Random partition meets mirror symmetry with reflections: the power of the rmodynamic limit




报告摘要: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 focus on 5d N = 1 Sp(N) gauge theory with N_f (≤2N + 3) flavors and explain the computations aboutNekrasov partition function based on topological vertex algorithm of5-brane web with O5-plane which corresponds to Sp(N) geometry. Withthe help of random partition technique, Nekrasov partition function can berewritten in terms of profile function, after taking thermodynamic limit andfunctional derivatives, the saddle point equation can be derived for theprofile 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 the5-brane web with O5-plane. This agreement gives further evidence formirror symmetry which relates Nekrasov partition function with Seiberg-Witten curve in the case with orientifold plane. This talk is based on joint work with Futoshi Yagi.

专家简介:李晓斌博士毕业于四川大学,现任教于西南交通大学。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),这也是代数几何、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, 并协助组织过多个学术活动。 他为MathSciNet撰写了70余个具有学科介绍性的Math Review,给读者一个清晰的整体图形。