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50 relations: Alexander Grothendieck, Alexandre Kirillov, American Academy of Arts and Sciences, Andrew M. Gleason, Belmont, Massachusetts, Borel set, Bornological space, C*-algebra, Calvin C. Moore, Caroline Series, Comparison of topologies, Complex analysis, Doctor of Philosophy, Dual topology, Ergodic theory, Groupoid, Harvard University, Induced representation, Irving Segal, James Glimm, John Wermer, Landon T. Clay, Lawrence G. Brown, Locally compact group, Locally convex topological vector space, Mackey topology, Marshall Harvey Stone, Massachusetts, Mathematical formulation of quantum mechanics, Mathematical physics, Mathematician, Missouri, National Academy of Sciences, Nilpotent group, Noncommutative geometry, Operator algebra, Orbit method, Paul Chernoff, Quantum logic, Rice University, Richard Palais, Robert Zimmer, Semidirect product, Spectrum of a C*-algebra, St. Louis, Statistical mechanics, System of imprimitivity, Topological tensor product, Unitary representation, William Lowell Putnam Mathematical Competition.
Alexander Grothendieck
Alexander Grothendieck (28 March 1928 – 13 November 2014) was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry.
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Alexandre Kirillov
Alexandre Aleksandrovich Kirillov (Алекса́ндр Алекса́ндрович Кири́ллов, born 1936) is a Soviet and Russian mathematician, known for his works in the fields of representation theory, topological groups and Lie groups.
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American Academy of Arts and Sciences
The American Academy of Arts and Sciences is one of the oldest learned societies in the United States of America.
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Andrew M. Gleason
Andrew Mattei Gleason (19212008) was an American mathematician who as a young World War II naval officer broke German and Japanese military codes, then over the succeeding sixty years made fundamental contributions to widely varied areas of mathematics, including the solution of Hilbert's fifth problem, and was a leader in reform and innovation in teaching at all levels.
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Belmont, Massachusetts
Belmont is a town in Middlesex County, Massachusetts.
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Borel set
In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement.
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Bornological space
In mathematics, particularly in functional analysis, a bornological space is a type of space which, in some sense, possesses the minimum amount of structure needed to address questions of boundedness of sets and functions, in the same way that a topological space possesses the minimum amount of structure needed to address questions of continuity.
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C*-algebra
C∗-algebras (pronounced "C-star") are an area of research in functional analysis, a branch of mathematics.
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Calvin C. Moore
Calvin C. Moore (born November 2, 1936 in New York City) is an American mathematician who works in the theory of operator algebras and topological groups.
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Caroline Series
Caroline Mary Series (born 24 March 1951) is an English mathematician known for her work in hyperbolic geometry, Kleinian groups and dynamical systems.
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Comparison of topologies
In topology and related areas of mathematics, the set of all possible topologies on a given set forms a partially ordered set.
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Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
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Doctor of Philosophy
A Doctor of Philosophy (PhD or Ph.D.; Latin Philosophiae doctor) is the highest academic degree awarded by universities in most countries.
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Dual topology
In functional analysis and related areas of mathematics a dual topology is a locally convex topology on a dual pair, two vector spaces with a bilinear form defined on them, so that one vector space becomes the continuous dual of the other space.
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Ergodic theory
Ergodic theory (Greek: έργον ergon "work", όδος hodos "way") is a branch of mathematics that studies dynamical systems with an invariant measure and related problems.
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Groupoid
In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in several equivalent ways.
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Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts.
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Induced representation
In mathematics, and in particular group representation theory, the induced representation is one of the major general operations for passing from a representation of a subgroup to a representation of the (whole) group itself.
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Irving Segal
Irving Ezra Segal (September 13, 1918 – August 30, 1998) was an American mathematician known for work on theoretical quantum mechanics.
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James Glimm
James Gilbert Glimm (born 24 March 1934) is an American mathematician, former president of the American Mathematical Society, and distinguished professor at Stony Brook University.
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John Wermer
John Wermer is a mathematician specializing in Complex analysis.
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Landon T. Clay
Landon T. Clay (born Landon Thomas Clay, 1926 – 29 July 2017) was an American businessman and founder of the Clay Mathematics Institute.
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Lawrence G. Brown
Lawrence G. Brown (born February 6, 1943 in St. Louis, Missouri) is an American mathematician who studies operator algebras.
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Locally compact group
In mathematics, a locally compact group is a topological group G for which the underlying topology is locally compact and Hausdorff.
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Locally convex topological vector space
In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces.
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Mackey topology
In functional analysis and related areas of mathematics, the Mackey topology, named after George Mackey, is the finest topology for a topological vector space which still preserves the continuous dual.
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Marshall Harvey Stone
Marshall Harvey Stone (April 8, 1903 – January 9, 1989) was an American mathematician who contributed to real analysis, functional analysis, topology and the study of Boolean algebras.
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Massachusetts
Massachusetts, officially known as the Commonwealth of Massachusetts, is the most populous state in the New England region of the northeastern United States.
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Mathematical formulation of quantum mechanics
The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics.
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Mathematical physics
Mathematical physics refers to the development of mathematical methods for application to problems in physics.
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Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
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Missouri
Missouri is a state in the Midwestern United States.
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National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization.
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Nilpotent group
A nilpotent group G is a group that has an upper central series that terminates with G. Provably equivalent definitions include a group that has a central series of finite length or a lower central series that terminates with.
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Noncommutative geometry
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions (possibly in some generalized sense).
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Operator algebra
In functional analysis, an operator algebra is an algebra of continuous linear operators on a topological vector space with the multiplication given by the composition of mappings.
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Orbit method
In mathematics, the orbit method (also known as the Kirillov theory, the method of coadjoint orbits and by a few similar names) establishes a correspondence between irreducible unitary representations of a Lie group and its coadjoint orbits: orbits of the action of the group on the dual space of its Lie algebra.
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Paul Chernoff
Paul Robert Chernoff (21 June 1942, Philadelphia – 17 January 2017) was an American mathematician, specializing in functional analysis and the mathematical foundations of quantum mechanics.
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Quantum logic
In quantum mechanics, quantum logic is a set of rules for reasoning about propositions that takes the principles of quantum theory into account.
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Rice University
William Marsh Rice University, commonly known as Rice University, is a private research university located on a 300-acre (121 ha) campus in Houston, Texas, United States.
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Richard Palais
Richard Sheldon Palais (born May 22, 1931) is a mathematician working in geometry who introduced the Principle of Symmetric Criticality, the Mostow–Palais theorem, the Lie–Palais theorem, the Morse–Palais lemma, and the Palais–Smale compactness condition.
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Robert Zimmer
Robert Jeffrey Zimmer (born November 5, 1947) is an American mathematician and academic administrator.
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Semidirect product
In mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product.
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Spectrum of a C*-algebra
In mathematics, the spectrum of a C*-algebra or dual of a C*-algebra A, denoted Â, is the set of unitary equivalence classes of irreducible *-representations of A. A *-representation π of A on a Hilbert space H is irreducible if, and only if, there is no closed subspace K different from H and which is invariant under all operators π(x) with x ∈ A. We implicitly assume that irreducible representation means non-null irreducible representation, thus excluding trivial (i.e. identically 0) representations on one-dimensional spaces.
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St. Louis
St.
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Statistical mechanics
Statistical mechanics is one of the pillars of modern physics.
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System of imprimitivity
The concept of system of imprimitivity is used in mathematics, particularly in algebra and analysis, both within the context of the theory of group representations.
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Topological tensor product
In mathematics, there are usually many different ways to construct a topological tensor product of two topological vector spaces.
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Unitary representation
In mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π(g) is a unitary operator for every g ∈ G. The general theory is well-developed in case G is a locally compact (Hausdorff) topological group and the representations are strongly continuous.
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William Lowell Putnam Mathematical Competition
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 (regardless of the students' nationalities).
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References
[1] https://en.wikipedia.org/wiki/George_Mackey
