Arithmetic algebraic geometry, geometry and integral geometry, representation theory.
Arithmetic algebraic geometry: mixed motives, motivic Galois groups, motivic cohomology, special values of L-functions of algebraic varieties, regulators, polylogarithms and their generalizations, motivic fundamental groups, geometry of modular varieties, Feynman integrals.
Geometry: higher Teichmuller theory and its quantization, quantum dilogarithm, quantum groups.
D-module approach to integral geometry.
I was educated at Moscow, participated at the seminars of Gelfand, Manin, Beilinson and others.
ALEXANDER GONCHAROV, Ph. D 1987 (USSR)
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