Roger Lyndon — Wikipedia

Roger Conant Lyndon (1917–1988) is an American mathematician, professor at the University of Michigan ^{[ first ]} . He is known for Lyndon’s words, the theorem of Curtis-Hedlund-Lyndon (in) , the interpolation of Craig-Lyndon and the spectral suite of Lyndon-Hochschild-Serre (in) .

He began his higher education at Undergraduate level at Harvard University, first in literature, then in mathematics, and obtained a license (Bachelor) in 1939. He worked as a bank employee, but quickly returned to Harvard University, In the Graduate School, and obtained a master’s degree in 1941. After a brief teaching experience at the Georgia Institute of Technology, he returned for a third time to Harvard. While teaching as part of the V-12 Navy College Training Program, the objective of which was to give basic training to the recruits of the American navy, he prepares a pH. D. ^{[ first ]} Under the direction of Saunders Mac Lane ^{[ first ] , [ 2 ]} that he obtained in 1946.

After his thesis, Lyndon worked at the Office of Naval Research, then for five years as assistant and assistant professor (professor assistant) at Princeton University.
Influenced by Tarski, Lyndon worked on model theory. The visit, to Princeton, of Ralph Fox and Kurt Reidemeister in 1948 prompted him to work in combinatorial theory of groups.

In 1953, he was appointed to the University of Michigan in 1953 ^{[ first ]} . He remains there with the exception of visits to Berkeley, London, Montpllier and Amiens. At University
From Michigan, he notably shares an office with Donald G. Higman ^{[ 3 ]} . He has many students, including Kenneth Appel, Joseph Kruskal and Paul Schupp ^{[ 2 ]} .

Group cohomology

Lyndon’s thesis concerns group cohomology ^{[ first ]} ; The spectral suite of Lyndon-Hochschild-Serre is a consequence of this work. It links the cohomology of a group to the cohomologies of its normal subgroups and their quotient groups.

Lyndon words

A Lyndon word is a word on an ordered alphabet which is strictly smaller, for the lexicographic order, that all the words obtained by circular permutation (its conjugated words). Lyndon introduced these words in 1954 when he was looking for free group bases ^{[ 4 ]} .

Curtis-Hedlund-Landon theorem

The Curtis-Hedlund-Lyndon theorem is a characterization of cellular automata in terms of their symbolic dynamic. The discovery of this theorem is co-attributed to Morton L. Curtis and Roger Lyndon by Gustav Hedlund himself ^{[ 5 ]} .

Craig-Lyndon interpolation theorem

Craig-Lyndon’s interpolation theorem in formal logic claims that any logical involvement can be factorized in a composition of two implications, in such a way that any symbol other than a logical symbol that appears in the central formula is also used in two other formulas. A first version of this theorem was proven by William Lane Craig in 1957, and a stronger version by Lyndon in 1959 ^{[ 6 ]} .

Combinatory group theory

In addition, Lyndon made important contributions in combinatorial theory of groups, in the study of groups in terms of their presentations in relation to the theory of small simplification (in) ^{[ first ]} .

• (in) Roger C. Lyndon , Notes on Logic , From nostrand, coll.  « Van Nostrand Mathematical Studies » ( n ^O 6), 1966 , we+97
• (in) William W. Boone , Frank B. Cannonito and Roger C. Lyndon , Word problems : Decision problems and the Burnside problem in group theory , North-Holland, coll.  « Studies in Logic and the Foundations of Mathematics » ( n ^O 71), 1973 , xii+646

  Texts of a conference on group theory decision-making problems, University of California in Irvine, Calif., September 1965, devoted to the memory of Hanna Neumann (1914-1971)

• (in) Roger C. Lyndon and Paul E. Shed , Combinatorial Group Theory , Berlin/Heidelberg/New York, Springer-Verlag, coll. “Results of mathematics and its border areas” ( n ^O 89), 1977 , xiv+339 (ISBN  3-540-07642-5 )
• (in) Roger C. Lyndon and Paul E. Shed , Combinatorial Group Theory , Springer-Verlag, coll.  « Classics in Mathematics », 2001 , xiv+339 (ISBN  3-540-41158-5 , read online )

  Reprint of the 1977 edition

• (in) Roger C. Lyndon , Groups and geometry , Cambridge, Cambridge University Press, coll.  « London Mathematical Society Lecture Note Series » ( n ^O 101), 1985 , viii+217 (ISBN  0-521-31694-4 , read online )

  Coming from course notes entitled Groups and geometry , written by A. Boidin, A. Cheeseot and R. Lyndon, Uer de Mathematics, University of Picardy, Amiens, 1980-1981

The book Contributions to Group Theory (AMS, 1984 (ISBN  978-0-8218-5035-0 ) is a festschrift devoted to Lyndon for his 65 ^{It is} anniversary. This volume contains five articles on Lyndon and its mathematical research, and 27 guest and evaluated research articles.

The Roger Lyndon Collegiate Professorship of Mathematics of the University of Michigan, occupied by Hyman Bass since 1999 ^{[ 7 ]} , takes his name from Lyndon.