Wu-Chung Hsiang (; born 12 June 1935 in

Zhejiang Zhejiang ( or , ; , also romanized as Chekiang) is an eastern, coastal province of the People's Republic of China. Its capital and largest city is Hangzhou, and other notable cities include Ningbo and Wenzhou. Zhejiang is bordered by Jiang ...

) is a Chinese-American mathematician, specializing in

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

. Hsiang served as chairman of the Department of

Mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

from 1982 to 1985 and was one of the most influential topologists of the second half of the 20th century.

Biography

Hsiang hails from

Wenzhou Wenzhou (pronounced ; Wenzhounese: Yuziou �y33–11 tɕiɤu33–32 ), historically known as Wenchow is a prefecture-level city in southeastern Zhejiang province in the People's Republic of China. Wenzhou is located at the extreme south east ...

. He received in 1957 his bachelor's degree from the

National Taiwan University National Taiwan University (NTU; ) is a public research university in Taipei, Taiwan. The university was founded in 1928 during Japanese rule as the seventh of the Imperial Universities. It was named Taihoku Imperial University and served d ...

and in 1963 his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

under

Norman Steenrod Norman Earl Steenrod (April 22, 1910October 14, 1971) was an American mathematician most widely known for his contributions to the field of algebraic topology. Life He was born in Dayton, Ohio, and educated at Miami University and University of ...

from

with thesis ''Obstructions to sectioning fibre bundles''. At

Yale University Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wo ...

he became in 1962 a lecturer, in 1963 an assistant professor, and in 1968 a full professor. At Princeton University he was a full professor from 1972 until retiring in 2006 as professor emeritus and was the department chair from 1982 to 1985. He was a visiting scholar at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

for the academic years 1965–1966, 1971–1972, and 1979–1980. He was a visiting professor at the

University of Warwick , mottoeng = Mind moves matter , established = , type = Public research university , endowment = £7.0 million (2021) , budget = £698.2 million (2020� ...

in 1966, the

University of Amsterdam The University of Amsterdam (abbreviated as UvA, nl, Universiteit van Amsterdam) is a public research university located in Amsterdam, Netherlands. The UvA is one of two large, publicly funded research universities in the city, the other being ...

in 1969, the

University of Bonn The Rhenish Friedrich Wilhelm University of Bonn (german: Rheinische Friedrich-Wilhelms-Universität Bonn) is a public research university located in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the ( en, Rhine U ...

in 1971, the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

in 1976, and the

Mathematical Sciences Research Institute The Simons Laufer Mathematical Sciences Institute (SLMath), formerly the Mathematical Sciences Research Institute (MSRI), is an independent nonprofit mathematical research institution on the University of California campus in Berkeley, Califo ...

and

Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...

in 1980. Hsiang has made important contributions to algebraic and differential topology. Works by Hsiang, Julius Shaneson,

C. T. C. Wall Charles Terence Clegg "Terry" Wall (born 14 December 1936) is a British mathematician, educated at Marlborough College, Marlborough and Trinity College, Cambridge. He is an :wikt:emeritus, emeritus professor of the University of Liverpool, where ...

Robion Kirby Robion Cromwell Kirby (born February 25, 1938) is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology. Together with Laurent C. Siebenmann he invented the Kirby–Siebenmann invariant f ...

, Laurent Siebenmann and

Andrew Casson Andrew John Casson FRS (born 1943) is a mathematician, studying geometric topology. Casson is the Philip Schuyler Beebe Professor of Mathematics at Yale University. Education and Career Casson was educated at Latymer Upper School and Trinity Co ...

led in the 1960s to the proof of the annulus theorem (previously known as the annulus conjecture). The annulus theorem is important in the theory of triangulation of manifolds. With

F. Thomas Farrell Francis Thomas Farrell (born November 14, 1941, in Ohio, United States) is an American mathematician who has made contributions in the area of topology and differential geometry. Farrell is a distinguished professor emeritus of mathematics at B ...

he worked on a program to prove the

Novikov conjecture The Novikov conjecture is one of the most important unsolved problems in topology. It is named for Sergei Novikov who originally posed the conjecture in 1965. The Novikov conjecture concerns the homotopy invariance of certain polynomials in the ...

and the

Borel conjecture In mathematics, specifically geometric topology, the Borel conjecture (named for Armand Borel) asserts that an aspherical closed manifold is determined by its fundamental group, up to homeomorphism. It is a rigidity conjecture, asserting that a ...

with methods from geometric topology and gave proofs for special cases. For example, they gave a proof of the integral Novikov conjecture for compact Riemannian manifolds with non-positive

sectional curvature In Riemannian geometry, the sectional curvature is one of the ways to describe the curvature of Riemannian manifolds. The sectional curvature ''K''(σ''p'') depends on a two-dimensional linear subspace σ''p'' of the tangent space at a poi ...

. Hsiang also made contributions to the topological study of simply-connected 4-manifolds. From 1967 to 1969 he was a Sloan Fellow and for the academic year 1975–1976 a Guggenheim Fellow. In 1980 he was elected a member of

Academia Sinica Academia Sinica (AS, la, 1=Academia Sinica, 3=Chinese Academy; ), headquartered in Nangang, Taipei, is the national academy of Taiwan. Founded in Nanking, the academy supports research activities in a wide variety of disciplines, ranging from ...

. He was an Invited Speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in 1970 in

Nice Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative c ...

, with a talk on ''Differentiable actions of compact connected Lie groups on

R^n

'' and a Plenary Speaker in 1983 in

Warsaw Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officia ...

, with a talk on ''Geometric applications of algebraic K-theory''. In 2005 there was a conference at Stanford University in honor of his 70th birthday.Algebraic & Differential Topology: A Conference in Honor of Wu-chung's 70th Birthday, Stanford U., August 6th and 7th, 2005
/ref> His doctoral students include Ruth Charney,

, Thomas Goodwillie, Michael W. Davis, and Lowell E. Jones.

References

{{DEFAULTSORT:Hsiang, Wu Chung 1935 births Living people 20th-century American mathematicians 21st-century American mathematicians Chinese emigrants to the United States Topologists Institute for Advanced Study visiting scholars Members of Academia Sinica National Taiwan University alumni Yale University faculty Princeton University faculty University of California, Berkeley faculty Educators from Wenzhou Scientists from Wenzhou Sloan Research Fellows Mathematicians from Zhejiang