Lara BOSSINGER
Toric degenerations and maps to toric varieties.
Abstract
I will report on recent joint work in progress with Takuya Murata. Motivated by work of Harada—Kaveh and the desire to construct moment map type maps to Newton-Okounkov polytopes we study maps to toric varieties. As algebro-geometric methods turn out to not be appropriate we use results of Mather involving Whitney stratifications to obtain a collapsing map. Although the result is more general our main application concerns toric degenerations where we construct a map from the general to the special fibre. Moreover, we generalize a result of Harada-Kaveh constructing an integrable system on a projective variety that admits a toric degeneration induced by the moment map on the toric variety. A first preprint of the work is available on arxiv:2210.13137.
Vyjayanthi CHARI
Higher order KR-modules, imaginary modules and monoidal categorification
Abstract
We discuss a connection between cluster algebras, the representation theory of quantum affine algebras of type, the existence of imaginary modules and the relationship with the representation theory of the general linear group over a non-archimedean field. The talk is based on joint work with Matheus Brito.
Emily CLIFF
Quasi-universal sheaves and generic modules
Abstract
This is based on joint work-in-progress with Colin Ingalls and Charles Paquette. Given a finite-dimensional algebra, we can associate a quiver and choose a dimension vector. Work of Alistair King shows that, if the dimension vector is unimodular, there is a moduli space of stable representations with a universal sheaf. Work of Reineke–Schröer and Hoskins–Schaffhauser shows that this does not hold for all dimension vectors; in general, we obtain a only “quasi-universal sheaf”. I will discuss this construction from several perspectives, and explain applications to the representation theory of finite-dimensional algebras.
Colleen DELANEY
HQFT interpretation of the zesting construction on ribbon categories
Abstract
The zesting construction is a way to describe braided or ribbon categories whose fusion rings are related by central extension of a grading group by invertible objects. At the level of string diagrams this construction has a strong topological flavor that allows one to give a physical characterization of the relationship between the categories’ associated 3D Reshetikhin-Turaev TQFTs.
In this talk we will dis