Etienne Rassart

H. C. Wang Assistant Professor of Mathematics

Web Site www.math.cornell.edu/~rassart Contact Information Office:  587 Malott Hall Phone:  (607) 255-4030 Fax:  (607) 255-7149 Email:  rassart@math.cornell.edu Courses & Office Hours

Education

Ph.D. (2004) Massachusetts Institute of Technology

Research Area: Algebraic combinatorics, combinatorial aspects of the representation theory of complex semisimple Lie algebras, convex geometry, and combinatorial aspects of symplectic geometry

The interplay between combinatorics, the representation theory of complex semisimple Lie algebras, symplectic geometry and convex geometry has been a rich source of mathematical developments in recent years. Most of my recent work has been in using tools from all these areas to explore combinatorial invariants of the irreducible representations of the classical complex semisimple Lie algebras (types A, B, C, D), particularly the weight multiplicities and Clebsch-Gordan coeffcients. For type A, these appear in the combinatorial theory of symmetric functions in the form of the Kostka numbers and the Littlewood-Richardson coefficients respectively. Efficiently computing the weight multiplicities and Clebsch-Gordan coefficients has been a long-standing problem. A variety of formulas and methods exist for them, some of which are efficient for certain ranges of the parameters, but no single approach seems to provide a fast way of computing these combinatorial invariants. The need for efficient algorithms is motivated by the fact that these numbers appear in quantum physical computations. My current research project ties into all these areas of mathematics, using tools from combinatorics, convex geometry and symplectic geometry to study the behavior of the Kostka numbers and Littlewood-Richardson coefficients.

Selected Publications

Enumeration of symmetry classes of convex polyominoes in the square lattice (with Pierre Leroux and Ariane Robitaille), Adv. in Appl. Math. 21 no. 3 (1998), 343–380.

Path counting and random matrix theory (with Ioana Dumitriu), Electronic Journal of Combinatorics 10 no. 1 (2003), #R43.

A vector partition function for the multiplicities of sl_k(C) (with Sara Billey and Victor Guillemin), Journal of Algebra 278 no. 1 (2004), 251–293.

Signature quantization and representations of compact Lie groups (with Victor Guillemin), Proceedings of the National Academy of Sciences (USA) 101 (2004), 10884–10889.

A polynomiality property for Littlewood-Richardson coefficients, Journal of Combinatorial Theory, Series A 107 no. 2 (2004), 161–179.

Last modified: August 26, 2005