Sami H. Assaf

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


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:

Previously:
Fall 2010 18.304 Undergraduate Seminar in Discrete Mathematics
Fall 2009 18.314 Combinatorial Analysis
Spring 2009 18.304 Undergraduate Seminar in Discrete Mathematics
Fall 2008 18.02 Multivariable Calculus (recitations)

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.


For Fun:



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