Rostyslav Hryhorchuk

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Rostyslav Iwanowytsch Hryhortschuk ( Ukrainian Ростислав Іванович Григорчук , Russian Ростислав Иванович Григорчук , Rostislav Grigorchuk , English transcription Rostislav Grigorchuk * 23 February 1953 in Mukhavets (now in Vyshnivets ) zbarazh raion , oblast Ternopil , USSR , now Ukraine ) is a Soviet and Russian mathematician of Ukrainian origin. He is a professor at Texas A&M University .

Rostyslaw Hryhortschuk (left) with Manfred Karbe in Oberwolfach in 2006

Hryhortschuk studied mathematics at Lomonosov University with a degree in 1975 and a doctorate (candidate title) in 1978 with Anatoly Michajlowitsch Stepin. He obtained his Russian doctorate (habilitation) at the Steklow Institute in 1985 . In the 1980s he was at the State University of Transportation and then at the Steklow Institute and Lomonosov University. From 2002 he was a professor at Texas A&M University. In 2008 he became a Distinguished Professor there .

He is known for fundamental contributions to geometric group theory. In particular, in 1984 he later discovered groups called Grigorchuk groups after him with special growth properties. Consider infinite groups with a finite number of generators and ask how the number of group elements increases after a finite number n of iterations of the generators. In 1968 Milnor hypothesized that there is only polynomial and exponential growth, Hryhortschuk proved that there is another group, Grigorchuk groups with sub-exponential growth, but which is larger than polynomial growth. They often have a recursive description as automorphism groups of trees and sets with self-similar properties ( fractals ) and were used in the theory of fractals and holomorphic dynamics (e.g. properties of Julia sets ), in finite automata, in the spectral theory of graphs and in functional analysis. Hryhortschuk applied it, among other things, in topology (counterexample to a conjecture by Michael Atiyah about L 2 -Betti numbers of closed manifolds).

He also looked at random walks ( Random Walk ) on groups and indirect groups ( Amenable Groups ).

He received the Leroy P. Steele Prize for 2015 in the Fundamental Research Contribution category. In 2012 he became a Fellow of the American Mathematical Society . In 1990 he was invited speaker at the International Congress of Mathematicians in Kyoto ( On growth in group theory ).

He is the editor of Groups, Geometry and Dynamics .

Fonts

  • with Igor Pak: Groups of intermediate growth: an introduction. In: L'Enseignement Mathématique. Volume 54, 2008, p. 251 ( unige.ch ).
  • with Tatiana Nagnibeda: Complete growth functions of hyperbolic groups. In: Invent. Math. 130, No. 1, 1997, pp. 159-188.
  • On growth in group theory. In: Proceedings of the International Congress of Mathematicians. Vol. I, II (Kyoto, 1990), pp. 325-338, Math. Soc. Japan, Tokyo 1991.
  • Degrees of growth of finitely generated groups and the theory of invariant means. In: Izv. Akad. Nauk SSSR Ser. Mat. 48, No. 5, 1984, pp. 939-985.
  • On the Milnor problem of group growth. In: Dokl. Akad. Nauk SSSR. 271, No. 1, 1983, pp. 30-33.
  • On Burnside's problem on periodic groups. In: Functional. Anal. i prilozhen. 14, No. 1, 1980, pp. 53-54.

Web links

Individual evidence

  1. ↑ инвариантных банаховых средних на однородных простран. 1978 (Dissertation, Russian, German Banach means on homogeneous spaces and random paths. ). Rostyslaw Hryhortschuk in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ^ RI Grigortschuk: Degrees of growth of finitely generated groups and the theory of invariant means. In: Izv. Akadd. Nauka SSSR, Ser. Math. Volume 48, 1984, No. 5, pp. 939-985. He had already constructed the groups in 1980: Bernside's Problem on periodic groups. Functional Analysis and Applications, Volume 14, 1980, pp. 41-43 (referring to Burnside's problem).
  3. ↑ RI Grigorchuk, P. Linnell, T. Schick , A. Zuk: On a question of Atiyah . In: Comptes Rendus de l'Académie des Sciences. Série I. Mathématique. Volume 331, 2000, pp. 663-668.
  4. ^ Steele Prize for Grigorchuk
personal data
SURNAME Hryhortschuk, Rostyslav
ALTERNATIVE NAMES Grigorchuk, Rostislav; Grigorchuk, Rostislaw Ivanovich; Григорчу́к, Ростисла́в Іва́нович (Ukrainian spelling); Григорчук, Ростислав Иванович (Russian spelling)
BRIEF DESCRIPTION Russian mathematician
DATE OF BIRTH February 23, 1953
PLACE OF BIRTH Ternopil Oblast