Dr. Alexander Goncharov
Functional analysis: topological vector spaces, linear topological invariants, bases and their properties.
Asymptotics of extremal (Chebyshev and orthogonal) polynomials, polynomial inequalities, Widom factors.
Potential theory: metric properties of harmonic measures, Green functions.
Complex dynamics: generalized Julia sets, polynomial preimages.
Construction of measures with preassigned properties.