Raoul Bott (Harvard University News Office)

Raoul Bott, FRS (born September 24, 1923, died December 20, 2005) was a mathematician known for numerous basic contributions to geometry in its broad sense. Image File history File links Bott. ... Image File history File links Bott. ... The Fellowship of the Royal Society was founded in 1660. ... September 24 is the 267th day of the year (268th in leap years) in the Gregorian calendar. ... 1923 (MCMXXIII) was a common year starting on Monday (link will take you to calendar). ... December 20 is the 354th day of the year (355th in leap years) in the Gregorian calendar. ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Table of Geometry, from the 1728 Cyclopaedia. ...

He was born in Budapest, grew up in Slovakia, but spent his working life in the USA. His family emigrated to Canada in 1938; there he studied at McGill University. He was a professor at Harvard University from 1959 to 1999, and received the Wolf Prize in 2000. In 2005, he was elected an Overseas Fellow of the Royal Society of London. He died in San Diego after a battle with cancer. Nickname: Paris of the East, Pearl of the Danubeor Queen of the Danube Location of Budapest in Hungary Country Hungary County Pest Mayor Gábor Demszky (SZDSZ) Area    - City 525,16 km²  - Land n/a km²  - Water n/a km² Population    - City (2006) 1,695,000  - Density 3570/km... McGill University is a publicly funded, non-denominational, co-educational research university located in the city of Montreal, Quebec, Canada. ... Harvard University (incorporated as The President and Fellows of Harvard College) is a private university in Cambridge, Massachusetts. ... The Wolf Prize has been awarded annually since 1978 to living scientists and artists for achievements in the interest of mankind and friendly relations among peoples . ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ... ... Flag Seal Nickname: Americas Finest City Location Location of San Diego within San Diego County Coordinates , Government County San Diego Mayor City Attorney         City Council District One District Two District Three District Four District Five District Six District Seven District Eight Jerry Sanders (R) Michael Aguirre Scott Peters Kevin...

Initially he worked on the theory of electrical circuits (Bott-Duffin theorem from 1949), then switched to pure mathematics. An electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ... 1949 (MCMXLIX) was a common year starting on Saturday (the link is to a full 1949 calendar). ...

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. An illustration of a homotopy between the two bold paths In topology, two continuous functions from one topological space to another are called homotopic (Greek homeos = identical and topos = place) if one can be continuously deformed into the other, such a deformation being called a homotopy between the two functions. ... In mathematics, a Lie group is a group whose elements can be continuously parametrized by real numbers, such as the rotation group, which can be parametrized by the Euler angles. ... A Morse function is also an expression for an anharmonic oscillator In differential topology, the techniques of Morse theory give a very direct way of analyzing the topology of a manifold by studying differentiable functions on that manifold. ... In mathematics, the Bott periodicity theorem is a result from homotopy theory discovered by Raoul Bott during the latter part of the 1950s, which proved to be of foundational significance for much further research, in particular in K-theory. ... A Morse function is also an expression for an anharmonic oscillator In differential topology, the techniques of Morse theory give a very direct way of analyzing the topology of a manifold by studying differentiable functions on that manifold. ...

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 [1]). 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 results of Ivan Petrovsky on 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. Sir Michael Francis Atiyah, OM, FRS (born 22 April 1929) is a mathematician who was born in London. ... In mathematics, K-theory is, firstly, an extraordinary cohomology theory which consists of topological K-theory. ... In the mathematics of manifolds and differential operators, the Atiyah-Singer index theorem is an important unifying result that connects topology and analysis. ... In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms. ... In mathematics, the Atiyah–Bott fixed-point theorem, proven by Michael Atiyah and Raoul Bott in the 1960s, is a general form of the Lefschetz fixed-point theorem for smooth manifolds M , which uses an elliptic complex on M. This is a system of elliptic differential operators on vector bundles... In mathematics, specifically in complex analysis and algebraic geometry, the Riemann–Roch theorem is an important tool in the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles. ... In mathematics, the Lefschetz fixed-point theorem counts the number of fixed points of a mapping from a topological space X to itself (subject to some mild conditions on X), by means of traces of the induced mappings on the homology groups of X. The counting is subject to some... Woods Hole is a census-designated place and village within the town of Falmouth in Barnstable County, Massachusetts, at the extreme southwest corner of Cape Cod, near the island of Marthas Vineyard, and is the site of three famous scientific institutions: Woods Hole Oceanographic Institution, the Marine Biological Laboratory... In mathematics, the Atiyah–Bott fixed-point theorem is a general form of Lefschetz fixed-point theorem for smooth manifolds M , which uses an elliptic complex on M. This is a system of elliptic differential operators on vector bundles, which can replace the de Rham complex constructed from smooth differential... Ivan G. Petrovsky. ... A hyperbolic partial differential equation is usually a second-order partial differential equation of the form with . ... Lars GÃ¥rding (born 1919) is a Swedish mathematician. ...

Official photo

He is also 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. Image File history File links Raoul_Bott. ... Image File history File links Raoul_Bott. ... In mathematics, the Borel-Bott-Weil theorem is a basic result in the representation theory of Lie groups, showing how a family of representations can be obtained from holomorphic sections of certain complex vector bundles, and, more generally, from higher sheaf cohomology groups associated to such bundles. ... In mathematics, a sheaf F on a topological space X is something that assigns a structure F(U) (such as a set, group, or ring) to each open set U of X. The structures F(U) are compatible with the operations of restricting the open set to smaller subsets and... In mathematics, a foliation is a geometric device used to study manifolds. ...

His students included Robert MacPherson, Peter Landweber, Daniel Quillen and Stephen Smale. Daniel Quillen (born June 21, 1940) is an American mathematician, a Fields Medallist, and the current Waynflete Professor of Pure Mathematics at Magdalen College, Oxford. ... Stephen Smale Stephen Smale (born July 15, 1930) is an American mathematician from Flint, Michigan, and winner of the Fields Medal in 1966. ...

His mother and aunts spoke Hungarian. His Czech stepfather did not, so the principal language at home was German. He had an English governesses from a young age, so he also spoke perfect English (and retained a very faint English accent throughout his life). The language of his high school was Slovak. Despite all this Bott claimed a distaste for learning languages. The English language is a West Germanic language that originates in England. ...

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" (NY Times/ January 8, 2006)