# Workshop on Gromov-Witten Invariants and Integrable Systems

December 28-30, 2018, USTC, Hefei

## 日程安排 (28-30研讨会, 30-31冬季学校)

### 12月29号 (星期六), 学术报告, 地点: 数学科学学院1308

09:20 ~ 10:10, 王芝兰

Title: BKP hierarchy, matrix integrals solution and Pfaffian point process

Abstract: Inspired by Okounkov's discovery of the relationship between KP hierarchy and determinant point process, we establish a relationship between BKP hierarchy and Pfaffian point process using neutral fermions. We further show that the matrix integrals solution of BKP hierarchy can also induce a certain Pfaffian point process. This is a joint work with Shi-Hao Li.

10:10 ~ 10:40, 茶歇

10:40 ~ 11:30, 黄民信

Title: Refined topological strings on compact Calabi-Yau spaces

Abstract: Refined topological string theory is motivated by Omega background in supersymmetric gauge theory. Previous works consider only non-compact Calabi-Yau spaces. In this talk we discuss a class compact elliptic Calabi-Yau spaces and compare the results with geometric calculations. The talk is based on parts of a work in progress with S. Katz and A. Klemm.

11:30 ~ 14:30, 午餐 (中科大教工餐厅) 和自由讨论

14:30 ~ 15:20, 张友金

Title: KdV 方程簇的超 tau-覆盖

Abstract: 我们构造了 KdV 方程簇的一个超 tau-覆盖，这一构造使得我们能够在同一个框架下研究 KdV 方程簇的哈密顿结构以及它的 Virasoro 对称之间的内在联系。我们也将这一构造推广到了更一般的可积系统的研究。

15:20 ~ 15:50, 茶歇

15:50 ~ 16:40, 刘思齐

Title: TBA

Abstract: TBA

16:40 ~ 17:30, 柯华忠

Title: On semisimplicity of quantum cohomology of $\mathbb{P}^1$-orbifolds

Abstract: For a $\mathbb{P}^1$-orbifold $\mathcal{C}$, we prove that its big quantum cohomology is generically semisimple. As a corollary, we verify a conjecture of Dubrovin for orbi-curves. We also show that the small quantum cohomology of $\mathcal{C}$ is generically semisimple iff $\mathcal{C}$ is Fano, i.e. it has positive orbifold Euler characteristic.

17:30 ~ 18:00, 自由讨论

18:00 ~ 20:30, 晚餐 (中科大东区专家楼餐厅)

### 12月30号 (星期日) 上午, 学术报告, 地点: 数学科学学院1308

9:00 ~ 9:50, 周坚

Title: Graph sums and applications

Abstract: Many problems in Gromov-Witten theory can be reduced to a sum over graphs, distiguished by various Feynman rules. We will talk about general facts about sums over graphs indepedent of the Feynaman rules. Some applications will be given to some special cases with specified Feynman rules.

9:50 ~ 10:20, 茶歇

10:20 ~ 11:10, 吴朝中

Title: On Virasoro symmetries for Drinfeld-Sokolov hierarchies

Abstract: We represent Virasoro symmetries for Drinfeld-Sokolov hierarchies with their tau functions.

11:10 ~ 12:00, 周春辉

Title: On a particular tau function of the Gelfand-Dickey hierarchy

Abstract: The Brezin-Gross-Witten (BGW) tau function is a tau function of the KdV hierarchy, which is uniquely determined by a “string-type” equation. This tau function arises in the weak coupling phase of the BGW model. In this talk, we define an analogous paritcular tau function for the Gelfand-Dickey hierarchy. Then we prove that this tau function satisfies a system of linear equations, constructed from the associated quantum W-algebra.

12:00 ~ 14:30, 午餐 (中科大教工餐厅)、自由讨论和研讨会 farewell

### 12月31号 (星期一) 9:00-12:00, 冬季课程: 从KdV方程谈起 (Part B), 授课人: 刘思齐教授, 地点: 数学科学学院1308

Scientific Committee

Yi Cheng, Youjin Zhang, Jian Zhou

Organizing Committee

Di Yang, Dafeng Zuo

Invited Speakers

Min-Xin Huang (中国科学技术大学）

Hua-Zhong Ke (中山大学)

Si-Qi Liu (清华大学)

Zhi-Lan Wang (中国矿业大学)

Chao-Zhong Wu (中山大学)

Youjin Zhang (清华大学)

Chunhui Zhou (中国科学技术大学)

Jian Zhou (清华大学)

E-mail: diyang@ustc.edu.cn

E-mail: dfzuo@ustc.edu.cn