# The PIMS Postdoctoral Fellow Seminar: Matthew Rupert

## Topic

Equivalences of Categories of Modules Over Quantum Groups and Vertex Algebras

## Details

Vertex operator algebras are the symmetry algebras of two dimensional conformal field theory. In a famous series of papers, Kazhdan and Lusztig proved an equivalence between particular semisimple categories of modules over affine Lie algebras and quantum groups, the former of which can also be realized as modules over a corresponding vertex operator algebra. Such equivalences between representation categories of vertex operator algebras and quantum groups are now broadly referred to as the Kazhdan-Lusztig correspondence. There has been substantial research interest over the last two decades in understanding the Kazhdan-Lusztig correspondence for vertex operator algebras with non-semisimple representation theory. In this talk I will present an overview of this research area and discuss recent results and future directions.

**Speaker biography:** Matthew Rupert is a PIMS postdoctoral fellow at the University of Saskatchewan under the supervision of Steven Rayan, Alex Weekes, and Curtis Wendlandt. His research interests are in quantum algebra, category theory, and the Kazhdan-Lusztig correspondence for vertex algebras. He obtained his PhD in pure mathematics at the University of Alberta in 2020 under the supervision of Thomas Creutzig, where he studied unrolled quantum groups and their representation theoretic connections to the singlet vertex operator algebras. After completing his PhD, Matthew was a Visiting Assistant Professor at Utah State University from August 2020 to June 2022.

**Medium:** Read more about Matthew and their research here.

This event is part of the Emergent Research: The PIMS Postdoctoral Fellow Colloquium Series.

## Additional Information

This seminar takes places across multiple time zones: 9:30 AM Pacific/ 10:30 AM Mountain / 11:30 AM Central

Register via Zoom to receive the link for this event and the rest of the series.

See past seminar recordings on MathTube.

Matthew Rupert, University of Saskatchewan

**Scientific, Seminar**

**April 12, 2023**

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