Research

Research interests

Representation theory and its interactions with algebraic geometry and combinatorics. One particular topic I enjoy thinking about is McKay correspondence. Objects associated to quivers
(Nakajima quiver varieties, Hall algebras arising from categories of representations of quivers over finite fields, to name a few) are of great interest to me as well.

Papers

  1. (with K. Kaveh and C. Manon) Toric vector bundles over a discrete valuation ring and Bruhat-Tits buildings, arXiv
  2. The universe inside Hall algebras of coherent sheaves on toric resolutions, arXiv, submitted to Int. Math. Res. Not. IMRN
  3. On categories O of quiver varieties overlying the bouquet graphs, arXiv, to appear in Represent. Theory, Amer. Math. Soc.
  4. On Poincare polynomials of shuffle algebra representations, arXiv
  5. (with M. Elhamdadi and N. Fernando) Ring theoretic aspects of quandles, arXiv, Journal of Algebra, 526, 2019, pp 166-187
  6. Nontrivial Topological Quandles, arXiv, Arnold Mathematical Journal, 8, 2022, pp 535-542

Applied Mathematics

  1. (with M. Diss) Manipulable outcomes within the class of scoring voting rules, arXiv, Mathematical Social Sciences 111, May 2021, pp 11-18

Surveys

  1. (with D. Matvieievskyi) Soergel's V and the Kazhdan-Lusztig conjecture, chapter in Introduction to Soergel bimodules, RSME Springer Series, 2020

Expository texts

Soergel bimodules, Hecke algebras, and Kazhdan-Lusztig basis. Notes for the MIT-NEU Graduate seminar on category O and Soergel bimodules, Fall 2017.
Shuffle Algebras. Notes for the MIT-NEU Graduate Student Seminar on Double affine Hecke algebras and elliptic Hall algebras, Spring 2017.
Classification of solutions of the classical Yang- Baxter equation (CYBE). Notes for a talk given for the course "Differential equations and Quantum groups", Spring 2016
Gieseker moduli space as a Nakajima quiver variety. Notes for the MIT-NEU Graduate seminar on quiver varieties, Spring 2015.