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

内容簡介：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.

報告人：李曉斌   副研究員（西南交通大學）

報告人簡介：李曉斌博士畢業于四川大學，現任教于西南交通大學數學學院。主要研究整體微分幾何中與軌道流形相關的拓撲不變量（如Gromov-Witten不變量等），這是代數幾何、辛拓撲與數學物理的交叉。主要研究基于Gromov-Witten不變量的Ruan猜想（又稱爬行變換猜想，英文名為Crepant Transformation Conjecture）及廣義Nekrasov猜想，其研究工作得到了國家自然科學基金委及國家留學基金委的資助。李曉斌博士在國内外多個研究機構訪問研究，協助組織過多個學術活動。他為MathSciNet及Zbmath撰寫了70餘個具有學科介紹性的數學評論，給讀者們一個清晰的整體圖形。

時  間：2023年4月12日（周三）下午 15：00 始

地  點：太阳集团app首页石牌校區教學樓A513

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