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Hsien Chung Wang

From Wikipedia, the free encyclopedia
Hsien Chung Wang
王宪钟
Born(1918-04-18)18 April 1918
Beijing
Died25 June 1978(1978-06-25) (aged 60)
New York City
EducationTsinghua University
Manchester University
Known forWang sequence
Boothby-Wang construction
Scientific career
FieldsMathematics
WorkplacesAcademia Sinica
Louisiana State University
Institute for Advanced Study
Alabama Polytechnic Institute
University of Washington in Seattle
Columbia University in New York
Northwestern University
Cornell University
Thesis I. Homogeneous spaces with non-vanishing Euler characteristics. II. Simply-connected homogeneous manifolds with prime Euler characteristics  (1948)
Max Newman
Doctoral students
Stephen Halperin

Hsien Chung (or Hsien-Chung or Hsien-chung) Wang (王宪钟 Wang Xian Zhong; 18 April 1918 in Beijing – 25 June 1978 in New York City) was a Chinese-American mathematician, specializing in differential geometry, Lie groups, and algebraic topology.

Biography

[edit]

Hsien Chung Wang was part of a family from Shandong Province that had produced distinguished scholars for several generations, including the archeologist Wang Yirong.[1]

He studied in Tianjin at Nankai High School and in 1936 he matriculated at Tsing Hua University in Beijing. Due to the outbreak of the Second Sino-Japanese War in 1937, the university had to be moved to Southwest China. Wang graduated in 1941 and began to study under Chern. He was awarded a master's degree in 1944 and began teaching in a school.[1][2][3]

However, after one year, he was awarded a British Council Scholarship to continue his studies in England. He studied first in Sheffield and then at Manchester University under Newman, and received a Ph.D. in 1948.[1][2][3]

Returning to China, Wang took a research position at the Academia Sinica, which was soon moved to Taiwan following the end of the Chinese Civil War.[1][2]

In 1949 Wang moved to the United States, obtaining a lecturer position at Louisiana State University. In the subsequent years, he hold a series of temporary positions at the Institute for Advanced Study at Princeton, the Alabama Polytechnic Institute, the University of Washington in Seattle and Columbia University in New York.[2][3]

He obtained his first permanent position in 1957 at Northwestern University. In 1966 he accepted a professorship at Cornell University, which he hold until his sudden death from leukemia.[2][3]

Research and awards

[edit]

While he was a PhD student in Manchester,[4] Wang worked in algebraic topology. He discovered an exact sequence (called nowadays the Wang sequence) involving the homology groups associated with fiber bundles over spheres.[1][2]

At the same time,[5] he also solved an open problem arising from the work of Hopf and Samelson:[6] determine the closed subgroups of maximal rank in a compact Lie group.[1][2] In 1952[7] he showed that any connected compact metric space, such that any two pairs of points separated by the same distance are related by an isometry, is a homogeneous space of a compact Lie group.[1][2]

Since 1956[8] and until the end of his career he worked mostly on discrete subgroups of Lie groups.[1][2]

Among other topics in differential geometry,[1][9][2] he worked on complex manifolds,[10][11] he described a construction of contact manifolds which is now called the Boothby-Wang construction,[12] and he studied transformation groups of n-spheres.[13]

Wang was an Invited Speaker at the ICM in 1958 in Edinburgh.[14] He was a Guggenheim Fellow for the academic year 1960–1961.[15]

His doctoral students include J. Stephen Halperin.[16]

Selected publications

[edit]
  • with S. S. Chern: "Differential geometry in symplectic space." I, Sci. Rep. Nat. Tsing Hua Univ 4 (1947): 453–477.
  • "Axiom of the plane in a general space of paths." Annals of Mathematics (1948): 731–737. doi:10.2307/1969056
  • "The homology groups of the fibre-bundles over a sphere." Duke Math. J 16 (1949): 33–38.
  • "Homogeneous spaces with non-vanishing Euler characteristics." Annals of Mathematics (1949): 925–953. doi:10.2307/1969588
  • "A problem of PA Smith." Proceedings of the American Mathematical Society 1, no. 1 (1950): 18–19. MR 0033288
  • "A remark on transformation groups leaving fixed an end point." Proceedings of the American Mathematical Society 3, no. 4 (1952): 548–549. MR 0048803
  • "One-dimensional cohomology group of locally compact metrically homogeneous space." Duke Mathematical Journal 19, no. 2 (1952): 303–310. MR 0047672
  • "Complex parallisable manifolds." Proceedings of the American Mathematical Society 5, no. 5 (1954): 771–776. MR 0074064
  • with Kentaro Yano: "A class of affinely connected spaces." Transactions of the American Mathematical Society 80, no. 1 (1955): 72–92. MR 0073254
  • "Discrete subgroups of solvable Lie groups I." Annals of Mathematics (1956): 1–19. doi:10.2307/1969948
  • with William M. Boothby: "On contact manifolds." Annals of Mathematics (1958): 721–734. doi:10.2307/1970165
  • "Compact transformation groups of Sn with an (n–1)-dimensional orbit." American Journal of Mathematics 82, no. 4 (1960): 698–748. doi:10.2307/2372936
  • with Samuel Pasiencier: "Commutators in a semi-simple Lie group." Proceedings of the American Mathematical Society 13, no. 6 (1962): 907–913. MR 0169947
  • "On the deformations of lattice in a Lie group." American Journal of Mathematics 85, no. 2 (1963): 189–212. doi:10.2307/2373209
  • with William M. Boothby and Shoshichi Kobayashi: "A note on mappings and automorphisms of almost complex manifolds." Annals of Mathematics (1963): 329–334. doi:10.2307/1970219
  • "A remark on co-compactness of transformation groups." American Journal of Mathematics 95, no. 4 (1973): 885–903. doi:10.2307/2373700

References

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  1. 1 2 3 4 5 6 7 8 9 "Wang, Hsien Chung". Complete Dictionary of Scientific Biography. Charles Scribner's Sons. 2008.
  2. 1 2 3 4 5 6 7 8 9 10 O'Connor, John J.; Robertson, Edmund F., "Hsien Chung Wang", MacTutor History of Mathematics Archive, University of St Andrews
  3. 1 2 3 4 Rosenberg, Alex; Rothaus, Oscar S.; Fuchs, Wolfgang H. "Hsien Chung Wang 1918–1978, Cornell University Faculty Memorial Statement" (PDF). ecommons.cornell.edu. Retrieved 2023-09-08.
  4. ↑ Wang, Hsien-Chung (1949-03-01). "The homology groups of the fibre bundles over a sphere". Duke Mathematical Journal. 16 (1). doi:10.1215/S0012-7094-49-01603-8. ISSN 0012-7094.
  5. ↑ Wang, Hsien-Chung (1949). "Homogeneous Spaces with Non-Vanishing Euler Characteristics". Annals of Mathematics. 50 (4): 925. doi:10.2307/1969588.
  6. ↑ Hopf, H.; Samelson, H. (1940). "Ein Satz über die Wirkungsräume geschlossener Liescher Gruppen" [A theorem on the action spaces of closed Lie groups]. Commentarii Mathematici Helvetici (in German). 13. ISSN 0010-2571. Archived from the original on 2026-06-07.
  7. ↑ Wang, Hsien-Chung (1952). "Two-Point Homogeneous Spaces". Annals of Mathematics. 55 (1): 177–191. doi:10.2307/1969427. ISSN 0003-486X.
  8. ↑ Wang, Hsien-Chung (1956). "Discrete Subgroups of Solvable Lie Groups I". Annals of Mathematics. 64 (1): 1. doi:10.2307/1969948.
  9. ↑ Boothby, William Munger; Chern, Shiing-Shen; Wang, Shu Ping (1980). "The mathematical work of H. C. Wang". Bulletin of the Institute of Mathematics Academia Sinica. 8 (2, 3 Part 1): XIII–XXIV. MR 0595525. Zbl 0446.01026.
  10. ↑ Wang, Hsien-Chung (1954). "Complex parallisable manifolds". Proceedings of the American Mathematical Society. 5 (5): 771–776. doi:10.1090/S0002-9939-1954-0074064-3. ISSN 1088-6826.
  11. ↑ Wang, Hsien-Chung (1954). "Closed Manifolds with Homogeneous Complex Structure". American Journal of Mathematics. 76 (1): 1. doi:10.2307/2372397.
  12. ↑ Boothby, W. M.; Wang, H. C. (1958). "On Contact Manifolds". Annals of Mathematics. 68 (3): 721–734. doi:10.2307/1970165. ISSN 0003-486X.
  13. ↑ Wang, Hsien-Chung (1960). "Compact Transformation Groups of Sn with an (n - 1)-Dimensional Orbit". American Journal of Mathematics. 82 (4): 698–748. doi:10.2307/2372936. ISSN 0002-9327.
  14. ↑ Todd, John Arthur, ed. (1960). Proceedings of the International Congress of Mathematician 1958 (PDF). Cambridge: Cambridge University Press. pp. 500–509.
  15. ↑ "Hsien Chung Wang". Guggenheim Fellowships. Retrieved 2026-08-19.
  16. ↑ "Cornell Mathematics Doctorates, 1970-1979". Retrieved 2023-09-08.
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