Kottwitz studied at the University of Washington (B.A.) and then went to the Harvard University, where he received his Ph.D. in 1977 under the supervision of Phillip Griffiths and John T. Tate (Orbital Integrals on ). In 1976 he was assistant professor and later professor at the University of Washington and went in 1989 as a professor to the University of Chicago.
He is a fellow of the American Academy of Arts and Sciences and the American Mathematical Society (AMS). He was an invited speaker at the International Congress of Mathematicians in Berlin in 1998 (Harmonic analysis on semisimple Lie p-adic algebras).
- Goresky, Mark; Kottwitz, Robert; MacPherson, Robert (1998), "Equivariant cohomology, Koszul duality, and the localization theorem", Inventiones Mathematicae, 131: 25–83, CiteSeerX 10.1.1.42.6450, doi:10.1007/s002220050197
- With Diana Shelstad Foundations of Twisted Endoscopy, Astérisque, 255, 1999
- With James Arthur, David Ellwood (editor): Harmonic analysis, the trace formula and Shimura varieties, Proc. Clay Mathematics Institute, 2003 Summer School, The Fields Institute, Toronto, June 2003, AMS 2005
- member book of IAS in 1980
- Robert Kottwitz at the Mathematics Genealogy Project
- Laurent Clozel Nombre de points des variétés de Shimura sur un corps fini, d'après R. Kottwitz, Séminaire Bourbaki 766, 1992/93
- List of Fellows of the American Mathematical Society, retrieved 2013-11-27.