Stephen M. Gersten (born 2 December 1940) is an American mathematician, specializing in finitely presented groups and their geometric properties. Gersten graduated in 1961 with an AB from

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

and in 1965 with a PhD from

Trinity College, Cambridge Trinity College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any ...

. 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 William Marsh Rice University, commonly referred to as Rice University, is a Private university, private research university in Houston, Houston, Texas, United States. Established in 1912, the university spans 300 acres. Rice University comp ...

. In 1972–1973 he was a visiting scholar at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

. In 1973 he became a professor at the

University of Illinois at Urbana–Champaign The University of Illinois Urbana-Champaign (UIUC, U of I, Illinois, or University of Illinois) is a public land-grant research university in the Champaign–Urbana metropolitan area, Illinois, United States. Established in 1867, it is the f ...

. In 1974 he was an Invited Speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

in Vancouver. At the

University of Utah The University of Utah (the U, U of U, or simply Utah) is a public university, public research university in Salt Lake City, Utah, United States. It was established in 1850 as the University of Deseret (Book of Mormon), Deseret by the General A ...

he became a professor in 1975 and is now semi-retired there. His PhD students include Roger C. Alperin,

R. Keith Dennis Roger Keith Dennis (March 10, 1944 – December 12, 2024), known as R. Keith Dennis or Keith Dennis, was an American mathematician who worked in algebraic K-theory and group theory. His career was spent as a professor in the Department of Mathema ...

and Edward W. Formanek. Gersten's conjecture has motivated considerable research.

Gersten's theorem

If is an automorphism of a finitely generated

free group In mathematics, the free group ''F'S'' over a given set ''S'' consists of all words that can be built from members of ''S'', considering two words to be different unless their equality follows from the group axioms (e.g. ''st'' = ''suu''− ...

then is finitely generated.

Selected publications

* * * * * (See

Weierstrass preparation theorem In mathematics, the Weierstrass preparation theorem is a tool for dealing with analytic functions of several complex variables, at a given point ''P''. It states that such a function is, up to multiplication by a function not zero at ''P'', a poly ...

.) * (This paper presents a proof of a conjecture made by

G. Peter Scott Godfrey Peter Scott, known as Peter Scott, (1944 – 19 September 2023) was a British-American mathematician, known for the Scott core theorem. Education and career He was born in England to Bernard Scott (a mathematician) and Barbara Scott (a ...

.) * * * * * * *

References

1940 births Living people Group theorists American topologists 20th-century American mathematicians 21st-century American mathematicians Princeton University alumni Alumni of Trinity College, Cambridge Rice University faculty University of Utah faculty University of Illinois Urbana-Champaign faculty {{mathematician-stub

Gersten's theorem

Selected publications

See also

References