My work has always tried to unite the true with the beautiful and when I had to choose one or the other,
I usually chose the beautiful. -- Hermann Weyl.

My area of research is algebraic combinatorics and representation theory. My focus is in applying
combinatorics to answer algebraic questions related to the Coxeter groups and their related algebras,
e.g. Hecke algebras, Brauer algebras, partition algebras. I am particularly interested in the interplay
between Markov traces, centralizer algebras, quantum groups, Hopf algebras, symmetric functions,
and knot theory. I have a special fondness towards Young diagrams and the symmetric group.

PUBLICATIONS AND PREPRINTS:

    The Hecke algebra of type B at roots of unity,  Markov traces and subfactors.
        Ph.D. Thesis, UCSD 1999.

   Weights of Markov traces on Hecke algebras, J. Reine Angew Math. 508, (1999)
        157-178.

    Markov traces and Hecke algebras at roots of unity, Proceedings of the Formal Power
        Series and Algebraic Combinatorics, 1999. pp. 405-416.

    Hecke algebras of type B and type D and Subfactors, Pacific Journal of Math.  Vol
       199, No. 1 (2001) 137-161.

    (with H. Wenzl) q-Centralizer algebras for spin groups, Journal of Algebra, 253 (2002)
        237-275.

    (with M. Orrison and D. Rockmore) Rooted trees and the representation theory of 
        iterated wreath products of abelian groups, Advances in Applied Math. 33, Issue 3,
        (2004), 531-547.  

    On the algebraic decomposition of centralizer algebras of the hyperoctahedral group,
        Contemporary Math. 376, (2005), 345-357.  

   (with C. Ballantine) On the Kronecker product $s_{(n-p,p)}\ast s_{\lambda}$,
        Elec. Journal of Combinatorics. Vol. 12, (2005), #R28, 1-26.

    (with M. Aguiar and K. Nyman) New Results on the Peak algebra,
        J. of Algebraic Combinatorics. Vol. 23, No.2 (2006), pg. 149-188

   (with A. Ram) Affine Braids, Markov traces and the category O, Algebraic groups
        and homogeneous spaces, 423-473, Tata Inst. Fund. Res. Stud. Math., Tata Inst. Fund. Res.,
       Mumbai, 2007. http://lanl.arxiv.org/abs/math.RT/0401317  

    (with C. Ballantine) A combinatorial interpretation for the coefficients in the Kronecker
       product $s_{(n,n-p)}\ast s_{\lambda}$. S\'em. Lothar. Combin. 54A (2005/06), Art. B54Af, 29 pp.

     On the partition algebras of complex reflection groups, Journal of Algebra, 313 (2007) 590-616.

    (with M. Aguiar) The Hopf Algebra of Uniform block Permutations., J. Algebraic Combin. 28
       (2008), no. 1, 115--138.
       
       An extended abstract of 13 pages appeared in:
        Proceedings of the Formal Power Series and Algebraic Combinatorics 2005
        Available at: http://lanl.arxiv.org/abs/math.RA/0505199.

    (with A. Mathas)  Cyclotomic Solomon Algebras Adv. Math. 219 (2008), no. 2, 450--487.

    (with E. Briand and M. Rosas)   Reduced Kronecker coefficients and counter-examples
        to Mulmuley's saturation conjecture SH, with an appendix by Ketan Mulmuley. To appear in
       computational complexity

    (with E. Briand and M. Rosas)   Quasipolynomial formulas for the Kronecker coefficients
        indexed by two two-row shapes FPSAC 2009, Hagenberg, Austria, Discrete Mathematics and
       Theoretical Computer Science proc. AK, 2009, 241-252

    (with E. Briand and M. Rosas)   The stability of the Kronecker product of Schur functions
       submitted for publication

    (with M. Zabrocki) The Hilbert series for the ring of Hook Schur functions.
        Preprint available at: http://lanl.arxiv.org/abs/math.CO/0008152