Nikolai Georgievich Makarov

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Nikolai Georgievich Makarov
BornJanuary 1955 (age 66)
Alma materLeningrad State University
Steklov Institute of Mathematics
AwardsSalem Prize(1986)
Rolf Schock Prize(2020)
Scientific career
FieldsMathematics
InstitutionsCalifornia Institute of Technology
Doctoral advisor Nikolai Nikolski
Doctoral studentsStanislav Smirnov

Nikolai Georgievich Makarov (Russian: Николай Георгиевич Макаров; born January 1955) is a Russian mathematician, specializing in harmonic analysis.

Career[]

Makarov belongs to the Leningrad school of geometric function theory. He studied at the Leningrad State University with undergraduate degree in 1982. He completed his Ph.D. (Candidate of Science) from the Steklov Institute of Mathematics in 1986 under Nikolai Nikolski with thesis Metric properties of harmonic measure (title translated from Russian).[1][2]

In 1986 he was an Invited Speaker of the ICM in Berkeley, California.[3] 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. In 2020, he was awarded the Rolf Schock Prize .[2]

His doctoral students include the Fields medallist Stanislav Smirnov and . With Zhan, Makarov published research on the stochastic properties of iterated polynomial maps (theory of Julia sets).

Makarov's theorem[]

Let Ω be a simply connected domain in the complex plane. Suppose that ∂Ω (the boundary of Ω) is a Jordan curve. Then the harmonic measure on ∂Ω has Hausdorff dimension 1.[4][5]

Selected publications[]

  • Probability methods in the theory of conformal mappings, Algebra i Analiz, 1:1 (1989), pp. 3–59; English version: Leningrad Mathematical Journal, 1990, 1:1, 1–56
  • Fine structure of harmonic measure, St. Petersburg Math. J. 10 (1999), 217–268
  • with S. Smirnov: On thermodynamics of rational maps, I. Negative spectrum, Comm. Math. Phys. 211 (2000), 705–743 doi:10.1007/s002200050833
  • with L. Carleson: Aggregation in the plane and Loewner's equation, Comm. Math. Phys. 216 (2001), 583–607 doi:10.1007/s002200000340
  • with L. Carleson: Laplacian path models, J. Analyse Math. 87 (2002), 103–150 doi:10.1007/BF02868471
  • with I. Binder and S. Smirnov: Harmonic measure and polynomial Julia sets, Duke Math. J. 117 (2003), 343–365 doi:10.1215/S0012-7094-03-11725-1
  • with Y. Ameur and H. Hedenmalm: Fluctuations of eigenvalues of random normal matrices, Duke Math. J. 159 (2011), 31-81 doi:10.1215/00127094-1384782
  • with Seung-Yeop Lee: Topology of quadrature domains, Journal of the American Mathematical Society 29, no. 2 (2016): 333–369 doi:10.1090/jams828

References[]

  1. ^ Nikolai G. Makarov at the Mathematics Genealogy Project
  2. ^ Jump up to: a b "Nikolai Makarov Honored with 2020 Schock Prize". California Institute of Technology. Retrieved 2021-06-22.
  3. ^ Makarov, N. G. (1987). "Metric properties of harmonic measure". In: Proceedings of the International Congress of Mathematicians, Berkeley, 1986. Amer. Math. Soc. pp. 766–776.
  4. ^ Makarov, On the distortion of boundary sets under conformal mappings, Proc. London Math. Soc. Ser. 3, 52, vol. 1985, pp. 369–384 doi:10.1112/plms/s3-51.2.369
  5. ^ Ivrii, Oleg (9 August 2017). "On Makarov's principle in conformal mapping". International Mathematical Research Notes. 2019 (5): 1543–1567. arXiv:1604.05619. doi:10.1093/imrn/rnx129. S2CID 119655503. arXiv.org preprint, 2016

External links[]

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