Michael Handel is an American mathematician known for his work in

Geometric group theory Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these group ...

. He is a professor in the Department of Mathematics at

Lehman College Lehman College is a public college in New York City, United States. Founded in 1931 as the Bronx campus of Hunter College, it became an independent college in 1967. The college is named after Herbert H. Lehman, a former New York governor, United ...

of the

City University of New York The City University of New York (CUNY, pronounced , ) is the Public university, public university system of Education in New York City, New York City. It is the largest urban university system in the United States, comprising 25 campuses: eleven ...

and a professor of mathematics at the

CUNY Graduate Center The Graduate School and University Center of the City University of New York (CUNY Graduate Center) is a public research institution and postgraduate university in New York City. Formed in 1961 as Division of Graduate Studies at City University ...

Career

Michael Handel graduated with a B.A. in mathematics from

Brandeis University Brandeis University () is a Private university, private research university in Waltham, Massachusetts, United States. It is located within the Greater Boston area. Founded in 1948 as a nonsectarian, non-sectarian, coeducational university, Bra ...

in 1971. He received his Ph.D. from

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

, in 1975 under the supervision of

Robion Kirby Robion Cromwell Kirby (born February 25, 1938) is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology. Together with Laurent C. Siebenmann he developed the Kirby–Siebenmann invariant ...

. From 1975 to 1978, he was an instructor at

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 ...

. He joined the faculty of

Michigan State University Michigan State University (Michigan State or MSU) is a public university, public Land-grant university, land-grant research university in East Lansing, Michigan, United States. It was founded in 1855 as the Agricultural College of the State o ...

as an assistant professor in 1978, and was promoted to associate professor in 1983. Handel 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 ...

from 1978 to 1979, and again from 1987 to 1988. In 1990, he joined the Mathematics Department at Lehman College. Handel is best known for developing the

Train track map In the mathematical subject of geometric group theory, a train track map is a continuous map ''f'' from a finite connected Graph (discrete mathematics), graph to itself which is a homotopy equivalence and which has particularly nice cancellation p ...

method in

in collaboration with

Mladen Bestvina Mladen Bestvina (born 1959) is a Croatian-American mathematician working in the area of geometric group theory. He is a Distinguished Professor in the Department of Mathematics at the University of Utah. Life and career Mladen Bestvina is a thre ...

in 1992.Mladen Bestvina, and Michael Handel
''Train tracks and automorphisms of free groups.''

Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as t ...

(2), volume 135 (1992), number 1, pages 1–51 Bestvina, Feighn and Handel later proved that the group Out(''F_n'') satisfies the

Tits alternative In mathematics, the Tits alternative, named after Jacques Tits, is an important theorem about the structure of finitely generated linear groups. Statement The theorem, proven by Tits, is stated as follows. Consequences A linear group is not ...

, settling a long-standing open problem.Mladen Bestvina, Mark Feighn, and Michael Handel
''The Tits alternative for Out(F_n). I. Dynamics of exponentially-growing automorphisms.''

(2), volume 151 (2000), number 2, pages 517–623Mladen Bestvina, Mark Feighn, and Michael Handel.
''The Tits alternative for Out(F_n). II. A Kolchin type theorem.''

(2), volume 161 (2005), number 1, pages 1–59

Awards and honors

*In 1984, Handel won a

Sloan Research Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...

. *In 2014, he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Selected publications

*Handel, Michael. "One Dimensional Minimal Sets and the Seifert Conjecture ". ''

(2)'' 111 (1980), number 1, pages 35-66
DOI:10.2307/1971216
*Feighn, Mark; Handel, Michael. "Mapping tori of free group automorphisms are coherent". ''

(2)'' 149 (1999), number 3, pages 1061–1077
MR 1709311
*Bestvina, Mladen; Feighn, Mark; Handel, Michael
''The Tits alternative for Out(F_n). I. Dynamics of exponentially-growing automorphisms.''

(2), volume 151 (2000), number 2, pages 517–623 *Bestvina, Mladen; Feighn, Mark; Handel, Michael.
''The Tits alternative for Out(F_n). II. A Kolchin type theorem.''

(2), volume 161 (2005), number 1, pages 1–5
MR 2150382
*Handel, Michael; Mosher, Lee. "The free splitting complex of a free group, I: hyperbolicity". ''

Geometry & Topology ''Geometry & Topology'' is a peer-refereed, international mathematics research journal devoted to geometry and topology, and their applications. It is currently based at the University of Warwick, United Kingdom, and published by Mathematical S ...

'' 17 (2013), number 3, pages 1581–1672
MR 3073931

References

External links

Department of Mathematics - Faculty - Lehman College
{{DEFAULTSORT:Handel, Michael Year of birth missing (living people) Living people 20th-century American mathematicians 21st-century American mathematicians University of California, Berkeley alumni Fellows of the American Mathematical Society Institute for Advanced Study visiting scholars Lehman College faculty CUNY Graduate Center faculty Mathematicians from New York (state)

Career

Awards and honors

Selected publications

See also

References

External links