Organisers
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Simon Goodwin, University of Birmingham
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Lewis Topley, University of Bath
Scientific committee
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Tomoyuki Arakawa , RIMS, University of Kyoto
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Roman Bezrukavnikov , Massachusetts Institute of Technology
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Victor Ginzburg , University of Chicago
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Ivan Losev , Yale University
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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 |