Mark Sapir

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Mark Valentinovich Sapir , Russian Марк Валентинович Сапир , (born February 12, 1957 ) is a Russian-American mathematician.

Life

Sapir studied mathematics at the State University of the Urals in Sverdlovsk with the degree in 1978 and received his doctorate there and at the State Pedagogical Institute in Moscow with Lev Naumowitsch Shevrin . He was at the Urals State University (assistant professor 1979 to 1984 and 1989/90) and at the Pedagogical Institute in Sverdlovsk (assistant professor 1984 to 1989 and deputy director of the computer science laboratory) before moving to the USA around 1990. There he was Visiting Associate Professor at California State University in Chico and at the University of Nebraska in 1991 (Visiting Associate Professor from 1991, Associate Professor from 1993) before becoming Professor at Vanderbilt University in 1997 . From 2001 he was a Centennial Professor there.

Among other things, he was visiting scholar and visiting professor at the Max Planck Institute for Mathematics , at IHES , at the Mittag-Leffler Institute and MSRI , at CRM in Barcelona, ​​at Technion (Lady Davis visiting professor), the Universities of Lille and Bordeaux, the University of Illinois at Urbana-Champaign , at the Stevens Institute of Technology , at the Hebrew University in Jerusalem, in Brno, at Monash University and the Universities of Paris VI and VII.

In 2003 he became a US citizen. He is married and has three children. His daughter Jenya Sapir is also a mathematician and professor (Binghamton University).

plant

He deals with combinatorial algebra, geometric and algorithmic group theory, theory of semigroups.

In 2002, together with Jean-Camille Birget and Eliyahu Rips , he described the possible growth rates of stretching functions of finally presented groups . In the same year he proved with Birget, Rips and Alexander Jurjewitsch Olschanski that the word problem for finitely presented groups lies in NP if and only if these groups are subgroups of a finitely presented group with a polynomial increasing expansion function. With John Meakin he introduced groups of diagrams in 1993 , about which he also wrote a monograph.

In 2003 he gave with Olschanski the first example of a finally presentable group that refuted the von Neumann conjecture. This was refuted by Olschanski in 1980 and states that a group is non-indirect if and only if it contains a subgroup that is a free group with two generators.

With Cornelia Druțu , he investigated relatively hyperbolic groups about their effect in tree graded spaces, which in turn are asymptotic cones of groups.

In the Soviet Union he published a widespread computer science textbook (with Gejn, Linetsky, Sholokhovich) and related educational software (Roo and Robby / Schoolworks, originally for Z80, later adapted for IBM PCs), which he also makes available on his homepage . In 1990 he received a gold medal from the Soviet Ministry of Education for the book.

Honors and Editing

In 2012 he became a Fellow of the American Mathematical Society . In 2016 he was invited speaker at the International Congress of Mathematicians in Madrid ( Algorithmic and asymptotic properties of groups ).

From 2016 he was the founding editor of the Journal of Combinatorial Algebra .

Fonts (selection)

  • Problems of Burnside type and the finite basis property in varieties of semigroups, Mathematics of the USSR-Izvestiya, Volume 30, 1988, p. 295
  • with John Meakin: Congruences on free monoids and submonoids of polycyclic monoids, Journal of the Australian Mathematical Society, Series A., Volume 54, 1993, pp. 236-253
  • with Olga Kharlampovich : Algorithmic Problems in Varieties, a survey, International Journal of Algebra and Computation, Volume 12, 1995, pp. 379-602
  • with Victor Guba: Diagram groups, Memoirs of the American Mathematical Society 130, 1997
  • with Jean-Camille Birget, Eliyahu Rips: Isoperimetric and isodiametric functions of groups, Annals of Mathematics, Volume 156, 2002, pp. 345-466.
  • with Jean-Camille Birget, Alexander Yu. Ol'shanskii, Eliyahu Rips: Isoperimetric functions of groups and computational complexity of the word problem, Annals of Mathematics, Volume 156, 2002, pp. 467-518
  • with Alexander Ol'shanskii: Non-amenable finitely presented torsion-by-cyclic groups, Publications Mathématiques de l'IHÉS, Volume 96, 2003, pp. 43–169
  • with Alexander Yu. Olʹshanskii: Non-amenable finitely presented torsion-by-cyclic groups, Publications Mathématiques de l'IHÉS, Volume 96, 2003, pp. 43–169
  • with Alexander Borisov: Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms, Inventiones Mathematicae, Volume 160, 2005, pp. 341-356
  • with Cornelia Drutu: Tree-graded spaces and asymptotic cones of groups, Topology, Volume 44, 2005, pp. 959-1058
  • with Cornelia Drutu: Groups acting on tree-graded spaces and splittings of relatively hyperbolic groups, Advances in Mathematics, Volume 217, 2008, pp. 1313-1367
  • Combinatorial algebra: syntax and semantics, Springer 2014

Web links

personal data
SURNAME Sapir, Mark
ALTERNATIVE NAMES Sapir, Mark Valentinovich (full name); Сапир, Марк Валентинович (Russian)
BRIEF DESCRIPTION Russian-American mathematician
DATE OF BIRTH February 12, 1957