## 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 and other polynomial heights. 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. Discrete approximations of extremal problems in complex analysis and potential theory. Convergence in numerical methods for systems of linear equations.

#### Potential Theory

Potentials, capacities, equilibrium measures, Riesz decompositions, and applications.

#### Probability Theory

Random polynomials and analytic functions, random matrices. Probabilistic potential theory and number theory.