|Title||Towards a construction of higher dimensional loop Grassmannians|
|Presenter||Yaping Yang (The University of Melbourne)|
|Session||Geometry and Topology|
I will talk about a construction of higher dimensional loop Grassmannians, in the framework of local spaces over Hilbert scheme of points. The notion of local spaces is a refined version of the factorization space of Beilinson-Drinfeld. It has many applications, examples including loop Grassmannians associated to Kac-Moody groups, geometric Langlands duality in higher dimensions, and non-abelian higher class field theory. In dimension 1, this construction yields the recent reconstruction by Ivan Mirkovic of the usual loop Grassmannians from semi-infinite orbits. During the talk, I will mainly focus on the construction applied to dimension 2. I will briefly mention the difficulties in dimension 3. This talk is based on my joint work with Ivan Mirkovic and Gufang Zhao.
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