Stephen M. Gersten

Stephen M. Gersten (born 2 December 1940) is an American mathematician, specializing in finitely presented groups and their geometric properties.^[1]

Gersten graduated in 1961 with an AB from Princeton University^[1] and in 1965 with a PhD from Trinity College, Cambridge. His doctoral thesis was Class Groups of Supplemented Algebras written under the supervision of John R. Stallings.^[2] In the late 1960s and early 1970s he taught at Rice University. In 1972–1973 he was a visiting scholar at the Institute for Advanced Study.^[3] In 1973 he became a professor at the University of Illinois at Urbana–Champaign.^[1] In 1974 he was an Invited Speaker at the International Congress of Mathematicians in Vancouver.^[4] At the University of Utah he became a professor in 1975 and is now semi-retired there.^[1] His PhD students include Roger C. Alperin, R. Keith Dennis and Edward W. Formanek.^[2]

Gersten's conjecture has motivated considerable research.^[5]

Gersten's theorem

If φ is an automorphism of a finitely generated free group F then { x : x ∈ F and φ(x) ${\displaystyle =}$ x } is finitely generated.^[6][7]

Selected publications

• Gersten, S. M. (1972). "On the spectrum of algebraic ${\displaystyle K}$-theory". Bulletin of the American Mathematical Society. 78 (2): 216–220. doi:10.1090/S0002-9904-1972-12924-0.
• Gersten, S. M. (1973). "Higher ${\displaystyle K}$-theory for regular schemes". Bulletin of the American Mathematical Society. 79: 193–197. doi:10.1090/S0002-9904-1973-13150-7.
• Gersten, S. M. (1973). "Higher K-theory of rings". Higher K-Theories. Lecture Notes in Mathematics. Vol. 341. pp. 3–42. doi:10.1007/BFb0067049. ISBN 978-3-540-06434-3.
• Brown, Kenneth S.; Gersten, Stephen M. (1973). "Algebraic K-theory as generalized sheaf cohomology". Higher K-Theories. Lecture Notes in Mathematics. Vol. 341. pp. 266–292. doi:10.1007/BFb0067062. ISBN 978-3-540-06434-3.
• Gersten, S. M. (1983). "A short proof of the algebraic Weierstrass preparation theorem". Proceedings of the American Mathematical Society. 88 (4): 751–752. doi:10.1090/S0002-9939-1983-0702313-2. (See Weierstrass preparation theorem.)
• Gersten, S. M. (1983). "On fixed points of automorphisms of finitely generated free groups". Bulletin of the American Mathematical Society. 8 (3): 451–455. doi:10.1090/S0273-0979-1983-15116-9. (This paper presents a proof of a conjecture made by G. Peter Scott.)
• Gersten, S. M. (1984). "On Whitehead's algorithm". Bulletin of the American Mathematical Society. 10 (2): 281–285. doi:10.1090/S0273-0979-1984-15246-7.
• Gersten, S. M. (1987). "Reducible Diagrams and Equations over Groups". Essays in Group Theory. Mathematical Sciences Research Institute Publications. Vol. 8. pp. 15–73. doi:10.1007/978-1-4613-9586-7_2. ISBN 978-1-4613-9588-1.
• Gersten, S. M.; Short, Hamish B. (1990). "Small cancellation theory and automatic groups". Inventiones Mathematicae. 102: 305–334. Bibcode:1990InMat.102..305G. doi:10.1007/BF01233430. S2CID 120267906.
• Baumslag, Gilbert; Gersten, S.M.; Shapiro, Michael; Short, H. (1991). "Automatic groups and amalgams". Journal of Pure and Applied Algebra. 76 (3): 229–316. doi:10.1016/0022-4049(91)90139-S.
• Gersten, S. M.; Short, H. B. (1991). "Rational Subgroups of Biautomatic Groups". Annals of Mathematics. 134 (1): 125–158. doi:10.2307/2944334. JSTOR 2944334.
• Gersten, S. M. (1992). "Dehn Functions and l₁-norms of Finite Presentations". In Baumslag G.; Miller C.F. (eds.). Algorithms and Classification in Combinatorial Group Theory. Mathematical Sciences Research Institute Publications. Vol. 23. New York: Springer. pp. 195–224. doi:10.1007/978-1-4613-9730-4_9. ISBN 978-1-4613-9732-8. ISSN 0940-4740.
• Gersten, S.M. (1993). "Isoperimetric and isodiametric functions of finite presentations". Geometric group theory. Vol. 1. Cambridge University Press. pp. 79–96. ISBN 9780521435291.

See also

• Baumslag–Gersten group