Person: Chow, Wei-Liang
Chow Wei-Liang was a Chinese mathematician known for his work in algebraic geometry.
Mathematical Profile (Excerpt):
- Chow disliked the atmosphere which had descended on Göttingen due to the Nazis so decided that he would rather go to Leipzig and study for his doctorate under van der Waerden.
- It was van der Waerden who introduced Chow to algebraic geometry at this time, pointing him towards the work of Severi, Bertini and Enriques.
- Chow went to Hamburg for a vacation in the summer of 1934 and there he met Margot Victor.
- In Zur algebraische geometry IX (published in Mathematische Annalen in 1937) he introduced the notion now known as Chow coordinates.
- In August there was savage fighting in Shanghai, but Chow decided that Shanghai was safer than Nanking so in September he escaped from Nanking to Shanghai (which was of course the city of his birth).
- During the next two or three years Chow was able to have some contacts with European mathematicians, in particular with van der Waerden.
- Chow had published three further papers in 1939 one of which was Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung in which he extended results by Carathéodory on Pfaffian systems.
- In a decade of war years Wei-Liang had practically stopped his mathematical activities, and the question was whether it was advisable or even possible for him to come back to mathematics.
- The 'miracle', of course, was partly due to Chern for without his help and encouragement it must rate as extremely unlikely that Chow would ever have even attempted to return to mathematics.
- Chow was admitted to the Institute for Advanced Studies in Princeton thanks to a letter from Chern to Lefschetz and he was a vistor at the Institute from March 1947.
- In 1955 Chow proved the so-called "Chow's moving lemma" in algebraic geometry, providing an intersection theory for algebraic cycles based on ideas and results of Severi, later also developed by van der Waerden, Hodge and Pedoe.
- Such equivalence classes make up the "Chow ring" of a nonsingular projective variety and provide the algebraic counterpart of the topological singular cohomology ring.
- The "Chow ring" is just as fundamental in algebraic geometry as its topological counterpart.
- Actually, wonderful developments of this analogy were included in Grothendieck's theory of motives, where algebraic cycles provide correspondences between algebraic varieties and their intersections provide their composition, yielding the category of "Chow motives".
- Notably, "Chow motives" are naturally included in Voevodsky's triangulated category of motives, showing the deepest roots of this analogy.
- Chow founded this school without causing any financial strain to the university.
- We became almost like relatives - some of us even spent summers together with the Chows at China Lake, Maine.
- In addition to his research and leadership of the algebraic geometry group, Chow played an important role as editor-in-chief of the American Journal of Mathematics from 1953 to 1977.
- It was typical of Chow that every thing he did was at the highest level of expertise.
Born 1 October 1911, Shanghai, China. Died 10 August 1995, Baltimore, Maryland, USA.
View full biography at MacTutor
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive