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 Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...

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 complex-valued functions. The name of the field dealing with the properties of function of several complex variables is called several complex variable ...

, 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 converg ...

Education and career

After study at

Phoenix College Phoenix College (PC) is a 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 High School and Juni ...

, Royden transferred in 1946 to

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 ...

, 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 Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

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 text on complex analysis. Background Ahlfors was born in Helsinki, Finland. His mother, S ...

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 organisati ...

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), 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 ...

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

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 in

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 ...

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

Leigh Royden Leigh "Wiki" H. Royden is an American Geologist. Early life Royden was born in Palo Alto, California. Royden's father was Halsey Royden, a mathematician. Education Royden received an A.B. degree in physics from Harvard University and a PhD i ...

, a noted geologist), a son, and several grandchildren. His doctoral students include Alan Huckleberry, 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 Mathematical analysts Textbook writers Differential geometers