Current teaching:
- Calculus I
Paper and preprint:
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.
Journal of Combinatorial Theory, Series A, 119 (2012), Issue 3, 747-764. | 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.