Bruce Alan Kleiner is an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, working in

differential geometry and topology Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

and

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 group (mathematics), groups and topology, topological and geometry, geometric pro ...

. He received his Ph.D. in 1990 from the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

. His advisor was Wu-Yi Hsiang. Kleiner is a professor of mathematics at

New York University New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then- Secretary of the Treasury Albert Gallatin. In 1832, th ...

. Kleiner has written expository papers on the

Ricci flow In the mathematical fields of differential geometry and geometric analysis, the Ricci flow ( , ), sometimes also referred to as Hamilton's Ricci flow, is a certain partial differential equation for a Riemannian metric. It is often said to be ana ...

. Together with John Lott of the

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

, he filled in details of

Grigori Perelman Grigori Yakovlevich Perelman ( rus, links=no, Григорий Яковлевич Перельман, p=ɡrʲɪˈɡorʲɪj ˈjakəvlʲɪvʲɪtɕ pʲɪrʲɪlʲˈman, a=Ru-Grigori Yakovlevich Perelman.oga; born 13 June 1966) is a Russian mathemati ...

's proof of the

Geometrization conjecture In mathematics, Thurston's geometrization conjecture states that each of certain three-dimensional topological spaces has a unique geometric structure that can be associated with it. It is an analogue of the uniformization theorem for two-dimens ...

(from which the

Poincaré conjecture In the mathematical field of geometric topology, the Poincaré conjecture (, , ) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. Originally conjectured ...

follows) in the years 2003–2006. Theirs was the first publication acknowledging Perelman's accomplishment (in May, 2006), which was shortly followed by similar papers by Huai-Dong Cao and Xi-Ping Zhu (in June) and John Morgan and Gang Tian (in July). Kleiner found a relatively simple proof of

Gromov's theorem on groups of polynomial growth In geometric group theory, Gromov's theorem on groups of polynomial growth, first proved by Mikhail Gromov, characterizes finitely generated groups of ''polynomial'' growth, as those groups which have nilpotent subgroups of finite index. Statement ...

. He also proved the Cartan–Hadamard conjecture in dimension 3.

References

;Citations ;Bibliography * *

External links

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Home page at NYU
{{DEFAULTSORT:Kleiner, Bruce 20th-century American mathematicians 21st-century American mathematicians Geometers Living people Topologists Yale University faculty Courant Institute of Mathematical Sciences faculty University of California, Berkeley alumni University of Michigan faculty Year of birth missing (living people)