- 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.
|March 10, 2008 - March 14, 2008||Lie Theory|
|March 17, 2008 - March 21, 2008||Topics in Combinatorial Representation Theory|