Peterson conjecture via Lagrangian correspondences and wonderful compactifications

Abstract: Let $G$ be a compact simply-connected semisimple Lie group and let $T$ be a maximal torus subgroup of $G$. Peterson conjecture says that the homology of the based loop space of $G$ and the quantum cohomology of the full flag variety $G/T$ are isomorphic as rings after a localization. In a joint work with Naichung Conan Leung, we found a geometric proof of the conjecture using Floer theoretic techniques. In this talk, I will first introduce the moment Lagrangian correspondence from the cotangent bundle of $G$ to the square $(G/T)^2$ of the flag variety $G/T$. Then I will discuss how to compute an $A$-infinity homomorphism associated to the Lagrangian correspondence and show that it induces the desired isomorphism.

mathematical physicsalgebraic geometrysymplectic geometry

Audience: researchers in the topic

IBS-CGP weekly zoom seminar

Series comments: Registration is required at cgp.ibs.re.kr/activities/talkregistration