(25 December 1927 – 10 October 2014) was a Japanese mathematician working on

algebraic group In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Man ...

s who introduced the Satake isomorphism and Satake diagrams. He was considered an iconic figure in the theory of

linear algebraic group In mathematics, a linear algebraic group is a subgroup of the group of invertible n\times n matrices (under matrix multiplication) that is defined by polynomial equations. An example is the orthogonal group, defined by the relation M^TM = I_n ...

s and symmetric spaces. Satake was born in

Tokyo, Japan Tokyo, officially the Tokyo Metropolis, is the capital of Japan, capital and List of cities in Japan, most populous city in Japan. With a population of over 14 million in the city proper in 2023, it is List of largest cities, one of the most ...

in 1927, and received his Ph.D. at the

University of Tokyo The University of Tokyo (, abbreviated as in Japanese and UTokyo in English) is a public research university in Bunkyō, Tokyo, Japan. Founded in 1877 as the nation's first modern university by the merger of several pre-westernisation era ins ...

in 1959 under the supervision of Shokichi Iyanaga. He was a professor at

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

from 1968 to 1983. After retirement he returned to Japan, where he spent time at

Tohoku University is a public research university in Sendai, Miyagi, Japan. It is colloquially referred to as or . Established in 1907 as the third of the Imperial Universities, after the University of Tokyo and Kyoto University, it initially focused on sc ...

and

Chuo University , commonly referred to as or , is a private research university in Hachioji, Tokyo, Japan. The university finds its roots in a school called Igirisu Hōritsu Gakkō (English Law School), which was founded in 1885, and became a university in 1 ...

. He died of

respiratory failure Respiratory failure results from inadequate gas exchange by the respiratory system, meaning that the arterial oxygen, carbon dioxide, or both cannot be kept at normal levels. A drop in the oxygen carried in the blood is known as hypoxemia; a r ...

on 10 October 2014. Although they are often attributed to

William Thurston William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds. Thurst ...

, Satake was the first to introduce

orbifold In the mathematical disciplines of topology and geometry, an orbifold (for "orbit-manifold") is a generalization of a manifold. Roughly speaking, an orbifold is a topological space that is locally a finite group quotient of a Euclidean space. D ...

, which he did in the 1950s under the name of ''V-manifold''. In , he gave the modern definition, along with the basic calculus of smooth functions and

differential form In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications ...

s. He demonstrated that the de Rham theorem and

Poincaré duality In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology (mathematics), homology and cohomology group (mathematics), groups of manifolds. It states that if ''M'' is an ''n''-dim ...

, along with their proofs, carry over to the orbifold setting. In , he demonstrated that the standard

tensor calculus In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other ...

of bundles, connections, and curvature also carries over to orbifolds, along with the Chern-Gauss-Bonnet theorem and

Shiing-Shen Chern Shiing-Shen Chern (; , ; October 26, 1911 – December 3, 2004) was a Chinese American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geome ...

's proof thereof.Shiing-shen Chern. ''A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds.'' Ann. of Math. (2) 45 (1944), 747–752.

Major publications

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References

External links

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FORMULA IN SIMPLE JORDAN ALGEBRAS ICHIRO SATAKE (Received May 7, 1984)
{{DEFAULTSORT:Satake, Ichiro 1927 births 2014 deaths Deaths from respiratory failure 20th-century Japanese mathematicians 21st-century Japanese mathematicians University of California, Berkeley faculty University of Tokyo alumni Academic staff of Tohoku University Academic staff of Chuo University University of Chicago faculty Mathematicians from Tokyo Group theorists Topologists