Stephen M. Gersten Explained

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. 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.^[2] 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.^[3] 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 and Edward W. Formanek.

Gersten's conjecture has motivated considerable research.^[4]

Gersten's theorem

If is an automorphism of a finitely generated free group then is finitely generated.^{[5] [6]}

Selected publications

• 10.1090/S0002-9904-1972-12924-0. On the spectrum of algebraic K -theory. Bulletin of the American Mathematical Society. 78. 2. 216–220. 1972. Gersten. S. M.. free.
• 10.1090/S0002-9904-1973-13150-7. Higher K -theory for regular schemes. Bulletin of the American Mathematical Society. 79. 193–197. 1973. Gersten. S. M.. free.
• Book: 10.1007/BFb0067049. Higher K-theory of rings. Higher K-Theories. 341. 3–42. Lecture Notes in Mathematics. 1973. Gersten. S. M.. 978-3-540-06434-3.
• Book: Kenneth Brown (mathematician)

. 10.1007/BFb0067062. Algebraic K-theory as generalized sheaf cohomology. Higher K-Theories. 341. 266–292. Lecture Notes in Mathematics. 1973. Brown. Kenneth S.. Kenneth Brown (mathematician). Gersten. Stephen M.. 978-3-540-06434-3.

• 10.1090/S0002-9939-1983-0702313-2. A short proof of the algebraic Weierstrass preparation theorem. . 88. 4. 751–752. 1983. Gersten. S. M.. free. (See Weierstrass preparation theorem.)
• 10.1090/S0273-0979-1983-15116-9. On fixed points of automorphisms of finitely generated free groups. Bulletin of the American Mathematical Society. 8. 3. 451–455. 1983. Gersten. S. M.. free. (This paper presents a proof of a conjecture made by G. Peter Scott.)
• 10.1090/S0273-0979-1984-15246-7. On Whitehead's algorithm. Bulletin of the American Mathematical Society. 10. 2. 281–285. 1984. Gersten. S. M.. free.
• Book: 10.1007/978-1-4613-9586-7_2. Reducible Diagrams and Equations over Groups. Essays in Group Theory. 8. 15–73. Mathematical Sciences Research Institute Publications. 1987. Gersten. S. M.. 978-1-4613-9588-1.
• 10.1007/BF01233430. Small cancellation theory and automatic groups. Inventiones Mathematicae. 102. 305–334. 1990. Gersten. S. M.. Short. Hamish B.. 1990InMat.102..305G. 120267906.
• 10.1016/0022-4049(91)90139-S. Automatic groups and amalgams. Journal of Pure and Applied Algebra. 76. 3. 229–316. 1991. Baumslag. Gilbert. Gilbert Baumslag. Gersten. S.M.. Shapiro. Michael. Short. H..
• 10.2307/2944334. 2944334. Rational Subgroups of Biautomatic Groups. Annals of Mathematics. 134. 1. 125–158. 1991. Gersten. S. M.. Short. H. B..
• Book: Gersten. S. M.. Dehn Functions and l₁-norms of Finite Presentations. 1992. 195–224. 0940-4740. 10.1007/978-1-4613-9730-4_9. Baumslag G.. Miller C.F.. Algorithms and Classification in Combinatorial Group Theory. 23. Mathematical Sciences Research Institute Publications. Springer. New York. 978-1-4613-9732-8.
• Book: Gersten, S.M.. 1993. Isoperimetric and isodiametric functions of finite presentations. Geometric group theory. 1. 79–96. Cambridge University Press . 9780521435291. https://books.google.com/books?id=lK2hpcVAtX0C&pg=PA79.

See also

• Baumslag–Gersten group

References

1. Web site: Stephen M. Gersten. Mathematics Department, University of Utah.
2. Web site: Stephen M. Gersten. Institute for Advanced Study. 9 December 2019 .
3. Book: Gersten, S. M.. Class Groups of Supplemented Algebras. Proceedings of the International Congress of Mathematicians, Vancouver, 1974. 1. 1975. 309–314.
4. Mochizuki, Satoshi. A survey of Gersten's conjecture. 2016. 1608.08114. math.KT.
5. Gersten, S. M.. Fixed points of automorphisms of free groups. Advances in Mathematics. 64. 1. 1987. 51–85. 10.1016/0001-8708(87)90004-1. free.
6. Book: Gersten, S. M.. Stallings, John R.. Combinatorial Group Theory and Topology. registration. 21 May 1987. Princeton University Press. 0-691-08410-6.