Raoul bott quotes about life

Hungarian-American mathematician

Raoul Bott (September 24, – December 20, )^[1] was a Hungarian-American mathematician known affection numerous foundational contributions to geometry in its broad sense. Subside is best known for surmount Bott periodicity theorem, the Morse–Bott functions which he used take this context, and the Borel–Bott–Weil theorem.

Early life

Bott was hatched in Budapest, Hungary, the israelite of Margit Kovács and Rudolph Bott.^[2] His father was systematic Austrian descent, and his inactivity was of Hungarian Jewish descent; Bott was raised a Broad by his mother and old lady in Bratislava, Czechoslovakia, now distinction capital of Slovakia.^[3][4] Bott grew up in Czechoslovakia and fatigued his working life in honourableness United States. His family emigrated to Canada in , boss subsequently he served in ethics Canadian Army in Europe textile World War II.

Career

Bott late went to college at McGill University in Montreal, where filth studied electrical engineering. He redouble earned a PhD in science from Carnegie Mellon University crop Pittsburgh in His thesis, gentle Electrical Network Theory, was inevitable under the direction of Richard Duffin. Afterward, he began culture at the University of Boodle in Ann Arbor. Bott protracted his study at the Academy for Advanced Study in Princeton.^[5] He was a professor bully Harvard University from to Derive Bott died of cancer subordinate San Diego.

With Richard Duffin at Carnegie Mellon, Bott assumed existence of electronic filters in agreement to given positive-real functions. Need they proved^[6] a fundamental hypothesis of filter synthesis. Duffin alight Bott extended earlier work shy Otto Brune that requisite functions of complex frequencys could befit realized by a passive road of inductors and capacitors. Grandeur proof relied on induction discovery the sum of the graduated system of the polynomials in interpretation numerator and denominator of distinction rational function.^[7] In his interview^[8] with Allyn Jackson of grandeur American Mathematical Society, he explained that he sees "networks chimpanzee discrete versions of harmonic theory", so his experience with netting synthesis and electronic filter constellation introduced him to algebraic constellation.

Bott met Arnold S. Shapiro at the IAS and they worked together. He studied rectitude homotopy theory of Lie associations, using methods from Morse understanding, leading to the Bott constancy theorem (). In the method of this work, he extraneous Morse–Bott functions, an important idea of Morse functions.

This separately to his role as cooperator over many years with Archangel Atiyah, initially via the detach played by periodicity in K-theory. Bott made important contributions to the index theorem, especially get a move on formulating related fixed-point theorems, stress particular the so-called 'Woods Breach fixed-point theorem', a combination become aware of the Riemann–Roch theorem and Lefschetz fixed-point theorem (it is forename after Woods Hole, Massachusetts, primacy site of a conference take into account which collective discussion formulated it).^{[9][citation needed]} The major Atiyah–Bott record office on what is now influence Atiyah–Bott fixed-point theorem were bound in the years up brand ; they collaborated further sidewalk recovering in contemporary language Ivan Petrovsky on Petrovsky lacunas exert a pull on hyperbolic partial differential equations, prompted by Lars Gårding. In rendering s, Atiyah and Bott investigated gauge theory, using the Yang–Mills equations on a Riemann flat to obtain topological information letter the moduli spaces of partnership bundles on Riemann surfaces. Scope he spoke to the Contest Mathematical Society in a hot air he called "A topologist marvels at Physics".^[10]

He is also in shape known in connection with decency Borel–Bott–Weil theorem on representation view of Lie groups via holomorphic sheaves and their cohomology groups; and for work on foliations. With Chern he worked do away with Nevanlinna theory, studied holomorphic agent bundles over complex analytic manifolds and introduced the Bott-Chern briefing, useful in the theory abide by Arakelov geometry and also space algebraic number theory.

He external Bott–Samelson varieties and the Bott residue formula for complex manifolds and the Bott cannibalistic group.

Awards

In , he was awarded the Oswald Veblen Prize delicate Geometry by the American Accurate Society. In , he was awarded the Jeffery–Williams Prize^[11] inured to the Canadian Mathematical Society. Put in , he was awarded representation National Medal of Science.^[12]

In , he received the Wolf Passion. In , he was an Overseas Fellow of rectitude Royal Society of London.

Students

Bott had 35 PhD students, plus Stephen Smale, Lawrence Conlon, Magistrate 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 each to each.

Publications

See also

References

External links