Derived and Noncommutative Geometry seminar：Loop Group and Grassmannian Through Analytic Geometry

Speaker: Yingdi Qin, SIMIS

Abstract：Affine Grassmannian are classically described as the equivalence classes of G-torsors on disc with trivializations on the punctured disc. A loop groups is defined as mapping stack from punctured disc to the group. However, formal punctured disc doesn’t exsit as an geometric object in classical geometry since it has an empty set of geometric points.

We make use of analytic geometry built on framework of condensed mathematics to make sense of formal punctured disc （and other versions of punctured discs）which has no points. And we construct a version of Grassmannian and Loop group over a universal analytic ring. If time permits， we will also talk about the determinant line bundle and Plucker embedding of the Grassmannian.

Time: 15:00-18:00, Monday, September 15

Location: R910, SIMIS