Adrian Albert Lectures in Algebra

Higher Representations of Lie Algebras: Algebra

Tuesday May 13, 4:30 pm, Room 206 Eckhart Hall, 1118 E 58th Street

Representation theory is a study of symmetries, via linear actions. Higher representation theory aims to introduce a new paradigm, where spaces are replaced by higher structures (abelian or triangulated categories, or higher categorical structures). An important aspect is the development of tools to construct categories. I will discuss the higher representation theory of complex semi-simple Lie algebras (and more general Kac-Moody algebras).


Higher Representations of Lie Algebras: Geometry

Wednesday May 14, 4:00 pm, Room 202 Eckhart Hall, 1118 E 58th Street

I will explain how to recast a part of geometric representation theory in the framework of higher representation theory. This brings in higher symmetries, which can be viewed geometrically as correspondences between correspondences. The main examples come from flag varieties and quiver varieties. Higher representation theory provides a substitute for some moduli spaces in geometry.


Higher Representations of Lie Algebras: Topology

Thursday, April 15, 4:30pm, Room 133 Eckhart Hall, 1118 E 58th Street

In this lecture, we will discuss the expected relation with 4-dimensional topological quantum field theory. We will explain how Khovanov's knot homology arises. A crucial feature is the construction of suitable tensor products.