Sami H. Assaf

 C. L. E. Moore Instructor
Massachusetts Institute of Technology


Office: Building 2, Room 378

Phone: (617) 258-6721

Email: sassaf [AT] math [DOT] mit [DOT] edu

Mailing Address:
    Department of Mathematics
    Massachusetts Institute of Technology
    77 Massachusetts Avenue
    Cambridge, MA 02139-4307

Curriculum Vita
Photographs from my travels

Courses:
Fall 2009
Spring 2009

Research:

My research interests lie in the general areas of algebraic combinatorics and combinatorial representation theory. In particular, I am interested in symmetric functions, tableaux combinatorics and the representation theory of classical groups.

My current research program is primarily concerned with developing the theory of dual equivalence graphs initiated in my dissertation, directed by Mark Haiman at UC Berkeley. Dual equivalence graphs, and their generalizations called D graphs, provide a combinatorial tool for establishing the symmetry and Schur positivity of a function expressed in terms of quasi-symmetric functions. So far, I have used this machinery to give a combinatorial proof of the Schur positivity of both LLT and Macdonald polynomials. In recent work with Sara Billey at the University of Washington, we use this tool to give a combinatorial proof of the Schur positivity of k-Schur functions. Since the inspiration for these graphs came from studying crystal graphs, I have also been looking in to connections between crystal graphs, which combinatorialize SL_n modules, and dual equivalence graphs, which, in some sense, combinatorialize S_n modules.

Recently I collaborated with Persi Diaconis and K. Soundararajan at Stanford to count the number of riffle shuffles required to randomize a deck with repeated cards, thereby earning myself an Erdös number of 2. Adriano Garsia has inspired me to try to find a 'kicking basis' for the Garsia-Haiman modules, a problem for which he has offered up $1000 for a solution. Peter McNamara and I discovered a cute Pieri rule for multiplying skew Schur functions while we were working on a related project in symmetric functions.

For abstracts and PDF versions of my publications and preprints, please refer to my publications page.


Conferences:

January 13 - 16, 2010 2010 Joint Mathematics Meeting, San Francisco, CA
March 07 - 11, 2010 Macdonald Polynomials and Geometry at the Clay Mathematics Institute, Cambridge, MA
March 15 - 19, 2010 Localization techniques in equivariant cohomology at the American Institute of Mathematics, Palo Alto, CA
March 21 - 27, 2010 Combinatorial Representation Theory at the Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany
April 10 - 11, 2010 AMS 2010 Spring Central Section Meeting, Macalester College, St. Paul, MN
June 06 - 11, 2010 Whittaker Functions, Crystal Bases, and Quantum Groups at the Banff International Research Station, Banff, Canada
June 14 - 17, 2010 SIAM Conference on Discrete Mathematics, Austin, TX
July 04 - 07, 2010 Lattice Path 2010, 7th International Conference on Lattice Path Combinatorics and Applications, Sienna, Italy
August 02 - 06, 2010 FPSAC 2010, 22nd International conference on Formal Power Series and Algebraic Combinatorics, San Francisco, CA
November 14 - 19, 2010 Quasisymmetric Functions at the Banff International Research Station, Banff, Canada





If a 'religion' is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one.
--John Barrow