Current Research:

Publications/Preprints/Works in Preparation: 

1. The Hom-Ext quiver and applications to exceptional collections, Sep. 2025, Preprint.

   • Joint with Kiyoshi Igusa

2. Enumeration families of clusters in type $\tilde{\mathbb{A}}$, Nov. 2023, Accepted to special issue of JAA

   • Joint with Nikolas Proskura

3. Five lectures on cluster theory, Feb 2023, Sur. in Math. and its App.

4. On clusters and exceptional sets in types A and $\tilde{A}_n$, June 2022 Accepted to special issue of JAA 

   • Joint with Kiyoshi Igusa

5. Combinatorics of exceptional sequences of type $\tilde{A}_n$, April 2022 Submitted 

6. A 4-fold categorical equivalence, June 2023, Proc. of the AMS

7. Solution to ΠME Journal Problem #1340, Spring 2018 Issue, May 2018

Talks:

1. The Hom-Ext quiver and applications to exceptional collections, CBB conference 2024, Auslander conference 2025, Geometric Models in Representation Theory and Beyond June 2025.

2. On the relationship between t-structures and exceptional collections over hereditary algebras, Queen's Algebra and Geometry Seminar, 2023, Auslander conference 2024.

3. Counting families of clusters in type affine A, Lancaster University, March 2024.

4. Combinatorics of exceptional sequences of type $\tilde{A}_n$, NCSU Algebra and Combinatorics Seminar, 2023.

5. Relative projectivity in exceptional collections, ARTA IX, Queen's University, Kingston, ON, CAN, 2023.

6. Exceptional collections in type $\tilde{A}$, Auslander Conference, Woods Hole, MA, 2022.

7. Lattice theoretic and combinatorial aspects of $\tau$-tilting theory. Mutations Summer School, UQAM, Canada, 2022.

8. Combinatorics of exceptional sequences of type $\tilde{A}_n$, Syracuse Annual NYSRG Mathematics Conference, 2022.

9. Serre duality and Auslander-Reiten triangles, Brandeis GSS, 2021.

10. The Auslander-Reiten components in the rhombic picture, Brandeis University, 2020.

11. Every projective variety is a quiver Grassmannian, Brandeis University, 2020.

12. Quiver representations in Matlab, Brandeis Graduate Student Seminar (GSS), 2019.

13. Topology in discrete dynamical systems and chaos, Manhattan College, 2018.

14. 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)