quantum groups, integrable systems, topological and conformal field theories; Teichmueller spaces.
Main publications:
Fock V. V., Rosly A. A. Poisson structure on moduli of flat connections on Riemann surfaces and r-matrix // Amer. Math. Soc. Transl. Ser. 2, 1999, 191(43), 67–86.
Fock V. V. Dual Teichmuller spaces // Preprint ITEP-TH-5-96, arXiv:math/9702087.
Bilal A., Fock V. V., Kogan I. I. On the origin of W-algebras // Nucear Phys. B, 1991, 359(2,3), 635–672.
V. V. Fock, L. O. Chekhov, “Quantum Mapping Class Group, Pentagon Relation, and Geodesics”, Trudy Mat. Inst. Steklova, 226 (1999), 163–179; Proc. Steklov Inst. Math., 226 (1999), 149–163
Dimers, clusters and integrable systems V. V. Fock General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences December 22, 2011 14:00
Cluster algebras Vladimir Fock General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences January 19, 2004