Raoul Bott
Raoul Bott  

Raoul Bott in 1986


Born  Budapest, Hungary 
September 24, 1923
Died  Script error: The function "death_date_and_age" does not exist. San Diego, California 
Residence  Czechoslovakia United States Canada 
Nationality  Hungarian American 
Fields  Mathematics 
Institutions  University of Michigan in Ann Arbor Harvard University 
Alma mater  McGill University Carnegie Mellon University 
Doctoral advisor  Richard Duffin 
Doctoral students  Edward B. Curtis Harold Edwards Robert MacPherson Daniel Quillen Stephen Smale András Szenes 
Notable awards  Veblen Prize (1964) National Medal of Science (1987) Steele Prize (1990) Wolf Prize (2000) 
Raoul Bott, ForMemRS (September 24, 1923 – December 20, 2005)^{[1]} was a HungarianAmerican mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem.
Early life
Bott was born in Budapest, Hungary, the son of Margit Kovács and Rudolph Bott.^{[2]} His father was of Austrian descent, and his mother was of Hungarian Jewish descent; Bott was raised a Catholic by his mother and stepfather.^{[3]}^{[4]} Bott grew up in Czechoslovakia and spent his working life in the United States. His family emigrated to Canada in 1938, and subsequently he served in the Canadian Army in Europe during World War II.
Career
Bott later went to college at McGill University in Montreal, where he studied electrical engineering. He then earned a Ph.D. in mathematics from Carnegie Mellon University in Pittsburgh in 1949. His thesis, titled Electrical Network Theory, was written under the direction of Richard Duffin. Afterward, he began teaching at the University of Michigan in Ann Arbor. Bott continued his study at the Institute for Advanced Study in Princeton.^{[5]} He was a professor at Harvard University from 1959 to 1999. In 2005 Bott died of cancer in San Diego.
With Richard Duffin at Carnegie Mellon, Bott studied existence of electronic filters corresponding to given positivereal functions . In 1949 they proved^{[6]} a fundamental theorem of filter synthesis. Duffin and Bott extended earlier work by Otto Brune that requisite functions of complex frequency s could be realized by a passive network of inductors and capacitors. The proof, relying on induction on the sum of the degrees of the polynomials in the numerator and denominator of the rational function, was published in Journal of Applied Physics, volume 20, page 816. In his 2000 interview^{[7]} with Allyn Jackson of the American Mathematical Society, he explained that he sees "networks as discrete versions of harmonic theory", so his experience with network synthesis and electronic filter topology introduced him to algebraic topology.
Bott met Arnold S. Shapiro at the IAS and they worked together. He studied the homotopy theory of Lie groups, using methods from Morse theory, leading to the Bott periodicity theorem (1956). In the course of this work, he introduced Morse–Bott functions, an important generalization of Morse functions.
This led to his role as collaborator over many years with Michael Atiyah, initially via the part played by periodicity in Ktheory. Bott made important contributions towards the index theorem, especially in formulating related fixedpoint theorems, in particular the socalled 'Woods Hole fixedpoint theorem', a combination of the Riemann–Roch theorem and Lefschetz fixedpoint theorem (it is named after Woods Hole, Massachusetts, the site of a conference at which collective discussion formulated it).^{[8]}^{[citation needed]} The major Atiyah–Bott papers on what is now the Atiyah–Bott fixedpoint theorem were written in the years up to 1968; they collaborated further in recovering in contemporary language Ivan Petrovsky on Petrovsky lacunas of hyperbolic partial differential equations, prompted by Lars Gårding. In the 1980s, Atiyah and Bott investigated gauge theory, using the Yang–Mills equations on a Riemann surface to obtain topological information about the moduli spaces of stable bundles on Riemann surfaces.
He is also well known in connection with the Borel–Bott–Weil theorem on representation theory of Lie groups via holomorphic sheaves and their cohomology groups; and for work on foliations.
He introduced Bott–Samelson varieties and the Bott residue formula for complex manifolds and the Bott cannibalistic class.
Awards
In 1964, he was awarded the Oswald Veblen Prize in Geometry by the American Mathematical Society. In 1983, he was awarded the Jeffery–Williams Prize by the Canadian Mathematical Society. In 1987, he was awarded the National Medal of Science.^{[9]}
In 2000, he received the Wolf Prize. In 2005, he was elected an Overseas Fellow of the Royal Society of London.
Students
Bott had 26 Ph.D. students, including Stephen Smale, Lawrence Conlon, Daniel Quillen, Peter Landweber, Robert MacPherson, Robert W. Brooks, Robin Forman, András Szenes, and Kevin Corlette.^{[10]}
Publications
 1995: Collected Papers. Vol. 4. Mathematics Related to Physics. Edited by Robert MacPherson. Contemporary Mathematicians. Birkhäuser Boston, xx+485 pp. ISBN 081763648X MR 1321890
 1995: Collected Papers. Vol. 3. Foliations. Edited by Robert D. MacPherson. Contemporary Mathematicians. Birkhäuser, xxxii+610 pp. ISBN 0817636471 MR 1321886
 1994: Collected Papers. Vol. 2. Differential Operators. Edited by Robert D. MacPherson. Contemporary Mathematicians. Birkhäuser, xxxiv+802 pp. ISBN 0817636463 MR 1290361
 1994: Collected Papers. Vol. 1. Topology and Lie Groups. Edited by Robert D. MacPherson. Contemporary Mathematicians. Birkhäuser, xii+584 pp. ISBN 0817636137 MR 1280032
 1982: (with Loring W. Tu) Differential Forms in Algebraic Topology. Graduate Texts in Mathematics #82. SpringerVerlag, New YorkBerlin. xiv+331 pp. ISBN 0387906134 MR 0658304^{[11]}
 1969: Lectures on K(X). Mathematics Lecture Note Series W. A. Benjamin, New YorkAmsterdam x+203 pp.MR 0258020
References
 ↑ Lua error in package.lua at line 80: module 'strict' not found.
 ↑ [1]
 ↑ http://wwwhistory.mcs.stand.ac.uk/Biographies/Bott.html
 ↑ http://www.ams.org/notices/200605/feabott2.pdf
 ↑ Community of Scholars from Institute for Advanced Study
 ↑ John H. Hubbard (2010) "The BottDuffin Synthesis of Electrical Circuits", pp 33 to 40 in A Celebration of the Mathematical Legacy of Raoul Bott, P. Robert Kotiuga editor, CRM Proceedings and Lecture Notes #50, American Mathematical Society
 ↑ Notices of the AMS 48(4):374
 ↑ [2]
 ↑ National Science Foundation
 ↑ http://www.genealogy.ams.org/id.php?id=7583
 ↑ Lua error in package.lua at line 80: module 'strict' not found.
External links
 Pages using Template:Postnominals with customized linking
 Articles with unsourced statements from July 2010
 1923 births
 2005 deaths
 20thcentury American mathematicians
 21stcentury American mathematicians
 American Jews
 American people of HungarianJewish descent
 Hungarian Jews
 Hungarian mathematicians
 Topologists
 Geometers
 Differential geometers
 Algebraic geometers
 Harvard University faculty
 University of Michigan faculty
 McGill University alumni
 Carnegie Mellon University alumni
 Foreign Members of the Royal Society
 National Medal of Science laureates
 Wolf Prize in Mathematics laureates
 Members of the French Academy of Sciences
 Cancer deaths in California
 Guggenheim Fellows
 Hungarian emigrants to Canada
 Deaths from cancer