Richard Sheldon Palais (born May 22, 1931) is a mathematician working in geometry who introduced the principle of symmetric criticality, the

Mostow–Palais theorem In mathematics, the Mostow–Palais theorem is an equivariant version of the Whitney embedding theorem. It states that if a manifold is acted on by a compact Lie group In mathematics, a Lie group (pronounced ) is a group that is also a d ...

, the

Lie–Palais theorem In differential geometry, the Lie–Palais theorem states that an action of a finite-dimensional Lie algebra on a smooth compact manifold can be lifted to an action of a finite-dimensional Lie group. For manifolds with boundary the action must pres ...

, the

Morse–Palais lemma In mathematics, the Morse–Palais lemma is a result in the calculus of variations and theory of Hilbert spaces. Roughly speaking, it states that a smooth enough function near a critical point can be expressed as a quadratic form after a suitable ...

, and the

Palais–Smale compactness condition The Palais–Smale compactness condition, named after Richard Palais and Stephen Smale, is a hypothesis for some theorems of the calculus of variations. It is useful for guaranteeing the existence of certain kinds of critical points, in particula ...

. From 1965 to 1967 Palais was a

Sloan Fellow The Sloan Fellows program is the world's first mid-career and senior career master's degree in general management and leadership. It was initially supported by a grant from Alfred P. Sloan, the late CEO of General Motors, to his alma mater, MI ...

. In 1970 he was an invited speaker (''Banach manifolds of fiber bundle sections'') 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 Nevanlinna Prize (to be rename ...

Nice Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative c ...

. From 1965 to 1982 he was an editor for the ''

Journal of Differential Geometry The ''Journal of Differential Geometry'' is a peer-reviewed scientific journal of mathematics published by International Press on behalf of Lehigh University in 3 volumes of 3 issues each per year. The journal publishes an annual supplement in boo ...

'' and from 1966 to 1969 an editor for the ''

Transactions of the American Mathematical Society The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 ...

''. In 2010 he received a

Lester R. Ford Award Lester is an ancient Anglo-Saxon surname and given name. Notable people and characters with the name include: People Given name * Lester Bangs (1948–1982), American music critic * Lester W. Bentley (1908–1972), American artist from Wisco ...

. In 2012 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 ...

.List of Fellows of the American Mathematical Society
retrieved 2013-05-05. He obtained his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is a ...

from

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...

in 1956 under the joint supervision of

Andrew M. Gleason Andrew Mattei Gleason (19212008) was an American mathematician who made fundamental contributions to widely varied areas of mathematics, including the solution of Hilbert's fifth problem, and was a leader in reform and innovation in teaching at ...

and

George Mackey George Whitelaw Mackey (February 1, 1916 – March 15, 2006) was an American mathematician known for his contributions to quantum logic, representation theory, and noncommutative geometry. Career Mackey earned his bachelor of arts at Rice Unive ...

. His doctoral students include

Edward Bierstone Edward Bierstone (born ) is a Canadian mathematician at the University of Toronto who specializes in singularity theory, analytic geometry, and differential analysis. Education and career He received his B.Sc. from the University of Toronto and ...

Leslie Lamport Leslie B. Lamport (born February 7, 1941 in Brooklyn) is an American computer scientist and mathematician. Lamport is best known for his seminal work in distributed systems, and as the initial developer of the document preparation system LaTeX and ...

Jill P. Mesirov Jill P. Mesirov is an American mathematician, computer scientist, and computational biologist who is the Associate Vice Chancellor for Computational Health Sciences at the University of California, San Diego. She previously held an adjunct facu ...

Chuu-lian Terng Chuu-Lian Terng () is a Taiwanese-American mathematician. Her research areas are differential geometry and integrable systems, with particular interests in completely integrable Hamiltonian partial differential equations and their relations to di ...

, and

Karen Uhlenbeck Karen Keskulla Uhlenbeck (born August 24, 1942) is an American mathematician and one of the founders of modern geometric analysis. She is a professor emeritus of mathematics at the University of Texas at Austin, where she held the Sid W. Richards ...

Selected publications

Books

*as editor
''Seminar on the Atiyah-Singer Index Theorem''
Annals of Mathematical Studies, no. 4, Princeton Univ. Press, 1964 *as author: *''A Global Formulation of the Lie Theory of Transformation Groups'', Memoirs AMS 1957 *''The classification of G-Spaces'', Memoirs AMS 1960 *''Foundations of Global Nonlinear Analysis'', Benjamin 1968 *''The geometrization of physics'', Tsinghua University Press 1981 *''Real algebraic differential topology'', Publish or Perish 1981 *with Chuu-Lian Terng: ''Critical point theory and submanifold geometry'', Lecture Notes in Mathematics, vol.1353, Springer 1988 *with Robert A. Palais: ''Differential Equations, Mechanic, and Computation'', AMS 2009

Articles

* Richard Palais and

Stephen Smale Stephen Smale (born July 15, 1930) is an American mathematician, known for his research in topology, dynamical systems and mathematical economics. He was awarded the Fields Medal in 1966 and spent more than three decades on the mathematics facult ...

''A generalized Morse theory''
Research Announcement,

Bulletin of the American Mathematical Society The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. ...

70 (1964), 165-172 * R. Palais, ''Morse Theory on Hilbert Manifolds'',

Topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...

2 (1963), 299–340. * R. Palais, ''Linear and Nonlinear Waves and Solitons'', in

The Princeton Companion to Mathematics ''The Princeton Companion to Mathematics'' is a book providing an extensive overview of mathematics that was published in 2008 by Princeton University Press. Edited by Timothy Gowers with associate editors June Barrow-Green and Imre Leader, it ...

, T. Gower Ed., Princeton Univ. Press 2008, 234-239

* R. Palais
''The Symmetries of Solitons''
Bulletin. Amer. Math. Soc., New Series 34, No. 4, 339-403 (1997)

SSN 0273-0979 SSN may refer to: Broadcasting *Setanta Sports News, a former 24-hour sports news network in the United Kingdom * Sky Sports News, a 24-hour sports news network in the United Kingdom * Soul of the South Network, an African-American oriented TV Netw ...

* R. Palais
''The Visualization of Mathematics: Towards a Mathematical Exploratorium''
Notices Amer. Math. Soc., 46, No. 6 (June–July 1999,

* R. Palais, ''A Simple Proof of the Banach Contraction Principle'', The Journal for Fixed Point Theory and its Applications, 2 (2007) 221–223,

A nearly complete list of all papers authored or co-authored by Richard Palais is available for downloading as PDF files at http://vmm.math.uci.edu/PalaisPapers

References

External links

*
Home pageHomepage of 3D-XplorMath, Mathematical Visualization software developed by R. Palais
with the

TeX Users Group Tex may refer to: People and fictional characters * Tex (nickname), a list of people and fictional characters with the nickname * Joe Tex (1933–1982), stage name of American soul singer Joseph Arrington Jr. Entertainment * ''Tex'', the Italian ...

{{DEFAULTSORT:Palais, Richard 20th-century American mathematicians 21st-century American mathematicians 1931 births Living people Fellows of the American Mathematical Society Brandeis University faculty Harvard University alumni Geometers Topologists