Anatol N. Kirillov's research topics

• Representation theory (Classical groups, Kac-Moody algebras and groups, Quantum groups, Hecke algebras)

• Algebraic Combinatorics (Symmetric functions, Young tableaux, Rigged configurations, Yang-Baxter equations, Bracket algebras, Schubert calculus)

• Tropical Combinatorics (Gelfand-Tsetlin patterns, Crystal basis, Convex polytops, Toric varieties, Continious analog of Robinson-Schensted-Knuth correspondence)

• Algebraic Geometry (Artin-Mazur formal groups, Mixed Hodge structures, Quantum cohomology, Quantum Schubert calculus)

• Special Functions (Clebsch-Gordan and Racah-Wigner coefficients, generalized Hypergeometric functions, Quantum polylogarithms)

• Exactly Solvable Models (Bethe ansatz, Formfactors, Dilogarithm identities, Bosonic and Fermionic formulae for characters and branching functions)

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