Abstract: Given a smooth and proper curve X and a reductive group G one can consider the stack Bun_{G,X} of principal G-bundles on X. This stack has an important role in Algebraic Geometry and Representation Theory especially with regard to the Langlands program. We shall study the geometry of Bun_{G,X} and the category 
D(G,X) of constructible  sheaves on Bun_{G,X}. We shall be especially interested in the subcategory D_{nil}(G,X) of sheaves with nilpotent singular support.

The course can be considered as an introduction to the paper https://arxiv.org/pdf/2010.01906.pdf.


In particular, we shall start by describing the unramified Langlands correspondence over function fields and in particular Drinfeld's proof for GL_2. We then discuss the idea of categorization of the Langlands correspondence via categorization. To achieve categorification we study the stack of Vector bundles over a curve and constructible sheaves over it. We shall then discuss the theory of singular support in both the topological 
and e'tale context. 

This will allow us to describe constructible sheaves with nilpotent support on the stack of Vector bundles. 
We shall then revisit the unramified Langlands correspondence as a proposed statement about categorical equivalence. 

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https://us02web.zoom.us/j/4114878653

Meeting ID: 411 487 8653