- positive combinatorial formulas: q-weight multiplicities, Kazhdan-Lusztig polynomials, generalized Littlewood-Richardson coefficients;
- combinatorial indexings and constructions of irreducible representations: Springer correspondences, Langlands classifications, path models, tableaux;
- the Virasoro conjecture: counting branched covers of Riemann surfaces, Hurwitz numbers, cycle types, symmetric functions, determinant formulas;
- representation theoretic interpretations of Macdonald polynomials: Hilbert scheme, diagonal invariants, affine and graded Hecke algebra modules: distributions and convergence of random processes: random matrices, subsequences of permutations, statistical mechanics models;
- decomposition numbers for representations: affine Lie algebras, modular representations, highest-weight categories, homology representations, finite goups of Lie type;
- product structure in cohomology and K-theory: Schubert varieties, quiver varieties, toric varieties, loop Grassmanians.
- cluster algebras: generalized associahedra associated with root systems, coordinate rings of flag varieties and their double Bruhat cells.
Primary Mathematics Subject Classification No Primary AMS MSC Secondary Mathematics Subject Classification No Secondary AMS MSC
|March 10, 2008 - March 14, 2008||Lie Theory|
|January 22, 2008 - January 25, 2008||Introductory Workshop on Combinatorial Representation Theory|
|March 17, 2008 - March 21, 2008||Topics in Combinatorial Representation Theory|