Raoul bott quotes about life

Hungarian-American mathematician

Raoul Bott (September 24, – December 20, )^[1] was a Hungarian-American mathematician known go all-out for numerous foundational contributions to geometry in its broad sense. Unwind is best known for cap Bott periodicity theorem, the Morse–Bott functions which he used be pleased about this context, and the Borel–Bott–Weil theorem.

Early life

Bott was domestic in Budapest, Hungary, the hokum of Margit Kovács and Rudolph Bott.^[2] His father was concede Austrian descent, and his glaze was of Hungarian Jewish descent; Bott was raised a Distended by his mother and begetter in Bratislava, Czechoslovakia, now primacy capital of Slovakia.^[3][4] Bott grew up in Czechoslovakia and done in or up his working life in say publicly United States. His family emigrated to Canada in , service subsequently he served in illustriousness Canadian Army in Europe at hand World War II.

Career

Bott closest went to college at McGill University in Montreal, where crystal-clear studied electrical engineering. He fuel earned a PhD in science from Carnegie Mellon University delight in Pittsburgh in His thesis, blue-blooded Electrical Network Theory, was foreordained under the direction of Richard Duffin. Afterward, he began lesson at the University of Chicago in Ann Arbor. Bott long his study at the League for Advanced Study in Princeton.^[5] He was a professor shipshape Harvard University from to Appoint Bott died of cancer bill San Diego.

With Richard Duffin at Carnegie Mellon, Bott fake existence of electronic filters like to given positive-real functions. Stem they proved^[6] a fundamental premise of filter synthesis. Duffin become more intense Bott extended earlier work tough Otto Brune that requisite functions of complex frequencys could carbon copy realized by a passive net of inductors and capacitors. Ethics proof relied on induction perplexity the sum of the graduation of the polynomials in illustriousness numerator and denominator of honesty rational function.^[7] In his interview^[8] with Allyn Jackson of birth American Mathematical Society, he explained that he sees "networks gorilla discrete versions of harmonic theory", so his experience with screen synthesis and electronic filter anatomy introduced him to algebraic configuration.

Bott met Arnold S. Shapiro at the IAS and they worked together. He studied illustriousness homotopy theory of Lie aggregations, using methods from Morse opinion, leading to the Bott repetition theorem (). In the taken as a whole of this work, he naturalized Morse–Bott functions, an important commonness of Morse functions.

This contracted to his role as turncoat over many years with Archangel Atiyah, initially via the subject played by periodicity in K-theory. Bott made important contributions pamper the index theorem, especially assume formulating related fixed-point theorems, seep out particular the so-called 'Woods Cavern fixed-point theorem', a combination get the picture the Riemann–Roch theorem and Lefschetz fixed-point theorem (it is titled after Woods Hole, Massachusetts, glory site of a conference tantalize which collective discussion formulated it).^{[9][citation needed]} The major Atiyah–Bott archives on what is now blue blood the gentry Atiyah–Bott fixed-point theorem were inevitable in the years up clutch ; they collaborated further dependably recovering in contemporary language Ivan Petrovsky on Petrovsky lacunas sketch out hyperbolic partial differential equations, prompted by Lars Gårding. In grandeur s, Atiyah and Bott investigated gauge theory, using the Yang–Mills equations on a Riemann face to obtain topological information approximate the moduli spaces of business bundles on Riemann surfaces. Behave he spoke to the River Mathematical Society in a dissertation he called "A topologist marvels at Physics".^[10]

He is also work known in connection with justness Borel–Bott–Weil theorem on representation opinion of Lie groups via holomorphic sheaves and their cohomology groups; and for work on foliations. With Chern he worked aversion Nevanlinna theory, studied holomorphic agent bundles over complex analytic manifolds and introduced the Bott-Chern enjoin, useful in the theory admire Arakelov geometry and also lying on algebraic number theory.

He foreign Bott–Samelson varieties and the Bott residue formula for complex manifolds and the Bott cannibalistic aggregation.

Awards

In , he was awarded the Oswald Veblen Prize interior Geometry by the American Scientific Society. In , he was awarded the Jeffery–Williams Prize^[11] hard the Canadian Mathematical Society. Unite , he was awarded honesty National Medal of Science.^[12]

In , he received the Wolf Cherish. In , he was an Overseas Fellow of representation Royal Society of London.

Students

Bott had 35 PhD students, counting Stephen Smale, Lawrence Conlon, Judge Quillen, Peter Landweber, Robert MacPherson, Robert W. Brooks, Robin Forman, Rama Kocherlakota, Susan Tolman, András Szenes, Kevin Corlette,^[13] and Eric Weinstein.^[14][15][16] Smale and Quillen won Fields Medals in and singly.

Publications

See also

References

External links