Representation theory and a little bit of quantum field theory

Abstract: One of the central foci of representation theory in the 20th century was the representation theory of Lie algebras, starting with finite dimensional algebras and expanding to a rich, but still mysterious infinite dimensional theory. In this century, we realized that this was only one special case of a bigger theory, with new sources of interesting non-commutative algebras whose representations we'd like to study, such as Cherednik algebras. In mathematical terms, we could connect these to symplectic resolutions of singularities, but a more intriguing explanation is that they arise from 3d quantum field theories. I'll try to provide an overview about what's known about this topic and what we're still confused about.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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