Shiing-shen Chern

Shiing-shen CHERN (陳省身; Pinyin: Chén Xǐngshēn; born October 26 1911) is a Chinese mathematician, who was one of the leading differential geometers of the twentieth century.

He was born in Kashing, Chekiang Province in China. From 1926, he was a student at Nankai University in Tientsin (where he moved to be with his father four years earlier), graduating in mathematics in 1930. He was a master student under Dan SUN at Tsing Hua University from 1931 to 1934, working on projective differential geometry.

In 1932 Wilhelm Blaschke from the University of Hamburg visited Tsing Hua and was impressed with Chern. In 1934 Chern went on a scholarship to Hamburg, working on the Cartan-Kähler theory, and finishing his PhD. degree in 1936. In 1936–1937 he learned directly from Élie Cartan in Paris, returning to Beijing, China to a professorial position in Tsing Hua (which had evacuated to Kunming after the Japanese attacks).

In 1943 Chern went to the Institute for Advanced Study (IAS) at Princeton, working there on characteristic classes in differential geometry. Shortly after he was invited by Solomon Lefschetz to be an editor of Annals of Mathematics. He returned to Shanghai in 1946 to found the Mathematical Institute of Academia Sinica, which was later moved to Nanking. From 1948 he was again at the IAS, becoming a professor at the University of Chicago in 1949. He moved to the University of California, Berkeley in 1960. The next year he became a naturalized citizen of the United States. At Berkeley, he founded the Mathematical Sciences Research Institute (MSRI) in 1981 and acted as the director until 1984. In 1985 he founded the Nankai Insititute of Mathematics in Tientsin.

Chern's work spreads over all the classic fields of differential geometry. It includes areas currently fashionable (the Chern-Simons theory arising from a joint paper in 1974), perennial (the Chern-Weil theory linking curvature invariants to characteristic classes from 1944, after the Allendoerfer-Weil paper of 1943 on the Gauss-Bonnet theorem), the quotidian (Chern classes), and some areas such as projective differential geometry and webs that have a lower profile. He published results in integral geometry, value distribution theory of holomorphic functions, and minimal submanifolds.

He was a true follower of Élie Cartan, working intensely on the 'theory of equivalence' in his time in China from 1937-1943, in relative isolation. In 1954 he published his own treatment of the pseudogroup problem that is in effect the touchstone of Cartan's geometric theory. He used the moving frame method with success only matched by its inventor; he preferred in complex manifold theory to stay with the geometry, rather than follow the potential theory. In his contribution to the IMU Millennium volume, Chern proposed that Finsler metrics would be important to the mathematics of the twenty-first century.

He was awarded a National Medal of Science in 1975; a Wolf Prize in mathematics in 1984; and a Shaw Prize in mathematical sciences in May, 2004.

Chern is married to ZHENG Shining (鄭士寧) with a daughter, Pu CHERN (陳璞).

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