【系综合学术报告】&【荷思系友报告】2026年第3期

报告人: 王哲博士 （日本理化学研究所）

报告题目: Quantum KdV hierarchy and vertex algebra

报告时间: 2026年4月24日13:30—14:10

报告地点: 文北楼102

报告摘要: The important problem of quantization of the KdV hierarchy with respect to its first Hamiltonian structure is addressed by the framework of symplectic field theory. There are many different ways to construct quantization of dispersionless KdV hierarchy: by using boson-fermion correspondence, using symplectic field theory for a disk, using double ramification hierarchies or using meromorphic differential hierarchies. In this talk, I will present an algebraic construction of quantum dispersionless KdV hierarchy using the Heisenberg vertex algebra. I introduce the notion of non-associative Weyl quantization, and apply it to construct the quantum Hamiltonians of dispersionless KdV hierarchy. I give explicit formula for computing these quantum Hamiltonians and study their properties.

【系综合学术报告】2026年第12期

报告人: 程家豪副教授（南昌航空大学）

报告题目: Brace B infinity algebras associated with Hopf algebroids

报告时间: 2026年4月24日14:20—15:00

报告地点: 文北楼102

报告摘要: In this talk, we apply the operadic modeling of brace B infinity algebras, as developed by Gerstenhaber and Voronov, to the context of Hopf algebroids in the sense of Xu. As an application of this framework, we examine two specific brace B infinity algebras derived from Lie algebra pairs, and reveal previously obscured relationships between them. One of these is the brace B infinity algebra governing deformations of algebraic dynamical twists, while the other arises from quantum groupoid comprised of particular invariant differential operators. This is a joint work with Zhuo Chen and Yu Qiao.

【系综合学术报告】&【荷思系友报告】2026年第4期

报告人: 周春辉教授（中国科学技术大学）

报告题目: Linear combinations of flows in almost duality

报告时间: 2026年4月24日15:10—15:50

报告地点: 文北楼102

报告摘要: In this talk, we will give an explicit formula on the relation between the flows of the principal hierarchies of a Frobenius manifold and its almost dual, which leads to the relation between the genus-zero tau functions. This result also gives an explanation for the choice of calibrations in almost dual side of the KdV hierarchy and the Toda hierarchy in lack of non-trivial Euler vector fields.

【系综合学术报告】&【荷思系友报告】2026年第5期

报告人: 杨迪教授（中国科学技术大学）

报告题目: The Camassa--Holm equation in rank-1 F-CohFTs

报告时间: 2026年4月24日16:00—16:40

报告地点: 文北楼102

报告摘要: Among 1-component bi-Hamiltonian integrable equations, the KdV equation and the Camassa-Holm equation are two of the most significant ones. The last 30 years have witnessed the discovery of deep relations between integrable hierarchies and topology of the moduli spaces of stable curves. These deep relations were first manifested in the Witten-Kontsevich theorem, stating that certain generating series of psi-class intersection numbers satisfy the KdV hierarchy. Around 2014, Buryak introduced the notion of Double Ramification (DR) hierarchy. In this talk, we perform bihamiltonian test for the DR hierarchy associated to rank-1 F-CohFT, and conjecture that the ones that are bihamiltonian form a 2-parameter family. In particular, we conjecture that there is a unique curve in the 2-parameter family such that the corresponding DR hierarchy is Miura equivalent to the Camassa–Holm hierarchy. To the best of our knowledge, this is first time that a connection of the Camassa–Holm hierarchy to the topology of the moduli space of stable curves is found. The talk is based on a joint work with A. Buryak and J. Xu.

邀请人：张友金 刘思齐