Number Theory

  • Ring Theory and Module Theory, especially Krull dimension, torsion theories, and localization
  • Algebraic Theory of Lattices, especially their dimensions (Krull, Goldie, Gabriel, etc.) with applications to Grothendieck categories and module categories equipped with torsion theories
  • Field Theory, especially Galois Theory, Cogalois Theory, and Galois cohomology
  • Algebraic Number Theory, especially rings of algebraic integers
  • Iwasawa Theory of Galois representations and their deformations, Euler and Kolyvagin systems, Equivariant Tamagawa Number Conjecture

Combinatorics

  • Combinatorial design theory, in particular metamorphosis of designs, perfect hexagon triple systems
  • Graph theory, in particular number of cycles in 2-factorizations of complete graphs
  • Coding theory, especially relation of designs to codes
  • Random graphs, in particular, random proximity catch graphs and digraphs

Differential Equations

  • Partial Differential Equations
  • Nonlinear Problems of Mathematical Physics
  • Dissipative Dynamical Systems
  • Scattering of classical and quantum waves
  • Wavelet analysis
  • Molecular dynamics

Analysis

  • Banach algebras, especially the structure of the second Arens duals of Banach algebras
  • Abstract Harmonic Analysis, especially the Fourier and Fourier-Stieltjes algebras associated to a locally compact group
  • Geometry of Banach spaces, especially vector measures, spaces of vector valued continuous functions, fixed point theory, isomorphic properties of Banach spaces

Mathematical Physics

  • Differential geometric, topologic, and algebraic methods used in quantum mechanics
  • Geometric phases and dynamical invariants
  • Supersymmetry and its generalizations
  • Pseudo-Hermitian quantum mechanics
  • Quantum cosmology

Numeric Analysis

  • Numerical Linear Algebra
  • Numerical Optimization
  • Perturbation Theory of Eigenvalues
  • Eigenvalue Optimization

Probability and Stochastic Processes

  • Mathematical finance
  • Stochastic optimal control and dynamic programming
  • Stochastic flows and random velocity fields
  • Lyapunov exponents of flows
  • Unicast and multicast data traffic in telecommunications
  • Probabilistic Inference

Statistics

  • Inference on Random Graphs (with emphasis on modeling email and internet traffic and clustering analysis)
  • Graph Theory (probabilistic investigation of graphs emerging from computational geometry)
  • Statistics (analysis of spatial data and spatial point patterns with applications in epidemiology and ecology and statistical methods for medical data and image analysis)
  • Classification and  Pattern Recognition (with applications in mine field and face detection)

Algebraic Geometry

  • Arithmetical Algebraic Geometry, Arakelov geometry, Mixed Tate motives
  • p-adic methods in arithmetical algebraic geometry, Ramification theory of arithmetic varieties

 Geometry and Topology

  • Topology of low-dimensional manifolds, in particular Lefschetz fibrations, symplectic and contact structures, Stein fillings
  • Symplectic topology and geometry, Seiberg-Witten theory, Floer homology
  • Foliation and Lamination Theory, Minimal Surfaces, and Hyperbolic Geometry