Research

My research interests are in the area of noncommutative algebra, with focus on quantum algebras and their connections to geometry, combinatorics, and representation theory. If you are a student at XULA and interested in doing research or learning more advanced topics in algebra, please send me an email or visit me during office hours.

Preprints:

  1. Root of unity quantum cluster algebras and discriminants

(with K. Trampel and M. Yakimov) arXiv:2012.02314


  1. The Deligne--Simpson problem for connections on $\mathbb {G}_m $ with a maximally ramified singularity

(with M. C. Kulkarni, N. Livesay, J. P. Matherne, and D. S. Sage) arXiv:2108.11029 (accepted to Adv. Math.)


  1. Poisson geometry and Azumaya loci of cluster algebras

(with G. Muller, K. Trampel, and M. Yakimov) arXiv:2209.11622

Publications:

  1. Actions of cocommutative Hopf algebras,

(with Martin Lorenz and Ramy Yammine)

Journal of Algebra, Vol. 546, March 2020, 703-722. arXiv: 1907.06958


  1. On the adjoint representation of a Hopf algebra,

(with Stefan Kolb, Martin Lorenz, and Ramy Yammine)

Proceedings of the Edinburgh Mathematical Society (2020) 63: 1092-1099. arXiv:1905.03020


  1. Irreducibility of the Cayley--Menger determinant, and of a class of related polynomials,

(with Mowaffag Hajja, Mostafa Hayajneh, and Shadi Shaqaqha)

Beitr Algebra Geom (2018) 59: 327-342. arXiv:1701.00407


  1. Distances from the vertices of a regular simplex,

(with Mowaffag Hajja, Mostafa Hayajneh, and Shadi Shaqaqha)

Results in Mathematics 72 (1-2), 633-648. arXiv:1609.06552


  1. Noncommutative discriminants via Poisson primes,

(with Kurt Trampel and Milen Yakimov)

Adv. Math. 322 (2017), 269-307. arXiv:1603.02585