Nikolai Georgievich Makarov


Nikolai Georgievich Makarov,, is a Russian mathematician, specializing in harmonic analysis.
Makarov belongs to the Leningrad school of geometric function theory. He studied at the Leningrad State University with undergraduate degree in 1982 and with Ph.D. in 1986 under Nikolai Nikolski with thesis Metric properties of harmonic measure. In 1986 he was an Invited Speaker of the ICM in Berkeley, California. In 1986 he was awarded the Salem Prize for solving difficult problems involving the boundary behavior of the conformal mapping of a disk onto a domain with a Jordan curve boundary using stochastic methods. He was an academic at the Steklov Institute of Mathematics in Leningrad. Since the 1990s he has been a professor at Caltech.
His doctoral students include the Fields medallist Stanislav Smirnov and Dapeng Zhan. With Zhan, Makarov published research on the stochastic properties of iterated polynomial maps.

Makarov's theorem

Let Ω be a simply connected domain in the complex plane. Suppose that ∂Ω is a Jordan curve. Then the harmonic measure on ∂Ω has Hausdorff dimension 1.

Selected publications