Geometric Representation Theory and W-algebras

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Geometric Representation Theory and W-algebras

 28 Aug - 01 Sep 2023

ICMS, Bayes Centre, Edinburgh

This workshop is at maximum capacity, there are no further spaces to attend. Talks will be recorded and uploaded to this webpage post event.

Organisers

  • Simon Goodwin, University of Birmingham
  • Lewis Topley, University of Bath

Scientific committee

  • Tomoyuki Arakawa , RIMS, University of Kyoto
  • Roman Bezrukavnikov , Massachusetts Institute of Technology
  • Victor Ginzburg , University of Chicago
  • Ivan Losev , Yale University
  • Anne Moreau , Université Paris-Saclay

About:

Some of the most exciting developments in geometric representation theory revolve around the relatively new theory of W-algebras. Broadly speaking these are obtained via the process of quantum Hamiltonian reduction from the some of the most influential structures in modern representation theory: enveloping algebras and universal affine vertex algebras. The applications of W-algebras are seemingly endless, but we list some key examples: the ordinary and modular representation theory of Lie algebras, the classification of integrable systems (especially generalisations of the KP hierarchy), a deeper understanding of smooth representations of affine Lie algebras, conformal field theories (and their associated AdS duals), modular tensor categories and the famous geometric Langlands program, once described by Edward Frenkel as “the grand unifying theory of mathematics”. 

The aim of this workshop is to bring the world's leading experts together to investigate recent developments in the theory of W-algebras and their representation theory, as well as interactions with other topics in geometric representation theory.

Programme:

Monday
Registration
Welcome & introduction
Ivan Losev, Yale University t-structures on the equivariant derived category of the Steinberg variety
Tea & coffee
Eric Vasserot, Université Paris Cité Non symmetric quantum groups and critical cohomology of quiver varieties
Gurbir Dhillon, Yale/MPIM Bonn Geometric representations of affine W-algebras
Lunch
David Yang, Massachusetts Institute of Technology Local geometric langlands and affine Beilinson-Bernstein localization at the critical level
Tea & coffee
Thomas Creutzig, University of Alberta Tensor categories of modules of W-algebras
Welcome reception
Tuesday
Tomoyuki Arakawa, RIMS, Kyoto University Hilbert Schemes of the points in the plane and quasi-lisse vertex superalgebras
Uhi Rinn Suh, Seoul National University N=2 primary superconformal structure of the classical SUSY W-algebra W(sl(n+1|n))
Tea & coffee
Naoki Genra, University of Tokyo Reduction by stages on W-algebras
Lunch
Martina Lanini, Università di Roma "Tor Vergata" Symmetric quivers and symmetric Varieties
Tea & coffee
Ben Webster, University of Waterloo / Perimeter Institute Finite W-algebras as Coulomb branches
Public Lecture at G03, Victor Kac, MIT Mathematics Colloquium- Exceptional de Rham Complexes
Wednesday
Anne Moreau, Université Paris-Saclay Functorial constructions of double Poisson vertex algebras
Tea & coffee
Weiqiang Wang, University of Virginia A Drinfeld presentation of twisted Yangians
Free afternoon
Thursday
Andrew Linshaw, University of Denver Universal vertex algebras beyond the W_{\infty}-algebras
Ana Balibanu, Louisiana State University Moment maps, multiplicative reduction, and Dirac geometry
Tea & coffee
Jethro van Ekeren, IMPA Modular tensor categories from exceptional W-algebras
Lunch
Juan Villarreal, University of Bath
Tea & coffee
Peng Shan, Tsinghua University Modularity for W-algebras and affine Springer fibers
Workshop dinner
Friday
Vera Serganova, UC Berkeley Invariant integration on homogeneous superspaces
Tea & coffee
Victor Kac, Massachusetts Institute of Technology Unitary representations of minimal W-algebras
End of the workshop