Research Interests

• Analytic Number Theory

  Extremal problems for polynomials with integer coefficients. Integer Chebyshev polynomials and constants. Distribution of conjugate algebraic numbers. Mahler's measure. Norms of products and factors of polynomials. Distribution of primes.

• Approximation Theory

  Convergence, asymptotics and zero distribution of polynomials and rational functions. Approximation of conformal mappings via the Bergman and the Szego kernel methods.

• Complex Analysis

  Extremal length, capacity, harmonic measure and boundary behavior of analytic and harmonic functions. Polynomials and polynomial inequalities.

• Numerical Analysis

  Orthonormalization methods for numerical approximation of conformal mappings. Convergence acceleration in numerical solution of systems of linear equations by iterative methods.

• Potential Theory

  Potentials, capacities, equilibrium measures and applications.