Paul Schupp

Paul Schupp (2017)

Paul Eugene Schupp (born March 12, 1937 in Cleveland , Ohio ) is an American mathematician and computer scientist .

Paul Schupp studied at Case Western Reserve University with a bachelor's degree in 1959 and at the University of Michigan in Ann Arbor with a master's degree in 1961 and his doctorate in 1966 with Roger Lyndon (dissertation On Dehn's Algorithm and the Conjugacy Problem ). Then he was 1966/67 Assistant Professor at the University of Wisconsin in Madison and from 1967 Assistant Professor, from 1971 Associate Professor and from 1975 Professor at the University of Illinois at Urbana-Champaign .

Schupp was visiting scholar at the Courant Institute (1969/70), at the University of London, the University of Singapore, at the Soviet Academy of Sciences (1982), at the University of Paris VII (from 1984 to 1992 in the Faculty of Computer Science) the University of Bordeaux and the University of Marne-la-Vallée.

He deals with the theory of infinite groups, combinatorial group theory (now known as geometric group theory ), automata theory and decision problems in algebraic systems. In particular, he deals with the relationship between group theory and predictability problems. With Lyndon he wrote a standard work on combinatorial group theory, in which they also gave the standard representation of the small cancellation theory .

With David Muller he proved in 1983 that for a finitely generated group the word problem corresponds to that of a context-free language if and only if it is virtually free, that is, there is a subgroup of finite index in which is isomorphic to a free group (theorem of Muller-Schupp). ${\ displaystyle G}$ ${\ displaystyle G}$ ${\ displaystyle H}$ ${\ displaystyle G}$

In 1977 he was a Guggenheim Fellow . In 2012 he became a Fellow of the American Mathematical Society .

Fonts

with Roger Lyndon: Combinatorial Group Theory, Springer 1977, reprint in the Classics in Mathematics 2001 series, ISBN 978-3-642-61896-3
with David E. Muller: Groups, the theory of ends, and context-free languages. Journal of Computer and System Sciences, Volume 26, 1983, pp. 295-310
with KI Appel : Artin groups and infinite Coxeter groups, Inventiones Mathematicae, Volume 72, 1983, pp. 201-220
A survey of small cancellation theory, in: WW Boone, FB Cannonito, R. Lyndon (Eds.): Word Problems: Decision Problem in Group Theory, North-Holland, 1973, pp. 569-589

literature

Ilya Kapovich: On the mathematical contributions of Paul E. Schupp, Illinois J. Math., Volume 54, 2010, pp. 1-9

Individual evidence

↑ Birth and career data according to American Men and Women of Science , Thomson Gale 2004
^ Paul Schupp in the Mathematics Genealogy Project (English) . Published in Mathematische Annalen, Volume 178, 1968, pp. 119–130
↑ It arose essentially from the work of Michail Leonidowitsch Gromow on hyperbolic groups in 1987 from combinatorial group theory. The work of Schupp and others on small cancellation theory was a forerunner for this. Combinatorial group theory emerged mainly as a result of the work of Max Dehn at the beginning of the 20th century.

personal data
SURNAME	Schupp, Paul
ALTERNATIVE NAMES	Schupp, Paul Eugene (full name)
BRIEF DESCRIPTION	American mathematician and computer scientist
DATE OF BIRTH	March 12, 1937
PLACE OF BIRTH	Cleveland , Ohio

[1] Birth and career data according to American Men and Women of Science , Thomson Gale 2004

[2] Paul Schupp in the Mathematics Genealogy Project (English) . Published in Mathematische Annalen, Volume 178, 1968, pp. 119–130

[3] It arose essentially from the work of Michail Leonidowitsch Gromow on hyperbolic groups in 1987 from combinatorial group theory. The work of Schupp and others on small cancellation theory was a forerunner for this. Combinatorial group theory emerged mainly as a result of the work of Max Dehn at the beginning of the 20th century.