- Algebraic combinatorics —
Hall–Littlewood polynomials, Kostka–Foulkes polynomials, the symmetric
group, Young tableaux.
- Basic and elliptic hypergeometric series — beta integrals,
series based on root systems.
- q-Series and partition theory —
the Bailey lemma,
the Borwein conjecture,
partial theta functions.
- Representation theory — characters of infinite-dimensional Lie
- Special functions — elliptic functions, orthogonal polynomials,