ResearchInterests

Research Interests in Mathematics Subject Classification 2010

Analysis

  • 42C05 orthogonal functions and polynomials, general theory,
  • 33C45 orthogonal polynomials and functions of hypergeometric type,
  • 30E05, 44A60 moment problems,
  • 30B70 continued fractions,
  • 65R10, 65R20 integral transforms and integral equations,
  • 35Q15 Riemann-Hilbert problems,
  • 34E05, 35C20 asymptotic expansions,
  • 34A34 nonlinear differential equations and systems, general,
  • 34A05 explicit solutions of differential equations and reductions,

Integrable Systems

  • 34M55 PainlevĂ© and other special equations, classification, hierarchies, and isomonodromic deformation,
  • 33E17 PainlevĂ©-type functions,
  • 58F07 completely integrable systems,

Combinatorics

  • 05A15 exact enumeration problems, generating functions,
  • 05E10 Tableaux, representations of the symmetric group,
  • 05E15 symmetric functions,

Probability Theory

  • 60E05 distributions, general theory,
  • 60E10 characteristic functions,
  • 60F05 central limit and other weak theorems,
  • 15A52 random matrices,
  • 60K35 Interacting random processes; statistical mechanics type models,
  • 82C22 interacting particle systems,

Mathematical Physics

  • 81T25 quantum field theory on lattices,
  • 82B10 quantum equilibrium statistical mechanics,
  • 82B23 exactly solvable models,
  • 82B26, 82B27 phase transitions and critical phenomena

Spectral Theory

  • 47A75, 58F19 eigenvalue and spectral problems,
  • 47A10 spectrum, resolvent,
  • 81U40 inverse scattering problems,

Representation Theory

  • 20F55 Reflection and Coxeter groups,