| CLAN Research Group | Upcoming Meeting | Directions | Past Meetings |
Date: Wednesday 25th June, 2025
Location: University of Leeds.
Invited Speakers:
Benjamin Dequêne (University of Leeds)
Francesca Fedele (University of Leeds)
Vanessa Miemietz (University of East Anglia)
| 11:00–11.45 | Registration and Coffee & Tea. |
| Location: Chemistry LT A (2.15) |
| 11:45–12:45 | Tilting mutations for exact structures on type A algebras |
| Benjamin Dequêne (University of Leeds) | |
| Location: Chemistry LT A (2.15) Abstract: A. H. Schofield and C. Riedtmann introduced tilting mutations in the early 90s. They form a way of obtaining new tilting complexes by slightly modifying known tilting complexes. By Rickard's Morita theorem, they are related algebras that are derived equivalent. In type A algebras, those mutations allow one to get any tilting module from any other one. In this talk, after introducing essential notions, we will focus on a subfamily of mutations, called admissible for a given exact structure, on the module category of a type A algebra, and the properties of the additive categories obtained via the equivalent classes of tilting modules. This is based on a joint work (in progress) with Sunny Roy. |
| 12:45–14:30 | Lunch |
| 14:30–15:30 | The N-stable category |
| Vanessa Miemietz (University of East Anglia) | |
| Location: Chemistry LT A (2.15) Abstract: A well-known theorem of Buchweitz provides equivalences between three categories: the stable category of Gorenstein projective modules over a Gorenstein algebra, the homotopy category of acyclic complexes of projectives, and the singularity category. To adapt this result to N-complexes, one must find an appropriate candidate for the N-analogue of the stable category. I will explain how to identify this “N-stable category” to obtain Buchweitz’s theorem for N-complexes over a Grothendieck abelian category. Time permitting, I will explain how to compute the Serre functor on the N-stable category over a self-injective algebra and obtain fractional Calabi–Yau properties. |
| 15:30–16:00 | Coffee Break |
| Location: Chemistry LT A (2.15) |
| 16:00–17:00 | Presentations of (complex) braid groups via cluster methods |
| Francesca Fedele (University of Leeds) | |
| Location: Chemistry LT A (2.15) Abstract: Coxeter classified the finite reflection groups and showed that they have beautiful presentations, now known as Coxeter presentations. More recently, cluster algebras and their surface models have been used by several authors to construct new families of presentations of reflection and braid groups.This talk will give an overview of a class of such families and introduce its complex analogue for complex braid groups. This is based on joint work with Bethany Marsh. |
| 17:00–17:40 | Flash Talks |
| Location: Chemistry LT A (2.15) Ellis Caird (University of Bath) : An Ext conjecture for SL_2 Web Immanants. Federico Campanini (Université catholique de Louvain) : Lattices of pretorsion classes. Iacopo Nonis (University of Leeds) : Tau-exceptional sequences for representations of quivers over local algebras. |