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String theory, QCD and confinement, Seiberg-Witten theory,
low-energy gauge theories and sigma-models, exact renorm-group,
non-critical strings, conformal theories, topological field theories,
classical integrable systems, quantum integrable systems, correlation
functions in two-dimensional systems
The main results:
Potential model of light mesons; QCD model for the double difraction
dissociation; central charge of the string describing QCD; p-adic
strings; asymptotics of the correlators in 1+1-dimensional systems;
matrix models in two-dimensional gravity: integrability and constraint
algebras; quantum deformations of integrable equations; matrix models
describing gauge theories; S-matrix in the Liouville theories; Whitham
averaging as a replace for RG in non-perturbative regime; Seiberg-Witten
theory: integrability, Whitham hierarchies and associativity equations;
generalized WDVV equations; low-energy QCD sigma-models; integrable
systems as symplectomorphisms of the free ones; exact RG; B-independence
of brane RR-charges.
Current interests:
String theory, stringy description of QCD, low-energy sigma-models,
Seiberg-Witten theory, generalized WDVV equations, classical integrability
in quantum integrable systems, quantum deformations of the classical
hierarchies, non-critical strings and Liouville theories, non-perturbative
renorm-group, Whitham hierarchies.
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