报告题目： A theory of counting surfaces in projective varieties

主  讲 人：蒋云峰 教授

单      位：美国堪萨斯大学

时      间：2024年6月18日 10：00-12：00

地      点：数学与统计学院106

摘      要：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.

简      介：蒋云峰，美国堪萨斯大学教授，研究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 Journal of differential geometry, Journal of algebraic geometry, Advances in Mathematic，Journal Reine Angew Math，Inter.Math.Res.Notices，Math. Annalen，Math.Research Letters 等著名数学杂志发表论文多篇，是国际知名的代数几何专家。