Home > Raoul Bott

He was born in Budapest, but has spent his working life in the USA. He was Professor at Harvard University 1959-1999, and received the Wolf Prize in 2000,

Initially he worked on the theory of electrical circuits ( Bott-Duffin theorem from 1949), then switched to pure mathematics.

He studied the homotopy theory of Lie groups, using methods from Morse theory, leading to the Bott periodicity theorem (1956).

This led to his role as collaborator over many years with Michael Atiyah, initially via the part played by periodicity in K-theory; he made important contributions towards the Index TheoremIn the mathematics of manifolds and differential operators, the Atiyah-Singer index theorem is an important unifying result that connects topology and analysis. It deals with elliptic differential operators (such as the Laplacian) on compact manifolds., especially in formulating related fixed-point theoremIn mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point, under some conditions on F that can be stated in general term. Results of this kind are amongst the most generally useful in mathematics The Bans (in particular the so-called 'Woods Hole' fixed-point theorem).

He is also known in connection with the Borel-Bott-Weil theoremIn 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 on representation theory of Lie groups via holomorphic sheavesAlternate meanings: River Sheaf, King Sceaf, sheaf toss In mathematics, a sheaf ''F on a given topological space X gives a set or richer structure F ''U for each open set U of X''. The structures F ''U are compatible with the operations of restricting the and their cohomology groups; and for work on foliationIn mathematics, a foliation structure on a manifold M gives it stripes''. For example if the dimension of M is two, there is a pattern of stripes on the Euclidean plane formed by all lines parallel to the x axis (lines y c , and a foliation on M is a conss.