A theory of counting surfaces in projective varieties


主讲人:蒋云峰 美国堪萨斯大学教授




主讲人介绍:蒋云峰,堪萨斯大学教授,研究方向为代数几何和数学物理,特别是Gromov-Witten理论和Donaldson-Thomas理论,以及与双有理几何,辛拓扑,几何表示论,枚举组合,S-对偶猜想和镜面对称间的联系。科研成果丰硕,在Adv. Math., JDG, JAG, IMRN, Math. Ann. 等著名数学杂志发表论文多篇,是国际著名的代数几何专家。

内容介绍:The theory of enumerative invariants of counting curves (Riemann surfaces) in projective varieties has been an important theory in the last decades. The enumerative invariants were motivated by theretical physics---string theory and gauge theory, and include Gromov-Witten theory, Donaldson-Thomas theory and more recently Vafa-Witten theory. It is hoped that there may exist a theory of counting algebraic surfaces in projective varieties. A theory of counting surface in a Calabi-Yau 4-fold has been constructed using Donaldson-Thomas theory of 4-folds. In this talk I will try to give evidences of a counting surface theory using stable maps, and explain why it is difficult to construct the counting surface invaraints.