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MULTIYEAR PROGRAM
CONFERENCE

Vertex algebras, geometric representation theory and quantum groups

Algèbres vertex, théorie géométrique des représentations et groupes quantiques

10 – 14 June, 2024

Scientific Committee 
Comité scientifique 

Hiraku Nakajima (IPMU Tokyo)
Vera Serganova (University of California Berkeley)
Peng Shan (Tsinghua University, Beijing)

Organizing Committee
Comité d’organisation

Drazen Adamovic (University of Zagreb)
Tomoyuki Arakawa (Kyoto University)
Anne Moreau (Université Paris-Saclay)
Nils Scheithauer (Technical University of Darmstadt)

Time schedule
Abstracts
Participants
Audiovisual Mathematics Library (after the event)

The goal of the conference is to explore connections between vertex algebras, geometric representation theory and the representation theory of quantum groups. The equivariant geometry of loop spaces of flag manifolds is essentially the same as that of affine Grassmannians which are the building blocks of the Coulomb branch of 3-dimensional gauge theories. This is one of the links between vertex algebras and geometric representation theory. Quantum groups are related to the representation theory of logarithmic vertex algebras, affine vertex algebras and $W$-algebras. It is expected that they are also connected to non $C_2$-cofinite vertex algebras and to higher rank logarithmic vertex algebras. Other subjects that will be covered are 4D/2D duality and conformal embeddings.

L’objectif de la conférence est d’explorer les liens entre les algèbres vertex, la théorie géométrique des représentations et la théorie des représentations des groupes quantiques. La géométrie équivariante des espaces de lacets des variétés de drapeaux est essentiellement la même que celle des Grassmanniens affines qui sont les éléments constitutifs de la branche de Coulomb des théories de jauge tridimensionnelles. C’est l’un des liens entre les algèbres vertex et la théorie géométrique des représentations. Les groupes quantiques sont liés à la théorie des représentations des algèbres vertex logarithmiques, celle des algèbres vertex affines et celle des W-algèbres. On s’attend également à ce qu’ils soient liés aux algèbres vertex non $C_2$-cofinies et aux algèbres vertex logarithmiques de rangs supérieurs. D’autres sujets comme la dualité 4D/2D et les plongements conformes seront abordés.  

SPEAKERS

Léa Bittmann (Université de Strasbourg)    Applications of quantum affine Schur-Weyl duality
Dylan Butson (University of Oxford)  Vertex algebras from divisors on Calabi-Yau threefolds
Xuanzhong Dai (Kyoto University)  Chiral differential operators over G/U and associated variety
Gurbir Dhillon (Yale University)  Highest weight representations of W-algebras
Jethro van Ekeren (IMPA)  Chiral homology and extensions
Maria Gorelik (The Weizmann Institute of Science)  On admissibility over Lie superalgebras
Reimundo Heluani (IMPA)   Basic complex for vertex algebra cohomology
David Hernandez (IMJ-PRG, Université Paris Cité)  Deformed W-algebras and representations of quantized Coulomb branches
Thibault Juillard (Université Paris Saclay)  Reduction by stages for W-algebras
Anna Lachowska (EPFL)  Hochschild cohomology of the small quantum group and beyond
Simon Lentner (University Hamburg)  Categorical structures appearing in conformal field theory
Sven Möller (University of Hamburg)  Quiver Vertex Algebras
Fyodor Malikov (University of Southern California)    Homotopy Chiral algebras
Hiraku Nakajima (Kavli iPMU, University of Tokyo)  Comments on Skein Algebras and Quantized Coulomb branches by Allegretti and Shan
Paolo Papi  (Sapienza University of Rome)  Unitary representations of minimal W-algebras
Vera Serganova (University of California, Berkeley)  Odd nilpotent cone for Lie superalgebras
Peng Shan (Tsinghua University)  On correspondences between representations of simple affine vertex algebras at elliptic levels and affine Springer fibres
Lewis Topley (University of Bath)  Shifted twisted Yangians and non-rectangular finite W-algebras
Eric Vasserot (Université Paris Cité)  Cohomological Hall algebras of quivers and Yangians
Ivana Vukorepa (University of Zagreb)  Classification of irreducible modules for the affine vertex algebra L_{-(2n+1)/2}(sl(2n)) in certain categories
Janik Wilhelm (Technical University of Darmstadt)  Reflective modular varieties and their cusps

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