Ray Maresca

activity

20222026

collaborators

8 papers

math.RT2026

Enumerating iterated tilted algebras in type $A$

Alexander E. Black, Jonathan E. Gordon, Ray Maresca

We show that isoclasses of iterated tilted algebras in type $A_{n}$ are in bijection with non-crossing spanning trees up to rotation on a convex n+1-gon. This is done by constructing…

math.RT2026

Pseudo-torsion classes

Kiyoshi Igusa, Ray Maresca

For a finite dimensional algebra $Λ$ , we consider a torsion class $G$ in $m o d$ - $Λ$ , which is not necessarily functorially finite. We construct a wall-and-chamber structure for $G$ …

math.RT2025

The Hom-Ext quiver and applications to exceptional collections

Kiyoshi Igusa, Ray Maresca

We study what we call the Hom-Ext quiver and characterize it as a type of `superquiver'. In type $A ~$ , the Hom-Ext quiver of an exceptional set is the tiling algebr…

math.RT2023

Enumerating families of clusters in type $A ~$

Ray Maresca, Nikolas Proskura

In this paper, we will place clusters in type $A ~$ (equivalently triangluations of an annulus) into infinite families parametrized by winding numbers of certain arc…

math.AG2022

A 4-fold categorical equivalence

Ray Maresca

In this note, we will illuminate some immediate consequences of work done by Reineke that may prove to be useful in the study of elliptic curves. In particular, we will construct a…

math.RT2022

Five Lectures on Cluster Theory

Ray Maresca

In this paper, we will present the author's interpretation and embellishment of five lectures on cluster theory given by Kiyoshi Igusa during the Spring semester of 2022 at Brandei…

math.RT2022

On Clusters and Exceptional Sets in Types $A$ and $A ~$

Kiyoshi Igusa, Ray Maresca

In this paper we first study clusters in type $A ~$ by collecting them into a finite number of infinite families given by Dehn twists of their corresponding triangul…

math.RT2022

Combinatorics of Exceptional Sequences of Type $A ~_{n}$

Ray Maresca

It is known that there are infinitely many exceptional sequences of quiver representations for Euclidean quivers. In this paper we study those of type $A ~_{n}$ and cl…

Enumerating iterated tilted algebras in type A

Pseudo-torsion classes

The Hom-Ext quiver and applications to exceptional collections

Enumerating families of clusters in type A~

A 4-fold categorical equivalence

Five Lectures on Cluster Theory

On Clusters and Exceptional Sets in Types A and A~

Combinatorics of Exceptional Sequences of Type A~n​

Enumerating iterated tilted algebras in type $A$

Enumerating families of clusters in type $A ~$

On Clusters and Exceptional Sets in Types $A$ and $A ~$

Combinatorics of Exceptional Sequences of Type $A ~_{n}$