Walter Lewis Baily Jr. (born July 5, 1930, in Waynesburg,

Pennsylvania Pennsylvania (; ( Pennsylvania Dutch: )), officially the Commonwealth of Pennsylvania, is a state spanning the Mid-Atlantic, Northeastern, Appalachian, and Great Lakes regions of the United States. It borders Delaware to its southeast, ...

; d. January 15, 2013 in Northbrook,

Illinois Illinois ( ) is a U.S. state, state in the Midwestern United States, Midwestern United States. Its largest metropolitan areas include the Chicago metropolitan area, and the Metro East section, of Greater St. Louis. Other smaller metropolita ...

) 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, structure, space, models, and change. History On ...

. Walter Baily's research focused on areas of

algebraic group In mathematics, an algebraic group is an algebraic variety endowed with a group structure which 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 (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the Group action (mathematics), group action of the modular group, and also satisfying a grow ...

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 of ...

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 In mathematics, the Baily–Borel compactification is a compactification of a quotient of a Hermitian symmetric space by an arithmetic group, introduced by . Example *If ''C'' is the quotient of the upper half plane by a congruence subgroup In ma ...

, 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 s ...

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 wh ...

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 symmetric ...

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 (regard ...

in 1952. He studied at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

(MIT), receiving a

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

in 1952, after which he attended

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 ...

, receiving a Masters in 1953 and a

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 a ...

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, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mult ...

. 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 and Canada. Overview This position is generally taken after earning a doctoral degree and general ...

and subsequently promoted to

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

in 1963 at the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

. He became a Professor

Emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

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, ja, 日本数学会) 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 ...

. He often visited the

University of Tokyo , abbreviated as or UTokyo, is a public research university located in Bunkyō, Tokyo, Japan. Established in 1877, the university was the first Imperial University and is currently a Top Type university of the Top Global University Project by ...

as a guest of

Shokichi Iyanaga was a 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 the ''Japanese ...

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 ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...

and

Saint Petersburg Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...

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 Nevanlinna Prize (to be rename ...

held in

Stockholm Stockholm () is the Capital city, capital and List of urban areas in Sweden by population, largest city of Sweden as well as the List of urban areas in the Nordic countries, largest urban area in Scandinavia. Approximately 980,000 people liv ...

(''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. He is a fellow of the American Mathematical Society since 2015, for "contributions to number theory, representation theory, combinatorics, and rando ...

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

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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