Publications and Talks
Areas of interest:
I am interested in representation theory, combinatorics, and algebraic geometry. My immediate research is on various aspects of cluster algebras. Here is my research statement (PDF), Dec. 2009.
Publications:
2. Combinatorial Expressions for F-polynomials in Classical Types.
We give combinatorial formulas for F-polynomials in cluster algebras of classical types in terms of the weighted paths in certain directed graphs. As a consequence we prove the positivity of F-polynomials in cluster algebras of classical types.
arXiv:0912.2332.1. Cluster algebras of finite type via Coxeter elements and principal minors (with Andrei Zelevinsky).
We construct a family of uniform geometric realizations for any cluster algebra of finite type as coordinate rings of certain reduced double Bruhat cells in the semisimple group of the same Cartan-Killing type. In each of these realizations, the cluster variables appear as certain (generalized) principal minors.
Transformation Groups 13 (2008), No. 3-4, 855-895. | arXiv:0804.3303.
Talks:
- 2009, June, Northeastern University, Tapas Seminar.
- 2008, Dec., MIT, Combinatorics seminar.
- 2008, July, Academic Sinica (Taipei, Taiwan), Algebra Seminar.
- 2008, Apr., Maurice Auslander Distinguished Lectures and International Conference, Woods Hole, MA, USA.
- 2007, Aug., XII International Conference on Representations of Algebras and Workshop, Torun, Poland.
- 2007, June, Northeastern University, Tapas Seminar.
- 2006, June, Northeastern University, Tapas Seminar.
"Word cloud" for the titles of my papers, made using http://www.wordle.net
Well..., not really a cloud yet.
Cluster Algebra Portal | math.CO | math.QA | math.RT | "Cluster" on arXiv | Quiver mutation in Java by Bernhard Keller