Nikolai Makarov
Nikolai Makarov
Richard Merkin Distinguished Professor of Mathematics
B.A., Leningrad University, 1982; Ph.D., LOMI Mathematics Institute (Leningrad), 1986. Visiting Professor, Caltech, 1991; Professor, 1991-13; Merkin Professor, 2013-.
Overview
Professor Nikolai Makarov works in complex analysis and related fields (potential theory, harmonic analysis, spectral theory) as well as on various applications to complex dynamics, mathematical conformal field theory, Coulomb gas models and random matrices.
His most recent work concerns topology of quadrature domains, Hele-Shaw flows, uncertainty principle for non-linear Fourier transform, universality laws and field convergence in normal random matrix ensembles, dynamics of Schwarz reflection as the mating of Kleinian groups and rational maps, classical function theory on compact Riemann surfaces via Liouville conformal field theory.
Selected Awards
- Rolf Schock Prize, 2020; "for his significant contributions to complex analysis and its applications to mathematical physics"
- Salem Prize, 1986
Selected Awards
- Rolf Schock Prize, 2020; "for his significant contributions to complex analysis and its applications to mathematical physics"
- Salem Prize, 1986
Related Courses
Ma 110 abc. Analysis.
9 units (3-0-6); first, second, third terms, 2025-26.
Prerequisites: Ma 108 or previous exposure to metric space topology, Lebesgue measure.
First term: integration theory and basic real analysis: topological spaces, Hilbert space basics, Fejer's theorem, measure theory, measures as functionals, product measures, L^p -spaces, Baire category, Hahn- Banach theorem, Alaoglu's theorem, Krein-Millman theorem, countably normed spaces, tempered distributions and the Fourier transform. Second term: basic complex analysis: analytic functions, conformal maps and fractional linear transformations, idea of Riemann surfaces, elementary and some special functions, infinite sums and products, entire and meromorphic functions, elliptic functions. Third term: harmonic analysis; operator theory. Harmonic analysis: maximal functions and the Hardy-Littlewood maximal theorem, the maximal and Birkoff ergodic theorems, harmonic and subharmonic functions, theory of H^p -spaces and boundary values of analytic functions. Operator theory: compact operators, trace and determinant on a Hilbert space, orthogonal polynomials, the spectral theorem for bounded operators. If time allows, the theory of commutative Banach algebras.
Instructors: Heinävaara, Makarov, Isett
Instructors: Heinävaara, Makarov, Isett