Mark Shimozono's Research Page
Combinatorial aspects of representation theory and algebraic
geometry, including double affine Hecke algebras and Macdonald
polynomials, Schubert calculus (especially quantum cohomology and
K-theory) for affine Grassmannians and affine flag varieties, quiver
degeneracy loci, and crystal graphs for quantum affine algebras.
I highly recommend the free open-source mathematical computational
system sage and the sage-combinat
extension for combinatorics (and many other things). One of my
favorite things is that I can develop code for it and the code will
be maintained and useful/useable in the future.
I was one of the principal investigators on an National Science
Foundation Focused Research Group
Schubert Calculus: Combinatorial, geometric, physical, and
papers on the math arXiv
presentation on crystal graphs