Walter Lewis Baily Jr. (July 5, 1930 – January 15, 2013) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

Life and career

Born in Waynesburg,

Pennsylvania Pennsylvania, officially the Commonwealth of Pennsylvania, is a U.S. state, state spanning the Mid-Atlantic (United States), Mid-Atlantic, Northeastern United States, Northeastern, Appalachian, and Great Lakes region, Great Lakes regions o ...

, Baily's research focused on areas of

algebraic group In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Man ...

modular form In mathematics, a modular form is a holomorphic function on the complex upper half-plane, \mathcal, that roughly satisfies a functional equation with respect to the group action of the modular group and a growth condition. The theory of modul ...

s and number-theoretical applications of

automorphic form In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group ''G'' to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G o ...

s. One of his significant works was with

Armand Borel Armand Borel (21 May 1923 – 11 August 2003) was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in alg ...

, now known as the Baily–Borel compactification, which is a

compactification Compactification may refer to: * Compactification (mathematics), making a topological space compact * Compactification (physics), the "curling up" of extra dimensions in string theory See also * Compaction (disambiguation) Compaction may refer t ...

of a quotient of a

Hermitian symmetric space In mathematics, a Hermitian symmetric space is a Hermitian manifold which at every point has an inversion symmetry preserving the Hermitian structure. First studied by Élie Cartan, they form a natural generalization of the notion of Riemannian ...

by an

arithmetic group In mathematics, an arithmetic group is a group obtained as the integer points of an algebraic group, for example \mathrm_2(\Z). They arise naturally in the study of arithmetic properties of quadratic forms and other classical topics in number theor ...

(that is, a

linear algebraic group In mathematics, a linear algebraic group is a subgroup of the group of invertible n\times n matrices (under matrix multiplication) that is defined by polynomial equations. An example is the orthogonal group, defined by the relation M^TM = I_n ...

over the rational numbers). Baily and Borel built on the work of

Ichirō Satake (25 December 1927 – 10 October 2014) was a Japanese mathematician working on algebraic groups who introduced the Satake isomorphism and Satake diagrams. He was considered an iconic figure in the theory of linear algebraic groups and symmetr ...

and others. Baily became a

Putnam Fellow The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regar ...

in 1952. He studied at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

(MIT), receiving a

Bachelor of Science A Bachelor of Science (BS, BSc, B.S., B.Sc., SB, or ScB; from the Latin ') is a bachelor's degree that is awarded for programs that generally last three to five years. The first university to admit a student to the degree of Bachelor of Scienc ...

Mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

in 1952. After that, he attended

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

, receiving a Masters in 1953 and a

Ph.D. A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

in 1955 under the direction of his thesis advisor

Kunihiko Kodaira was a Japanese mathematician known for distinguished work in algebraic geometry and the theory of complex manifolds, and as the founder of the Japanese school of algebraic geometers. He was awarded a Fields Medal in 1954, being the first Japanese ...

(''On the Quotient of a Complex Analytic Manifold by a Discontinuous Group of Complex Analytic Self-Homomorphisms''). Subsequently, he was an instructor at Princeton and then MIT. In 1957 he worked as a mathematician at

Bell Laboratories Nokia Bell Labs, commonly referred to as ''Bell Labs'', is an American industrial research and development company owned by Finnish technology company Nokia. With headquarters located in Murray Hill, New Jersey, the company operates several lab ...

. In 1957, he was appointed

Assistant Professor Assistant professor is an academic rank just below the rank of an associate professor used in universities or colleges, mainly in the United States, Canada, Japan, and South Korea. Overview This position is generally taken after earning a doct ...

and subsequently promoted to

Professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...

in 1963 at the

University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...

. He became a Professor

Emeritus ''Emeritus/Emerita'' () is an honorary title granted to someone who retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". In some c ...

at the University of Chicago in 2005. He was a member of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

and the

Mathematical Society of Japan The Mathematical Society of Japan (MSJ, ) is a learned society for mathematics in Japan. In 1877, the organization was established as the ''Tokyo Sugaku Kaisha'' and was the first academic society in Japan. It was re-organized and re-established i ...

. He often visited the

University of Tokyo The University of Tokyo (, abbreviated as in Japanese and UTokyo in English) is a public research university in Bunkyō, Tokyo, Japan. Founded in 1877 as the nation's first modern university by the merger of several pre-westernisation era ins ...

as a guest of

Shokichi Iyanaga was a Japanese people, Japanese mathematician. Early life Iyanaga was born in Tokyo, Japan on April 2, 1906. He studied at the University of Tokyo from 1926 to 1929. He studied under Teiji Takagi. As an undergraduate, he published two papers in ...

and

, spoke fluent Japanese and in Tokyo, 1963 married Yaeko Iseki, with whom he had a son. He owned an apartment in Tokyo for many years, where he spent his summers. In addition, he often visited

Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

and

Saint Petersburg Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland ...

and spoke fluent Russian. He was awarded an Alfred P. Sloan Fellowship in 1958. In 1962, 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 IMU Abacus Medal (known before ...

held in

Stockholm Stockholm (; ) is the Capital city, capital and List of urban areas in Sweden by population, most populous city of Sweden, as well as the List of urban areas in the Nordic countries, largest urban area in the Nordic countries. Approximately ...

(''On the moduli of Abelian varieties with multiplications from an order in a totally real number field''). His doctoral students include Paul Monsky, Timothy J. Hickey, and

Daniel Bump Daniel Willis Bump (born 13 May 1952) is a mathematician who is a professor at Stanford University working in representation theory. He is a fellow of the American Mathematical Society since 2015, for "contributions to number theory, representation ...

. Baily died in Northbrook,

Illinois Illinois ( ) is a U.S. state, state in the Midwestern United States, Midwestern United States. It borders on Lake Michigan to its northeast, the Mississippi River to its west, and the Wabash River, Wabash and Ohio River, Ohio rivers to its ...

,Obituary from the University of Chicago
/ref> at 82.

Bibliography

* * * * * ''On the orbit spaces of arithmetic groups'', in: ''Arithmetical Algebraic Geometry (Proc. Conf. Purdue Univ., 1963)'', Harper and Row (1965), 4–10 * ''On compactifications of orbit spaces of arithmetic discontinuous groups acting on bounded symmetric domains'', in: Algebraic Groups and Discontinuous Subgroups, Proceedings of Symposia in Pure Mathematics, 9,

(1966), 281–295

References

External links

Autoren-Profil
in the databank

zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastru ...

Guide to the Walter Baily Papers 1930–2005
from th
University of Chicago Special Collections Research Center
{{DEFAULTSORT:Baily, Walter Lewis 1930 births 2013 deaths University of Chicago faculty 20th-century American mathematicians People from Waynesburg, Pennsylvania Massachusetts Institute of Technology School of Science alumni Princeton University alumni Putnam Fellows Sloan Research Fellows Algebraic geometers Mathematicians from Pennsylvania