Time: 14:00-15:45, Wednesday, July 2 2025
Venue：E10-212
Speaker: Zhitong Su, Hunan Normal University
Biography: Zhitong Su received his Ph.D. from Rutgers University–Newark in 2022, under the supervision of Professor Xiaowei Wang. From 2022 to 2024, he conducted postdoctoral research at Sun Yat-sen University, working with Professor Changzheng Li. In 2025, he joined Hunan Normal University as a lecturer. His research interests lie in geometry, with a focus on quantum cohomology and the Gamma conjectures in Gromov-Witten theory, as well as the problem of isometric embeddings in Riemannian geometry. He has published a research article in the international journal Asian J. Math.
Title: Quantum cohomology, quantum D-modules, and Gamma conjectures
Abstract: The two lectures will briefly explore the connections between Gromov-Witten theory (quantum cohomology) and integrable systems. As one of the central conjectures in this area, I will introduce the Gamma conjectures proposed by Galkin-Golyshev-Iritani in their 2016 Duke article, along with our recent work related to them. A helpful introduction to the topic can be found in Iritani's article, "Gamma Classes and Quantum Cohomology," in the Proceedings of the ICM 2022.
In Lecture 1, we will introduce quantum cohomology, quantum differential equations (quantum D-modules), and the associated quantum connections. These concepts will be presented informally but with a focus on capturing the essentials. We will also discuss several important and interesting examples.
In Lecture 2, we will present the Gamma conjectures for Fano manifolds. To set the stage, we will define Givental's J-function, the fundamental solutions of the quantum connection (for Fano varieties), and the Gamma class. I will briefly summarize the known results for Gamma Conjectures I and II, and introduce our recent contributions in this direction. This is joint work with Sergey Galkin, Jianxun Hu, Hiroshi Iritani, Huazhong Ke, and Changzheng Li.
