ARTIG 8 - Abstracts

Abstracts of research talks

Igor Burban
Title: Exceptional hereditary curves and associated reflection groups
Abstract: It is well known that the set of full exceptional collections in a Hom-finite triangulated category D admits a natural braid group action. When this action is transitive, one can associate to D a reflection group W. In the case where D is the bounded derived category of finite-dimensional modules over a hereditary algebra A, the corresponding reflection group is the crystallographic Coxeter group associated with the Cartan matrix of A.
In my talk, I will introduce the notion of an exceptional hereditary curve. In this case, the braid group action on the corresponding bounded derived category of coherent sheaves is transitive. The associated reflection group W is fully determined by Lenzing’s symbol, which can be regarded as an analogue of a Cartan matrix. The resulting class of reflection groups includes all affine Weyl groups and elliptic Weyl groups of codimension one, as well as a new class of reflection groups, called cuspidal groups of canonical type.
The main result of the talk (based on joint work with Baumeister, Neaime, and Schwabe arXiv:2512.01729) describes a categorification of non-crossing partitions in this setting.

Alice Dell'Arciprete
Title: TBA
Abstract: TBA

Juan Omar Gomez
Title: Finite permutation resolutions via descent
Abstract: We show that for a broad class of infinite groups, every pseudo-coherent module over the integral group algebra, admits a finite resolution by finite p-permutation modules, up to direct summands. The key idea is to reduce the problem to finite subgroups via a descent argument, where an analogous result is already known. This is joint work in progress with Luca Pol.

Tal Gottesman
Title: TBA
Abstract: TBA

Gustavo Jasso
Title: Existence and uniqueness of DG enhancements: An obstruction-theoretic approach
Abstract: Building on the earlier work of Fernando Muro, recent joint work of ours shows that obstruction-theoretic methods provide a systematic approach to the study of differential graded enhancements of certain algebraic triangulated categories, specifically those admitting generators given by dZ-cluster tilting objects. In this setting, such methods can be used to prove that these triangulated categories admit an essentially unique DG enhancement and, under additional assumptions, to construct bimodule Calabi-Yau structures at the enhanced level.
However, the focus of this talk is not on these results themselves, but on the proof technique behind them. I will explain why obstruction theory arises naturally in this context, and also indicate why we expect that similar techniques can be applied more broadly.

Kevin Schlegel
Title: Classifying torsion pairs
Abstract: For an essentially small abelian category we classify torsion pairs through cosilting subsets of the Ziegler spectrum of the ind-completion of the abelian category. In the case of a module category of an Artin algebra, we characterize these cosilting subsets in terms of the Auslander-Reiten translation. Moreover, we introduce cosilting ideals of the module category and show that they are one to one with cosilting subsets of the Ziegler spectrum.

Jan Schröer
Title: On the additivity of projective presentations of maximal rank
Abstract: This talk is about projective presentations of finite-dimensional modules over finite-dimensional algebras. We discuss if the direct sum of copies of a projective presentation of maximal rank is again of maximal rank. This is joint work with Grzegorz Bobinski.

Catharina Stroppel
Title: TBA
Abstract: TBA

Tanguy Vernet
Title: Nilpotent quiver varieties with multiplicities and symmetrisable crystals
Abstract: The connection between representations of quivers and symmetric Kac-Moody algebras has been at the heart of many works in geometric representation theory over the past decades. Several approaches were also developed in order to include symmetrisable Kac-Moody algebras into this picture. One of these approaches, proposed by Geiss-Leclerc-Schröer a few years ago, consists in working with representations of quivers over rings of truncated power series, also called representations of quivers with multiplicities. In particular, Geiss-Leclerc-Schröer generalised the geometric construction of the crystal of the lower half of the quantised universal enveloping algebra (by Lusztig and Kashiwara-Saito) to the symmetrisable setting.
In this talk, I will report on joint work with Victoria Hoskins and Joshua Jackson, where we extend the construction of crystals of highest-weight irreducible representations of Kac-Moody algebras (by Saito) to the symmetrisable case. This relies on the construction of new quiver varieties with multiplicities, based on Geiss-Leclerc-Schröer's framework.