinde formula
报告人简介：孙笑涛，天津大学数学学院院长，教授、博导，教育部高等学校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科学基金资助，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.