Gustav A. Hedlund
Encyclopedia
Gustav Arnold Hedlund an American mathematician
, was one of the founders of symbolic
and topological dynamics
.
. He did his undergraduate studies at Harvard University
, earned a masters degree from Columbia University
, and returned to Harvard for his doctoral studies. He was a student of Marston Morse
, under whose supervision he received a Ph.D. in 1930.
While still studying at Columbia, Hedlund taught at Hunter College
, and after receiving his doctorate he took a position at Bryn Mawr College
, where he remained for nine years. From 1939 to 1948 he taught at the University of Virginia
, after which he moved to Yale University
. At Yale, he became the Philip Schuyler Beebe Professor of Mathematics, and chaired the mathematics department for ten years. He was also a member of the Institute for Advanced Study
in Princeton, New Jersey
, which he visited in 1933, 1938, and 1953. He retired from Yale in 1972, but afterwards held a visiting professorship at Wesleyan University
.
Hedlund died in 1993. He has over 200 academic descendants
, many of them through two of his students at Virginia, Walter Gottschalk and W. Roy Utz, Jr.
of geodesic flows. He also made significant contributions to symbolic dynamics
, whose origins as a field of modern mathematics can be traced to a 1944 paper of Hedlund, and to topological dynamics
.
The Curtis–Hedlund–Lyndon theorem
, a topological characterization of cellular automata, is named after Hedlund. Hedlund first published this theorem in 1969, crediting Morton L. Curtis
and Roger Lyndon
as co-discoverers.
Hedlund was the co-author of the book Topological Dynamics (with Walter Gottschalk, American Mathematical Society, 1955).
in 1943.
In 1972, a conference on topological dynamics was held to honor Hedlund on the occasion of his retirement from Yale. The editor of the festschrift
from the conference, Anatole Beck, wrote that it was "our token of respect to the man who did so much to foster and build this field".
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, was one of the founders of symbolic
Symbolic dynamics
In mathematics, symbolic dynamics is the practice of modeling a topological or smooth dynamical system by a discrete space consisting of infinite sequences of abstract symbols, each of which corresponds to a state of the system, with the dynamics given by the shift operator...
and topological dynamics
Topological dynamics
In mathematics, topological dynamics is a branch of the theory of dynamical systems in which qualitative, asymptotic properties of dynamical systems are studied from the viewpoint of general topology.- Scope :...
.
Biography
Hedlund was born May 7, 1904, in Somerville, MassachusettsSomerville, Massachusetts
Somerville is a city in Middlesex County, Massachusetts, United States, located just north of Boston. As of the 2010 census, the city had a total population of 75,754 and was the most densely populated municipality in New England. It is also the 17th most densely populated incorporated place in...
. He did his undergraduate studies at Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
, earned a masters degree from Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
, and returned to Harvard for his doctoral studies. He was a student of Marston Morse
Marston Morse
Harold Calvin Marston Morse was an American mathematician best known for his work on the calculus of variations in the large, a subject where he introduced the technique of differential topology now known as Morse theory...
, under whose supervision he received a Ph.D. in 1930.
While still studying at Columbia, Hedlund taught at Hunter College
Hunter College
Hunter College, established in 1870, is a public university and one of the constituent colleges of the City University of New York, located on Manhattan's Upper East Side. Hunter grants undergraduate, graduate, and post-graduate degrees in more than one hundred fields of study, and is recognized...
, and after receiving his doctorate he took a position at Bryn Mawr College
Bryn Mawr College
Bryn Mawr College is a women's liberal arts college located in Bryn Mawr, a community in Lower Merion Township, Pennsylvania, ten miles west of Philadelphia. The name "Bryn Mawr" means "big hill" in Welsh....
, where he remained for nine years. From 1939 to 1948 he taught at the University of Virginia
University of Virginia
The University of Virginia is a public research university located in Charlottesville, Virginia, United States, founded by Thomas Jefferson...
, after which he moved to Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
. At Yale, he became the Philip Schuyler Beebe Professor of Mathematics, and chaired the mathematics department for ten years. He was also a member of the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton, New Jersey
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
, which he visited in 1933, 1938, and 1953. He retired from Yale in 1972, but afterwards held a visiting professorship at Wesleyan University
Wesleyan University
Wesleyan University is a private liberal arts college founded in 1831 and located in Middletown, Connecticut. According to the Carnegie Foundation for the Advancement of Teaching, Wesleyan is the only Baccalaureate College in the nation that emphasizes undergraduate instruction in the arts and...
.
Hedlund died in 1993. He has over 200 academic descendants
Academic genealogy
An academic, or scientific, genealogy, organizes a family tree of scientists and scholars according to dissertation supervision relationships....
, many of them through two of his students at Virginia, Walter Gottschalk and W. Roy Utz, Jr.
Research
One of Hedlund's early results was an important theorem about the ergodicityErgodicity
In mathematics, the term ergodic is used to describe a dynamical system which, broadly speaking, has the same behavior averaged over time as averaged over space. In physics the term is used to imply that a system satisfies the ergodic hypothesis of thermodynamics.-Etymology:The word ergodic is...
of geodesic flows. He also made significant contributions to symbolic dynamics
Symbolic dynamics
In mathematics, symbolic dynamics is the practice of modeling a topological or smooth dynamical system by a discrete space consisting of infinite sequences of abstract symbols, each of which corresponds to a state of the system, with the dynamics given by the shift operator...
, whose origins as a field of modern mathematics can be traced to a 1944 paper of Hedlund, and to topological dynamics
Topological dynamics
In mathematics, topological dynamics is a branch of the theory of dynamical systems in which qualitative, asymptotic properties of dynamical systems are studied from the viewpoint of general topology.- Scope :...
.
The Curtis–Hedlund–Lyndon theorem
Curtis–Hedlund–Lyndon theorem
The Curtis–Hedlund–Lyndon theorem is a mathematical characterization of cellular automata in terms of their symbolic dynamics. It is named after Morton L. Curtis, Gustav A...
, a topological characterization of cellular automata, is named after Hedlund. Hedlund first published this theorem in 1969, crediting Morton L. Curtis
Morton L. Curtis
Morton Landers Curtis was an American mathematician, an expert on group theory and the W. L. Moody, Jr. Professor of Mathematics at Rice University....
and Roger Lyndon
Roger Lyndon
Roger Conant Lyndon was an American mathematician, for many years a professor at the University of Michigan. He is known for Lyndon words, the Curtis–Hedlund–Lyndon theorem, Craig–Lyndon interpolation and the Lyndon–Hochschild–Serre spectral sequence.-Biography:Lyndon was born on December 18, 1917...
as co-discoverers.
Hedlund was the co-author of the book Topological Dynamics (with Walter Gottschalk, American Mathematical Society, 1955).
Awards and honors
Hedlund was elected to Sigma XiSigma Xi
Sigma Xi: The Scientific Research Society is a non-profit honor society which was founded in 1886 at Cornell University by a junior faculty member and a handful of graduate students. Members elect others on the basis of their research achievements or potential...
in 1943.
In 1972, a conference on topological dynamics was held to honor Hedlund on the occasion of his retirement from Yale. The editor of the festschrift
Festschrift
In academia, a Festschrift , is a book honoring a respected person, especially an academic, and presented during his or her lifetime. The term, borrowed from German, could be translated as celebration publication or celebratory writing...
from the conference, Anatole Beck, wrote that it was "our token of respect to the man who did so much to foster and build this field".