Combinatorics: Alternating sign matrices and plane partitions

The successful student would develop knowledge and skills in several general areas of algebraic, geometric and enumerative combinatorics, including polytope theory, poset theory and symmetric function theory. The student would also gain high level expertise related to the specific areas of alternating sign matrices and plane partitions, including connections with integrable statistical mechanical models, fully packed loop configurations, dynamical algebraic combinatorics, lattice path techniques, and determinant and Pfaffian evaluations. Furthermore, substantial experience in the use of a computer algebra system, such as Mathematica, would be acquired.