Maya Ahmed, Lipika Deka, Tyrrell McAllister, and Ruriko Yoshida.
We had enjoyed the enthusiasm of several undergraduates:
David Haws, Peter Huggins, Austin Shapiro, Jeremy Tauzer, Jon Brooks, Ricardo Castro and Federico Arana. VRAP Raymond Hemmecke Faculty members Jes\'us De Loera (leader), Anne Schilling, and Craig Tracy. During this academic year we had also contributions from Greg Kuperberg and Alexander Soshnikov. Most of the students we mentioned are involved in a dissertation project that has a strong combinatorial component. For example, Maya Ahmed works on ``Combinatorics of Magic Squares'' and Lipika Deka works on ``Combinatorial representation of crystal bases''. COURSES: The general theme of the RFG has been to introduce students to the areas of research on combinatorics available in the department (algebraic combinatorics and representation theory, combinatorial algorithms, applications to optimization and physics). The program had two graduate courses: (1) ``Symmetric Functions'' Craig Tracy for Winter 2003 (2) ``Symmetric Functions II'' Anne Schilling in Spring 2003. SEMINARS: Along the academic year we also have been running the research seminar ``Discrete Mathematics'' with an emphasis on research lectures and visitors (to meet Thursdays). Parallel to this there is an active reading seminar where students will read a variety of background papers and/or books. For Spring quarter we have a selection of the following papers (Most available from the ArXiv):
``Hook length formula and Geometric Combinatorics'' Igor Pak
``Groups generated by Involutions, Gelfand Tsetlin Patterns, and Combinatorics of Young Tableaux'' Anatol Kirillov and Arkady Berenstein.
``Polyhedral Realizations of Crystal Bases for Quantized Kac-Moody Algebras'' by Toshiki Nakashima and Andrei Zelevinsky
``Polyhedral Realizations of Crystal Bases for Integrable Highest Weight Modules'' Toshiki Nakashima
``Polytopes for Crystallized Demazure Modules and Extremal Vectors'' Toshiki Nakashima
`` Tensor product multiplicities, Canonical bases, and totally positive varieties'' Arkady Berenstein and Andrei Zelevinsky.
seminars will also have talks of combinatorial interest. In addition we expect the students to present their work in front of their peers and craft a poster for presentation in the Bay Area Discrete Math day in October of 2002 and March 2003.