# [QSMS Monthly Seminar] Peterson conjecture via Lagrangian correspondences and wonderful compactifications

by qsms posted Nov 18, 2020
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일정시작 2020-10-29 #036eb7

일시: 10월29일 목요일 오후2시
장소: 27동 220호 (14:00 ~ 16:00)

Title: Peterson conjecture via Lagrangian correspondences and wonderful compactifications

Speaker: 배한울(SNU)

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 a Floer theoretic technique.

In this talk, I will first discuss the wonderful compactification of the complexified Lie group of G. Identifying the complexified Lie group with the cotangent bundle of G, this helps us to visualize the moment Lagrangian correspondence from the cotangent bundle of G to the square ($G/T^{-} \times G/T$) of the flag variety G/T. Then I will explain that the A-infinity functor associated to the Lagrangian correspondence induces the desired isomorphism.

장소: 27동 220호 (16:00 ~ 18:00)

Title: A glimpse of derived/spectral algebraic geometry

Speaker: 조창연(SNU)

Abstract:

Derived/spectral algebraic geometry is rather a new area where algebraic geometry is developed in the context of homotopy theory. I'll give a brief overview of this subject with at least one example in which working in the derived/spectral setting is indispensable. If time allows, I'll explain some of my contribution to the subject.