Bruce Alan Kleiner is an
AmericanThe United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematicianA mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, working in
differential geometry and topologyDifferential geometry is a mathematical discipline that uses the techniques of differential and integral calculus, as well as linear and multilinear algebra, to study problems in geometry. The theory of plane and space curves and of surfaces in the three-dimensional Euclidean space formed the basis...
and
geometric group theoryGeometric 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 groups act .Another important...
.
He received his Ph.D. in 1990 from the
University of California, BerkeleyThe University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
. His advisor was Wu-Yi Hsiang. He is now Professor of Mathematics at
New York UniversityNew York University is a private, nonsectarian research university based in New York City. NYU's main campus is situated in the Greenwich Village section of Manhattan...
.
Kleiner has studied the
Ricci flowIn differential geometry, the Ricci flow is an intrinsic geometric flow. It is a process that deforms the metric of a Riemannian manifold in a way formally analogous to the diffusion of heat, smoothing out irregularities in the metric....
. Together with
John LottJohn Lott is a Professor of Mathematics at the University of California, Berkeley. He is working on Ricci flow....
of the
University of MichiganThe University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
, he filled in details of
Grigori PerelmanGrigori Yakovlevich Perelman is a Russian mathematician who has made landmark contributions to Riemannian geometry and geometric topology.In 1992, Perelman proved the soul conjecture. In 2002, he proved Thurston's geometrization conjecture...
's proof of the
Geometrization conjectureThurston's geometrization conjecture states that compact 3-manifolds can be decomposed canonically into submanifolds that have geometric structures. The geometrization conjecture is an analogue for 3-manifolds of the uniformization theorem for surfaces...
(from which the
Poincaré conjectureIn mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere , which is the hypersphere that bounds the unit ball in four-dimensional space...
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 CaoHuai-Dong Cao is A. Everett Pitcher Professor of Mathematics at Lehigh University. He collaborated with Xi-Ping Zhu of Zhongshan University in verifying Grigori Perelman's proof of the Poincaré conjecture. The Cao–Zhu team is one of three teams formed for this purpose...
and
Xi-Ping ZhuZhu Xiping is a Professor of Mathematics at Sun Yat-sen University. He collaborated with Cao Huaidong of Lehigh University in verifying Grigori Perelman's proof of the Poincaré conjecture. The Cao–Zhu team was one of three teams formed for this purpose...
(in June) and
John MorganJohn Willard Morgan is an American mathematician, well known for his contributions to topology and geometry. He is currently the director of the Simons Center for Geometry and Physics at Stony Brook University.-Life:...
and
Gang TianTian Gang is a Chinese mathematician and an academician of the Chinese Academy of Sciences. He is known for his contributions to geometric analysis and quantum cohomology, among other fields...
(in July).
Kleiner found a relatively simple proof of
Gromov's theorem on groups of polynomial growthIn geometric group theory, Gromov's theorem on groups of polynomial growth, named for Mikhail Gromov, characterizes finitely generated groups of polynomial growth, as those groups which have nilpotent subgroups of finite index....
.
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