题  目：Random partition meets mirror symmetry: the power of thermodynamic limit

内容简介：What is mirror symmetry? Mirror symmetry is a relation between generating function of Gromov-Witten invariants (A-model) and period integrals (B-model). From viewpoint of gauge theory and instanton counting, it is a duality between Nekrasov partition function and Seiberg-Witten prepotential. In this talk, I will discuss new dualities appearing in 5d N = 1 Sp(N) gauge theory with N_f (≤2N + 3) flavors and explain the computations about Nekrasov partition function based on topological vertex algorithm of 5-brane web with O5-plane which corresponds to Sp(N) geometry. With the help of random partition technique, Nekrasov partition function can be rewritten in terms of profile function, after taking thermodynamic limit and functional derivatives, the saddle point equation can be derived for the profile function. By introducing the resolvent, the corresponding Seiberg-Witten geometry and boundary conditions are derived and the relations with the prepotential in terms of the cycle integrals are discussed. They coincide with those directly obtained from the dual graph of the 5-brane web with O5-plane. This agreement gives further evidence for mirror symmetry which relates Nekrasov partition function with Seiberg-Witten curve in the case with orientifold plane. This is joint work with Futoshi Yagi.

报告人：李晓斌   副研究员（西南交通大学）

报告人简介：李晓斌博士毕业于四川大学，现任教于西南交通大学数学学院。主要研究整体微分几何中与轨道流形相关的拓扑不变量（如Gromov-Witten不变量等），这是代数几何、辛拓扑与数学物理的交叉。主要研究基于Gromov-Witten不变量的Ruan猜想（又称爬行变换猜想，英文名为Crepant Transformation Conjecture）及广义Nekrasov猜想，其研究工作得到了国家自然科学基金委及国家留学基金委的资助。李晓斌博士在国内外多个研究机构访问研究，协助组织过多个学术活动。他为MathSciNet及Zbmath撰写了70余个具有学科介绍性的数学评论，给读者们一个清晰的整体图形。

时  间：2023年4月12日（周三）下午 15：00 始

地  点：暨南大学石牌校区教学楼A513

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信息科学技术学院

2023年3月31日