User:Kvwiki1234/EricWeinsteinRaoulBott

Education
Weinstein received his Ph.D. in mathematical physics from the Mathematics Department at Harvard University in 1992 under the supervision of Raoul Bott. In his dissertation, titled "Extension of Self-Dual Yang-Mills Equations across the Eighth Dimension", Weinstein showed that the self-dual Yang–Mills equations were not really peculiar to dimension four and admitted generalizations to higher dimensions.

Career
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).

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 the Fields Medals in 1966 and 1978 respectively.