Roger Evans Howe
Encyclopedia
Roger Evans Howe is the William R. Kenan Jr. Professor of Mathematics
at Yale University
. He is well known for his contributions to representation theory
, and in particular for the notion of a reductive dual pair
, sometimes known as a Howe pair, and the Howe correspondence.
He attended Ithaca High School
, then Harvard University
as an undergraduate, winning the William Lowell Putnam Mathematical Competition
in 1964. He obtained his Ph.D. from University of California, Berkeley
in 1969. His thesis, titled On representations of nilpotent groups, was written under the supervision of Calvin Moore. He has been a Yale faculty member since 1974.
He has been a member of the National Academy of Sciences
since 1994. He is also a member of the American Academy of Arts and Sciences
.
In 2006 he was awarded the American Mathematical Society
Award for Distinguished Public Service in recognition of his "multifaceted contributions to mathematics and to mathematics education."
on Minkowski addition
of non-convex set
s)
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at 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...
. He is well known for his contributions to representation theory
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
, and in particular for the notion of a reductive dual pair
Reductive dual pair
In the mathematical field of representation theory, a reductive dual pair is a pair of subgroups of the isometry group Sp of a symplectic vector space W, such that G is the centralizer of G ′ in Sp and vice versa, and these groups act reductively on W...
, sometimes known as a Howe pair, and the Howe correspondence.
He attended Ithaca High School
Ithaca High School (Ithaca, New York)
Ithaca High School is a public high school in Ithaca, New York. It is part of the Ithaca City School District, and has an enrollment of approximately 1,675. Jarett Powers has been principal since 2011.-About:...
, then 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...
as an undergraduate, winning the William Lowell Putnam Mathematical Competition
William Lowell Putnam Mathematical Competition
The William Lowell Putnam Mathematical Competition, often abbreviated to the Putnam Competition, is an annual mathematics competition for undergraduate college students of the United States and Canada, awarding scholarships and cash prizes ranging from $250 to $2,500 for the top students and $5,000...
in 1964. He obtained his Ph.D. from University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
in 1969. His thesis, titled On representations of nilpotent groups, was written under the supervision of Calvin Moore. He has been a Yale faculty member since 1974.
He has been a member of the National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
since 1994. He is also a member of the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
.
In 2006 he was awarded the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
Award for Distinguished Public Service in recognition of his "multifaceted contributions to mathematics and to mathematics education."
Selected Works
(Shapley–Folkman lemmaShapley–Folkman lemma
In geometry and economics, the Shapley–Folkman lemma describes the Minkowski addition of sets in a vector space. Minkowski addition is defined as the addition of the sets' members: for example, adding the set consisting of the integers zero and one to itself yields the set consisting of...
on Minkowski addition
Minkowski addition
In geometry, the Minkowski sum of two sets A and B in Euclidean space is the result of adding every element of A to every element of B, i.e...
of non-convex set
Convex set
In Euclidean space, an object is convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the object...
s)
- Roger Howe & William Barker (2007) Continuous Symmetry: From Euclid to Klein, American Mathematical Society, ISBN 978-0821839003 .
- Robin HartshorneRobin HartshorneRobin Cope Hartshorne is an American mathematician. Hartshorne is an algebraic geometer who studied with Zariski, Mumford, J.-P. Serre and Grothendieck....
(2011) Review of Continuous Symmetry, American Mathematical MonthlyAmerican Mathematical MonthlyThe American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894. It is currently published 10 times each year by the Mathematical Association of America....
118:565–8.
- Robin Hartshorne