A theory of counting surfaces in projective varieties

主讲人：蒋云峰 美国堪萨斯大学教授

时间：2024年6月14日10：30

地点：三号楼332室

举办单位：数理学院

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.