# Stephen M. Gersten

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Stephen M. Gersten (born 2 December 1940) was 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 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 : xF and φ(x) ${\displaystyle =}$ x } is finitely generated.[6][7]

## References

1. ^ a b c d "Stephen M. Gersten" (PDF). Mathematics Department, University of Utah.
2. ^ a b
3. ^
4. ^ Gersten, S. M. (1975). "Class Groups of Supplemented Algebras". Proceedings of the International Congress of Mathematicians, Vancouver, 1974. vol. 1. pp. 309–314. `|volume=` has extra text (help)
5. ^ Mochizuki, Satoshi (2016). "A survey of Gersten's conjecture". arXiv:1608.08114 [math.KT].
6. ^ Gersten, S. M. (1987). "Fixed points of automorphisms of free groups" (PDF). Advances in Mathematics. 64 (1): 51–85. doi:10.1016/0001-8708(87)90004-1.
7. ^ Gersten, S. M.; Stallings, John R., eds. (21 May 1987). Combinatorial Group Theory and Topology. Princeton University Press. ISBN 0-691-08410-6.