2025 CMS Summer Meeting
Quebec City, June 6 - 9, 2025
Combinatorial representation theory
Org: Thomas Brüstle (Bishop's and Université de Sherbrooke) and Monica Garcia Gallegos (UQAM and Université Laval)
[PDF]
Org: Thomas Brüstle (Bishop's and Université de Sherbrooke) and Monica Garcia Gallegos (UQAM and Université Laval)
[PDF]
- ESTHER BANAIAN, UC Riverside
- GRANT BARKLEY, Harvard
- AMANDA BURCROFF, Harvard University
- JUSTIN DESROCHERS, Sherbrooke
- BENJAMIN GRANT, UConn
- BLAKE JACKSON, University of Connecticut
A geometric model for the non-$\tau$-rigid modules of type $\widetilde{D}_n$ [PDF]
- GRANT BARKLEY, Harvard
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We give a geometric model for the non-$\tau$-rigid modules over acyclic path algebras of type $\widetilde{D}_n$. Similar models have been provided for module categories over path algebras of types $A_n, D_n,$ and $\widetilde{A}_n$ as well as the $\tau$-rigid modules of type $\widetilde{D}_n$. A major draw of these geometric models is the "intersection-dimension formulas" they often come with. These formulas give an equality between the intersection number of the curves representing the modules in the geometric model and the dimension of the extension spaces between the two modules. Essentially, this formula allows us to calculate the homological data between two modules combinatorially. Since there are infinitely many distinct homogenous stable tubes in the regular component of the Auslander-Reiten quiver of type $\widetilde{D}_n$, all of which are disjoint, our geometric data requires an extra decoration on the admissible tagged edges in our geometric model to prevent intersections between curves corresponding to modules in distinct connected components of the Auslander-Reiten quiver.
- SHIPING LIU, Université de Sherbrooke
Representations of hereditary artin algebras of Dynkin type [PDF]
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Let $H$ be a hereditary artin algebra of finite representation type. We shall study the category
mod$H$ of finitely generated left $H$-modules with a connection to the bounded derived category
$D^{\hspace{.5pt}b\hspace{-.6pt}}({\rm mod}H)$ and the associated cluster category $C_H$. By determining all its hammocks, we provide an effective method to construct the Auslander-Reiten quiver of ${\rm mod} H$ by simply viewing the ext-quiver of $H$. As easy applications, we compute the numbers of non-isomorphic indecomposable objects in ${\rm mod} H$ and $C_H$, and also the nilpotency of the radicals of ${\rm mod} H,$ $D^b({\rm mod} H)$ and $C_H$.
- SCOTT NEVILLE, University of Michigan
Cyclically ordered quivers [PDF]
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Quivers and their mutations play a fundamental role in the theory of cluster algebras. We focus on the problem of deciding whether two given quivers are mutation equivalent to each other. Our approach is based on introducing an additional structure of a cyclic ordering on the set of vertices of a quiver. This leads to new powerful invariants of quiver mutation.
This talk is partially based on joint work with Sergey Fomin.
- CHARLES PAQUETTE, Royal Military College of Canada / Queen's University
Brick directed algebras and brick-splitting torsion classes [PDF]
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In this talk, we will explore a new class of algebras called brick-directed algebras, which can be defined as those algebras having no oriented cycles of bricks in their module category. We characterize these algebras from many different viewpoints, including from their torsion theory and their wall-and-chamber structure. A key feature arising in the study of these algebras is the notion of brick-splitting torsion pairs, which are those torsion pairs with the property that any given brick is either torsion or torsion-free. We completely characterize the brick-splitting torsion classes combinatorially within the lattice of torsion classes and derive some consequences of this. This is joint work with Sota Asai, Osamu Iyama and Kaveh Mousavand.
- THÉO PINET, McGill
- DEEPANSHU PRASAD, Queens
- GORDANA TODOROV, Northeastern University
- KAYLA WRIGHT, UOregon
- DEEPANSHU PRASAD, Queens