Stephen M. Gersten

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 : x ∈ F and φ(x) x } is finitely generated.[6][7]

Selected publications

See also

References
  1. "Stephen M. Gersten" (PDF). Mathematics Department, University of Utah.
  2. Stephen M. Gersten at the Mathematics Genealogy Project
  3. "Stephen M. Gersten". Institute for Advanced Study.
  4. Gersten, S. M. (1975). "Class Groups of Supplemented Algebras". Proceedings of the International Congress of Mathematicians, Vancouver, 1974. vol. 1. pp. 309–314.
  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.


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