My research interests lie in the representation theory of quivers. In particular, I've been interested in:
Exceptional sequences, exceptional collections, and the braid group action
Tau-tilting theory, Tau-exceptional sequences, lattice of torsion classes, second Tau-Brauer-Thrall conjecture
Simple-minded collections
The cluster morphism category
Quiver Grassmannians
The rhombic picture and its relation to algebraic geometry
Publications/Preprints/Works in Preparation:
Enumeration families of clusters in type $\tilde{\mathbb{A}}$, Nov. 2023, Accepted to special issue of JAA
Five lectures on cluster theory, Feb 2023, Sur. in Math. and its App.
Combinatorics of exceptional sequences of type $\tilde{A}_n$, April 2022 Submitted
A 4-fold categorical equivalence, June 2023, Proc. of the AMS
Solution to ΠME Journal Problem #1340, Spring 2018 Issue, May 2018
Talks:
Combinatorics of exceptional sequences of type $\tilde{A}_n$, NCSU Algebra and Combinatorics Seminar, 2023.
Exceptional collections in type $\tilde{A}$, Auslander Conference, Woods Hole, MA, 2022.
Serre duality and Auslander-Reiten triangles, Brandeis GSS, 2021.
The Auslander-Reiten components in the rhombic picture, Brandeis University, 2020.
Every projective variety is a quiver Grassmannian, Brandeis University, 2020.
Quiver representations in Matlab, Brandeis Graduate Student Seminar (GSS), 2019.
Topology in discrete dynamical systems and chaos, Manhattan College, 2018.
The Zeckendorf decomposition, Spuyten Duyvil Undergraduate Mathematics Conference, 2018.
Talks (Rep. Theory Reading Group)
Tau-tilting Theory
Friezes (infinite and finite) and triangulations
Which Cluster Morphisms are CAT(0)
Continuous Quivers of Type A
Tau-Exceptional Sequences
Noetherian Hereditary Abelian Categories Satisfying Serre Duality
Foundations of Quiver Representations (Including Tilting Theory)