Ichirō Satake

Ichiro Satake
Ichiro Satake
	Ichirō Satake in Berkeley, California
Born	December 25, 1927; Tokyo, Japan
Died	October 10, 2014 (aged 86)
Nationality	Japanese
Alma mater	University of Tokyo
Known for	Satake isomorphism; Satake diagrams
	Scientific career
Fields	Mathematics
Institutions	University of Tokyo (1952-1963); University of Chicago (1963-1968); UC Berkeley (1968-1983); Tohoku University (1980-1991); Chuo University (1991-1998)
Doctoral advisor	Shokichi Iyanaga

Ichirō Satake (佐武一郎, Satake Ichirō) (25 December 1927 – 10 October 2014) was a Japanese mathematician working on algebraic groups who introduced the Satake isomorphism and Satake diagrams. He was considered an iconic figure in the theory of linear algebraic groups and symmetric spaces.^[1]

Satake was born in Tokyo, Japan in 1927, and received his Ph.D. at the University of Tokyo in 1959 under the supervision of Shokichi Iyanaga. He was a professor at University of California, Berkeley from 1968 to 1983. After retirement he returned to Japan, where he spent time at Tohoku University and Chuo University. He died of respiratory failure on 10 October 2014.^[2]

Although they are often attributed to William Thurston, Satake was the first to introduce orbifold, which he did in the 1950s under the name of V-manifold. In Satake (1956), he gave the modern definition, along with the basic calculus of smooth functions and differential forms. He demonstrated that the de Rham theorem and Poincaré duality, along with their proofs, carry over to the orbifold setting. In Satake (1957), he demonstrated that the standard tensor calculus of bundles, connections, and curvature also carries over to orbifolds, along with the Chern-Gauss-Bonnet theorem and Shiing-Shen Chern's proof thereof.^[3]

Major publications

Satake, I. (1956), "On a generalization of the notion of manifold", Proc. Natl. Acad. Sci. U.S.A., 42 (6): 359–363, Bibcode:1956PNAS...42..359S, doi:10.1073/pnas.42.6.359, PMC 528292, PMID 16578464
Satake, Ichirô (1957), "The Gauss-Bonnet theorem for V-manifolds", J. Math. Soc. Jpn., 9 (4): 464–492, doi:10.2969/jmsj/00940464
Satake, Ichirô (1963), "Theory of spherical functions on reductive algebraic groups over p-adic fields", Publications Mathématiques de l'IHÉS, 18 (18): 5–69, doi:10.1007/BF02684781, MR 0195863, S2CID 4666554
Satake, Ichirô (1980), Algebraic structures of symmetric domains, Kanô Memorial Lectures, vol. 4, Tokyo: Iwanami Shoten, ISBN 978-0-691-08271-4, MR 0591460

^ Joseph A. Wolf. "In Memoriam, Ichiro Satake". Retrieved 21 June 2018.
^ 佐武一郎氏死去（東北大名誉教授・整数論、微分幾何学） (in Japanese). Jiji Press. Archived from the original on 20 October 2014. Retrieved 20 October 2014.
^ Shiing-shen Chern. A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds. Ann. of Math. (2) 45 (1944), 747–752.