Scientific Committee
Comité scientifique
Kathrin Bringmann (University of Cologne)
Dennis Gaitsgory (Max Planck Institute for Mathematics)
Victor Kac (MIT)
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)
Trace functions relate vertex algebras and their modules to various types of automorphic forms, including modular forms for congruence subgroups, Jacobi forms and automorphic forms for orthogonal groups. This connection is an indispensable tool in both the structure and representation theory of vertex algebras. For example, the classification of holomorphic vertex operator algebras of central charge 24 can be deduced from the classification of the cusps of certain reflective modular varieties. One important question is to determine under what conditions the characters of modules of a vertex algebra are invariant under the modular group, and when an analogue of the Verlinde formula applies.
In cases where explicit constructions of vertex algebras and their modules are known, such properties can often be used to derive combinatorial identities such as the Rogers–Ramanujan identities and their generalizations. This makes vertex algebras an important tool in combinatorics.
At the conference we will present and discuss recent developments in the connection between vertex algebras, automorphic forms and combinatorics.
Les fonctions de trace relient les algèbres vertex et leurs modules à différents types de formes automorphes, notamment les formes modulaires pour les sous-groupes de congruence, les formes de Jacobi et les formes automorphes pour les groupes orthogonaux. Ce lien constitue un outil fondamental pour comprendre la structure et les représentations les algèbres vertex. Par exemple, la classification des algèbres d’opérateurs de vertex holomorphes de charge centrale 24 peut se déduire de la classification des formes cuspidales de certaines variétés modulaires réfléxives. Une question importante est de déterminer sous quelles conditions les caractères des modules d’une algèbre vertex sont invariants sous l’action du groupe modulaire, et quand un analogue de la formule de Verlinde s’applique.
Dans les cas où des constructions explicites d’algèbres vertex et de leurs modules sont connues, de telles propriétés peuvent souvent être utilisées pour établir des identités combinatoires telles que les identités de Rogers–Ramanujan et leurs généralisations. Cela fait des algèbres vertex un outil important en combinatoire.
Lors de la conférence, nous explorerons les développements récents sur le lien entre les algèbres vertex, les formes automorphes et la combinatoire.
SPEAKERS
Raphaël Beuzart-Plessis (CNRS, Aix-Marseille Université)
Arkadi Bojko (Fudan University) (q,T)-deformed vertex algebras from equivariant homology theories
Alexis Bouthier (Sorbonne University) Geometric Satake for Kac-Moody groups
Giulio Codogni (University of Rome Tor Vergata) Vertex operator algebras, partition functions and Teichmüller modular forms
Thomas Creutzig (University of Erlangen-Nuremberg) W-algebras and quantum super groups
John Duncan (Academia Sinicia) Vertex algebras, Jacobi forms and homotopy groups
Andrea Ferrari (University of Edinburgh) On hypertoric vertex operator (super)algebras and the 3d/2d correspondence
Vladimir Fock (Université de Strasbourg) Sato tau function is a GL(1) automorphic form
Maria Gorelik (Weizmann Institute of Science) Relative rationality of affine vertex superalgebras
Ching Hung Lam (Academia Sinicia) Lattice vertex algebras over a field of positive characteristic
Toshiki Matsusaka (Kyushu University) On q-series identities from Lie superalgebras
Antun Milas (University of Albany) Weil meets Weyl and Peter
Manuel Müller (Sapienza University of Rome) Eisenstein series for orthogonal groups and lattice neighbours
Shigenori Nakatsuka (University of Erlangen-Nuremberg) A decomposition theorem for W-superalgebras and rationality
Lara San Martin Suarez (Caltech) Quantum topology and VOA structures
Matthias Storzer (University College Cork) Nahm sums and their modularity
Qing Wang (Xiamen University) Classification of irreducible ordinary modules for affine vertex superalgebras
Katrin Wendland (Trinity College Dublin) Folding special Calabi-Yau threefolds that are obtained from Slodowy slices
Nina Yu (Xiamen University) Zhu algebras of permutation orbifold vertex operator algebras
Yongchang Zhu (BIMSA and Tsinghua University) Space of genus one coinvariants for quasi-lisse vertex operator algebras
SPONSORS
IRN in Representation Theory
