Halsey Lawrence Royden, Jr. (September 26, 1928 – August 22, 1993) was an American mathematician, specializing in

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

Riemann surface In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed vers ...

several complex variables The theory of functions of several complex variables is the branch of mathematics dealing with functions defined on the complex coordinate space \mathbb C^n, that is, -tuples of complex numbers. The name of the field dealing with the properties ...

, and complex differential geometry. Royden is the author of a popular textbook on

real analysis In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include co ...

Education and career

After study at

Phoenix College Phoenix College (PC) is a Public university, public community college in Encanto, Phoenix, Arizona. Founded in 1920, it is one of the oldest community colleges in the country. History The college was originally a part of the Phoenix Union Hi ...

, Royden transferred in 1946 to

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

, where he received his bachelor's degree in 1948 and his master's degree in 1949, with a master's thesis written under the supervision of Donald Spencer. Royden received his Ph.D. in 1951 at

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

under the supervision of

Lars Ahlfors Lars Valerian Ahlfors (18 April 1907 – 11 October 1996) was a Finnish mathematician, remembered for his work in the field of Riemann surfaces and his textbook on complex analysis. Background Ahlfors was born in Helsinki, Finland. His mothe ...

with thesis ''Harmonic functions on open Riemann surfaces''. At Stanford University he became an assistant professor in 1951, an associate professor in 1953, and a full professor in 1958. In addition to serving on the faculty of the mathematics department, for Stanford's School of Humanities and Sciences he was in 1962–1965 associate dean, in 1968–1969 executive dean (acting dean until the vacancy was resolved), and in 1973–1981 dean. In 1981 he resigned as dean to work full-time as a mathematics professor. He was on the editorial board of the

Pacific Journal of Mathematics The Pacific Journal of Mathematics is a mathematics research journal supported by several universities and research institutes, and currently published on their behalf by Mathematical Sciences Publishers, a non-profit academic publishing organisa ...

for the five years from 1956 to 1960. Royden was a visiting scholar at the

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

Princeton Princeton University is a private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the Unit ...

for 3 months in the fall of 1969, 3 months in the spring of 1974, and for the academic year 1982–1983. In 1970, he showed the equivalence of the Kobayashi metric and the Teichmüller metric on Teichmüller space. Royden was a Guggenheim Fellow for the academic year 1973–1974. In 1974 he was an Invited Speaker (''Intrinsic metrics on Teichmüller space'') at the

International Mathematical Congress 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 IMU Abacus Medal (known before ...

Vancouver Vancouver is a major city in Western Canada, located in the Lower Mainland region of British Columbia. As the List of cities in British Columbia, most populous city in the province, the 2021 Canadian census recorded 662,248 people in the cit ...

. Upon his death he was survived by his wife (the mathematician Virginia "Jinx" Voegeli), two daughters (one,

Leigh Royden Leigh "Wiki" Handy Royden (born October 15, 1955) is an American geologist. Early life Royden was born on October 15, 1955, in Palo Alto, California. Royden's father was Halsey Royden, a mathematician. Education Royden received an A.B. degr ...

, a noted geologist), a son, and several grandchildren. His doctoral students include

Alan Huckleberry Alan Trinler Huckleberry (born February 18, 1941) is an American mathematician who works in complex analysis, Lie groups actions and algebraic geometry. He is the Professor of Mathematics at Ruhr University Bochum and Wisdom Professor of Mathe ...

, Peter A. Loeb and John Wetzel.

Selected publications

Books

Papers

* *with P. R. Garabedian: * * * * * * * * * * *
''A History of Mathematics at Stanford''
in ''A century of mathematics in America'', American Mathematical Society, 1989, vol. 2.

References

{{DEFAULTSORT:Royden, Halsey Lawrence 1928 births 1993 deaths 20th-century American mathematicians Stanford University alumni Harvard University alumni Stanford University faculty Institute for Advanced Study visiting scholars People from Phoenix, Arizona Phoenix College alumni Complex analysts American mathematical analysts American textbook writers Differential geometers