Walter Lewis Baily Jr. (born July 5, 1930, in Waynesburg, Pennsylvania; d. January 15, 2013 in Northbrook, Illinois) was an American mathematician. Walter Baily's research focused on areas of algebraic groups,

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, 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 of a quotient of a Hermitian symmetric space by an arithmetic group (that is, a linear algebraic group over the rational numbers). Baily and Borel built on the work of Ichirō Satake and others. Baily became a Putnam Fellow in 1952. He studied at the Massachusetts Institute of Technology (MIT), receiving a Bachelor of Science in

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, receiving a Masters in 1953 and a Ph.D. in

in 1955 under the direction of his thesis advisor Kunihiko Kodaira (''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. In 1957, he was appointed Assistant Professor and subsequently promoted to Professor in 1963 at the University of Chicago. 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 and the Mathematical Society of Japan. He often visited the University of Tokyo 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 Kunihiko Kodaira, 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 and Saint Petersburg and spoke fluent Russian. He was awarded an

Alfred P. Sloan Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...

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 Paul Monsky (born June 17, 1936) is an American mathematician and professor at Brandeis University. After earning a bachelor's degree from Swarthmore College, he received his Ph.D. in 1962 from the University of Chicago under the supervision of ...

Timothy J. Hickey Timothy J. Hickey (born July 24, 1955) is a professor of computer science and former Chair of the Computer Science and Internet Studies Program (INET) at Brandeis University. Hickey's specialties include analysis of algorithms, logic programming ...

and Daniel Bump.

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, American Mathematical Society (1966), 281–295

References

External links

Autoren-Profil
in the databank zbMATH
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