Research Summary

I study the representation theory of quivers and associative algebras and related concepts in combinatorics, representation theory, and homological algebra. Some of my specific research interests are:

• Lattices of torsion classes and completely semidistributive lattices, combinatorial interpretations of τ-tilting theory

• Applications of homological algebra to topological data analysis

• Torsion classes and analogs of τ-tilting theory for exact categories

• Semi-invariant pictures, picture groups, and stability conditions

• Representations of continuous quivers

I also have an interest in privacy preserving data publication. The intuitive goal is to mathematically guarantee that a release of an (edited) dataset or statistic will not violate the privacy of those whose data it contains. I am particularly interested in how data weighting and editing impacts privacy guarantees.

Google Scholar and Research Gate profiles.

My papers on the arXiv.

Recent Papers and Preprints

1. Mutation of τ-exceptional pairs and sequences, with Aslak Bakke Buan and Bethany R. Marsh. arXiv:2402.10301.

2. Invariants of persistence modules defined by order embeddings, with Claire Amiot and Thomas Brüstle. arXiv:2402.09190.

3. Pop-stack operators for torsion classes and Cambrian lattices, with Colin Defant and Emily Barnard. arXiv:2312.03959.

4. Exact structures for persistence modules, with Benjamin Blanchette and Thomas Brüstle. arXiv:2308.01790.

5. A facial order for torsion classes. To appear in International Mathematics Research Notices rnae078. (doi, arXiv:2305.06031).

6. τ-exceptional sequences and the shard intersection order in type A. arXiv:2303.11517.

7. Homological approximations in persistence theory, with Benjamin Blanchette and Thomas Brüstle. Canadian Journal of Mathematics 76 (2024), no. 1, 66-103. (doi, manuscript)

8. Morphisms and extensions between bricks over preprojective algebras of type A, with Xinrui You. Journal of Algebra 639 (2024), 464-487. (doi, arXiv:2303.11513).

9. Decomposition of pointwise finite-dimensional S^1 persistence modules, with J. Daisie Rock. Journal of Algebra and its Applications 23 (2024), no. 3. (doi, manuscript).

10. Exceptional sequences in semidistributive lattices and the poset topology of wide subcategories, with Emily Barnard. To appear in Journal of Algebra and its Applications. arXiv:2209.11734.

11. Infinitesimal semi-invariant pictures and co-amalgamation, with Kiyoshi Igusa, Moses Kim, and Gordana Todorov. Journal of the London Mathematical Soceity 109 (2024), no. 1. (doi) (open source)

12. A uniqueness property for τ-exceptional sequences, with Hugh Thomas. Algebras and Representation Theory 27 (2024), 461-468. (doi, full text via publisher).

13. τ-perpendicular wide subcategories, with Aslak Bakke Buan. Nagoya Mathematical Journal  252 (2023), 959-984. (doi, arXiv:2107.01141)

14. Composition series of arbitrary cardinality in modular lattices and abelian categories, with J. Daisie Rock. Advances in Mathematics 433 (2023). (doi, manuscript).

15. Pairwise compatability for 2-simple minded collections II: preprojective algebras and semibrick pairs of full rank, with Emily Barnard. Annals of Combinatorics 26 (2022), 803-855. (doi, full text via publisher).

16. A counterexample to the 𝜙-dimension conjecture, with Kiyoshi Igusa. Mathematische Zeitschrift 300 (2022), 807-826. (doi, full text via publisher)

17. Differentially private k-nearest neighbor missing data imputation. With Chris Clifton, Keith Merrill, and Shawn Merrill.  ACM Transactions on Privacy and Security 25 (2022), no. 3, 1-23. (doi, manuscript)

18. The Bernardi formula for non-transitive deformations of the braid arrangement, with Ankit Bisain. The Electronic Journal of Combinatorics 28 (2021), no. 4. (doi) (open source)

19. Pairwise compatability for 2-simple minded collections, with Kiyoshi Igusa. Journal of Pure and Applied Algebra 225 (2021), no. 6. (doi, manuscript)

20. τ-cluster morphism categories and picture groups, with Kiyoshi Igusa. Communications in Algebra 49 (2021), no. 10, 4376-4415. (doi, manuscript)

21. A partitioned recoding scheme for privacy preserving data publishing. With Chris Clifton, Keith Merrill, Shawn Merrill, and Amjad Zahraa. Privacy in Statistical Databases (PSD 2020) (J. Domingo-Ferrer and K. Muralidhar eds.), Lecture Notes in Computer Science 12276 (2020), pp. 49-61. (doi, manuscript)

22. Resolution quiver and cyclic homology criteria for Nakayama algebras, with Kiyoshi Igusa. Journal of Algebra 553 (2020), 138-153. (doi, manuscript)