Vertex Algebras and Representation Theory
Algèbres vertex et théorie des représentations
6 – 10 June 2022
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Scientific Committee
Comité scientifique Sergei Gukov (California Institute of Technology) |
Organizing Committee
Comité d’organisation Drazen Adamovic (University of Zagreb) |
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In the last years there have been renewed interests in vertex algebras in various areas of mathematics and physics. For instance, although vertex algebras have their origin in two-dimensional conformal field theory, many new connections have been found recently between vertex algebras and higher dimensional quantum field theories. The AGT correspondence by Alday, Gaiotto, and Tachikawa, the 4D/2D duality by Beem, Lemos, Liendo, Peelaers, Rastelli, and van Rees, Vertex Algebras at the Corner by Gaiotto and Rapcak, and the vertex algebras VOA[M4] by Feigin and Gukov are examples of such phenomena. It has been also observed that certain vertex algebras called W-algebras play an essential role in the quantum geometric Langlands program. The Mathieu moonshine conjecture and its generalization are giving new insights to the theory of automorphic forms. All these exciting new developments are deeply connected with geometric representation theory.
This conference intends to bring together experts, including physicists, at an international scale on these new aspects of vertex algebras. This will be an opportunity to encourage young researchers to get involved in these promising developments. |
Les algèbres vertex ont connu ces dernières années un regain d’intérêt dans différentes branches des mathématiques et de la physique. Par exemple, bien que les algèbres vertex trouvent leur origine dans la théorie conforme des champs en dimension deux, de nombreux liens entre les algèbres vertex et des théories quantiques des champs en dimensions supérieures furent récemment établis. La correspondance AGT de Alday, Gaiotto et Tachikawa, la dualité 4D/2D de Beem, Lemos, Liendo, Peelaers, Rastelli et van Rees, les algèbres vertex d’angle de Gaiotto et Rapcak, ainsi que les algèbres vertex VOA[M4] de Feigin et Gukov sont des exemples de tels phénomènes. Soulignons de plus que certaines algèbres vertex, appelées W-algèbres, jouent un rôle essentiel dans le programme géométrique quantique de Langlands. Dans une direction un peu différente, la conjecture du Mathieu moonshine et ses généralisations apportent un éclairage nouveau sur la théorie des formes automorphes. Ces avancées spectaculaires sont inhérentes à la théorie géométrique des représentations.
Cette conférence a pour but de regrouper les meilleurs experts, notamment des physiciens, autour de ces aspects récents de la théorie des algèbres vertex. Elle sera une occasion d’encourager de jeunes chercheurs à poursuivre leurs travaux autour de ces nouveaux développements très prometteurs. |
Damien Calaque (Université de Montpellier) Vertex models and En-algebras
Thomas Creutzig (University of Alberta) Representation theory at admissible level
Gurbir Dhillon (Yale University) Kazhdan–Lusztig theory for vacuum algebras at critical level
Justine Fasquel (University of Lille) Rationality of exceptional W-algebras associated with sp_4
Zachary Fehily (University of Melbourne) Inverse Reduction For Subregular W-Algebras
Peter Fiebig (University of Erlangen) A model for quantum group representations and character generations
Nora Ganter (The University of Melbourne) Categorical traces and the HKR-isomorphism
Naoki Genra (Kavli IPMU) Feigin-Semikhatov duality
Sergei Gukov (California Institute of Technology) Surprising VOA structures from Quantum Topology
Gerald Höhn (Kansas State University) On the genus of the odd Moonshine module
David Jordan (The University of Edinburgh) Topological Langlands duality
Ana Kontrec (Max Planck Institute for Mathematics, Bonn) Bershadsky-Polyakov vertex algebras at positive integer levels and duality
Ching Hung Lam (Academia Sinica) A lattice theoretical interpretation of generalized deep holes
Antun Milas (University at Albany, State University of New York) Graphs, Quivers and Vertex Algebra Characters
Ivan Mirković (University of Massachusetts Boston) Some remarks on vertex operators
Sven Möller (University of Hamburg) On the Classification of Holomorphic Vertex Operator Superalgebras
Shigenori Nakatsuka (University of Alberta) Duality of hook-type W-superalgebras via convolution operations
Shoma Sugimoto (Kyushu University) On the multiplet W-algebras
Juan Villarreal (University of Bath) Logarithmic vertex algebras (LogVAs)
Jethro van Ekeren (IMPA) Chiral homology and Poisson homology of associated schemes
Ivana Vukorepa (University of Zagreb) On the representation theory of the vertex algebra L−5/2(sl(4))
Katrin Wendland (Trinity College Dublin) How do quarter BPS states cease being BPS?
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