What organization did Raoul Bott join in 1995?
Raoul Bott Raoul Bott ( September 24 , 1923 – December 20 , 2005 ) was a Hungarian-American 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 . His father was of Austrian descent , and his mother was of Hungarian Jewish descent ; Bott was raised a Catholic by his mother and stepfather . 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 . 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 positive-real functions . In 1949 they proved 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 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 ( 1957 ) . 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 K-theory . Bott made important contributions towards the index theorem , especially in formulating related fixed-point theorems , in particular the so-called Woods Hole fixed-point theorem , a combination of the Riemann–Roch theorem and Lefschetz fixed-point theorem ( it is named after Woods Hole , Massachusetts , the site of a conference at which collective discussion formulated it ) . The major Atiyah–Bott papers on what is now the Atiyah–Bott fixed-point 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 . In 1983 he spoke to the Canadian Mathematical Society in a talk he called A topologist marvels at Physics . 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 . With Chern he worked on Nevanlinna theory , studied holomorphic vector bundles over complex analytic manifolds and introduced the Bott-Chern classes , useful in the theory of Arakelov geometry and also to algebraic number theory . 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 . In 2000 , he received the Wolf Prize . In 2005 , he was elected an Overseas Fellow of the Royal Society of London . Students . Bott had 35 Ph.D . students , including Stephen Smale , Lawrence Conlon , Daniel Quillen , Peter Landweber , Robert MacPherson , Robert W . Brooks , Robin Forman , Rama Kocherlakota , András Szenes , Kevin Corlette , and Eric Weinstein . Smale and Quillen won Fields Medals in 1966 and 1978 respectively . Publications . - 1995 : Collected Papers . Vol . 4 . Mathematics Related to Physics . Edited by Robert MacPherson . Contemporary Mathematicians . Birkhäuser Boston , xx+485 pp . - 1995 : Collected Papers . Vol . 3 . Foliations . Edited by Robert D . MacPherson . Contemporary Mathematicians . Birkhäuser , xxxii+610 pp . - 1994 : Collected Papers . Vol . 2 . Differential Operators . Edited by Robert D . MacPherson . Contemporary Mathematicians . Birkhäuser , xxxiv+802 pp . - 1994 : Collected Papers . Vol . 1 . Topology and Lie Groups . Edited by Robert D . MacPherson . Contemporary Mathematicians . Birkhäuser , xii+584 pp . - 1982 : ( with Loring W . Tu ) Differential Forms in Algebraic Topology . Graduate Texts in Mathematics #82 . Springer-Verlag , New York-Berlin . xiv+331 pp . - 1969 : Lectures on K ( X ) . Mathematics Lecture Note Series W . A . Benjamin , New York-Amsterdam x+203 pp . External links . - Commemorative website at Harvard Math Department - The Life and Works of Raoul Bott , by Loring Tu . - Raoul Bott , an Innovator in Mathematics , Dies at 82 , The New York Times , January 8 , 2006 .