Organiser: Sven Möller (in collaboration with the Research Seminar “Algebra and Mathematical Physics” organised by Ingo Runkel and Christoph Schweigert)
| Room | Day | Time | Speaker | Title | Abstract |
|---|---|---|---|---|---|
| Geom. 414 | 20/06/2025 | 11:00-12:30 | Ethan Fursman (University of Melbourne) | W-Algebras and their Representations – Beyond the Standard Cases | Quantum hamiltonian reduction (QHR) is a procedure for enforcing gauge constraints on certain vertex operator algebras (VOA), resulting in a new VOA called a W-algebra. These gauge constraints may also be applied to modules, resulting in the more general notion of a QHR functor. Many interesting categories of VOA modules include relaxed highest weight modules and their spectral flows. In this talk I will review these notions and discuss their importance to non-semisimple categories of VOA modules. Then I will discuss ongoing work with D. Ridout and J. Fasquel where we develop new techniques for studying how reduction functors act on these modules. If time permits, I will also discuss ongoing work with J-E. Bourgine where we generalise some of these notions to q-deformed vertex algebras (quantum affine algebras). |
| Geom. 414 | 23/05/2025 | 11:00-12:00 | Rızacan Çiloğlu (Technische Universität Darmstadt) | Bezrukavnikov's equivalence for non-split reductive groups | For a split reductive group, Arkhipov-Bezrukavnikov have proven an equivalence of categories between Iwahori-Whittaker sheaves on the affine flag variety and coherent sheaves on the Springer resolution of its Langlands dual group. In this talk, I will discuss the extension of this equivalence to possibly non-split reductive groups, and work in progress aiming to extend Bezrukavnikov's equivalence to such groups. |
| Geom. 433 | 06/05/2025 | 14:15-15:45 | Thomas Creutzig (Friedrich-Alexander-Universität Erlangen-Nürnberg) | The category of weight modules of affine sl(2) at admissible level | The prime example of rational vertex algebras are affine vertex algebras at positive integer level. Similarly one expects that affine vertex algebras at admissible levels are prototypical examples of vertex algebras whose representation categories are non-semisimple. Very recently the case of sl(2) was finally understood and I plan to present the main results on the structure of the category of weight modules of the affine vertex algebra of sl(2) at any admissible level. |
| Geom. 414 | 25/04/2025 | 14:45-15:30 | Yuto Moriwaki (RIKEN, Japan) | Cohomology ring of unitary N=(2,2) full vertex algebra and mirror symmetry | |
| Geom. 428 | 17/12/2024 | 14:15-15:00 | Thomas Creutzig (Friedrich-Alexander-Universität Erlangen-Nürnberg) | From TQFT to the Waarnar-Zudilin conjecture | Three-dimensional topological quantum field theories often admit chiral boundary conditions that support a vertex operator algebra. I will discuss a two-parameter family of VOAs that supposedly arises in this way. The best check of the proposal is the verification of character identities, which in this instance coincides with a conjecture by Waarnar and Zudilin. |
| Geom. 428 | 17/12/2024 | 15:00-15:45 | Brandon Rayhaun (Yang Institute for Theoretical Physics, Stony Brook, USA) | Equivalence relations on vertex operator algebras | Inspired by results in the theory of integral lattices and the theory of tensor categories, I will describe an interconnected web of equivalence relations on (suitably regular) vertex operator algebras, and discuss some applications thereof. |
| Sedanstr. 19, 221 | 05/12/2024 | 14:15-15:00 | Thibault Juillard (Laboratoire de Mathématiques d'Orsay, France) | Reduction by stages for affine W-algebras, a geometric approach | Affine W-algebras form a family of vertex algebras indexed by the nilpotent orbits of a simple finite dimensional complex Lie algebra. Each of them is built as a noncommutative Hamiltonian reduction of the corresponding affine Kac-Moody algebra. In this talk, I will present a joint work with Naoki Genra about the problem of reduction by stages for these affine W-algebras: given a suitable pair of nilpotent orbits in the simple Lie algebra, it is possible to reconstruct one of the two affine W-algebras associated to these orbits as the Hamiltonian reduction of the other one. I will insist on how this problem uses our previous work about reduction by stages between Slodowy slices, which are Poisson varieties associated with affine W-algebras. I will also mention some applications and motivations coming from Kraft-Procesi rule for nilpotent Slodowy slices, and isomorphisms between simple affine admissible W-algebras. |
| Geom. 428 | 14/11/2023 | 14:15-15:00 | Hannes Knötzele (Universität Hamburg) | Towards cyclic orbifolds of rational vertex operator algebras | For a holomorphic vertex operator algebra (VOA) V with a finite cyclic group G of automorphisms, the category of modules of the fixed point vertex operator subalgebra V^G is equivalent to the module category of a twisted Drinfeld double of G. For a rational but not necessarily holomorphic VOA V, a general description of the category of modules of V^G is unknown. In this talk, I will sketch the main difficulties facing this problem. First, I will recall categorical prerequisites like equivariantisation and crossed modular categories. Then, I will apply these ideas to examples that generalise Tambara-Yamagami categories. |
| Geom. 435 | 06/07/2023 | 14:15-15:45 | Dražen Adamović (University of Zagreb, Croatia) | On weight and logarithmic modules for some affine W-algebras | |
| Geom. 435 | 06/07/2022 | 14:15-15:45 | Yuto Moriwaki (RIMS, Kyoto University, Japan) | Non-chiral conformal field theory and vertex algebra | |
| Geom. 435 | 28/06/2022 | 14:15-15:00 | Hiroshi Yamauchi (Tokyo Woman's Christian University, Japan) | An exceptional construction of the moonshine VOA |