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#### Geometric representations of vertex algebras

AbstractA powerful technique in representation theory is localization, wherein one identifies categories of modules for an algebra of interest with categories of D-modules or perverse sheaves. After reviewing the classical Beilinson”ŖBernstein theorem, which introduced localization for semisimple Lie algebras, we will describe some analogues for certain vertex algebras, notably W-algebras and...

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#### Introduction to Deligne-Lusztig theory

Course DescriptionDeligne-Lusztig theory aims to provide geometric methods (l-adic cohomology of varieties in positive characteristic) to study representations of finite groups of Lie type. We propose an introduction to this theory, starting with the enlightening example of the finite group SL_2(q) acting on Drinfeld curve.In the second part of this course, we will develop the general theory as...

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