Robert T. Powers is an American mathematician.
Powers earned his doctorate from Princeton University and taught at the University of Pennsylvania. [1] [2] In 2012, he was elected an inaugural fellow of the American Mathematical Society. [3] [4] His most famous paper is called "On Constructing Non -*Isomorphic Hyperfinite Factors of Type III" [5]
The University of Pennsylvania is a private Ivy League research university in Philadelphia, Pennsylvania, United States. It is one of nine colonial colleges and was chartered prior to the U.S. Declaration of Independence when Benjamin Franklin, the university's founder and first president, advocated for an educational institution that trained leaders in academia, commerce, and public service. Penn identifies as the fourth-oldest institution of higher education in the United States, though this representation is challenged by other universities since Franklin first convened the board of trustees in 1749, arguably making it the fifth-oldest.
In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. A group that is not simple can be broken into two smaller groups, namely a nontrivial normal subgroup and the corresponding quotient group. This process can be repeated, and for finite groups one eventually arrives at uniquely determined simple groups, by the Jordan–Hölder theorem.
The University of Pennsylvania Carey Law School is the law school of the University of Pennsylvania, a private Ivy League research university in Philadelphia, Pennsylvania. Penn Carey Law offers the degrees of Juris Doctor (J.D.), Master of Laws (LL.M.), Master of Comparative Laws (LL.C.M.), Master in Law (M.L.), and Doctor of the Science of Law (S.J.D.).
David John Chalmers is an Australian philosopher and cognitive scientist specializing in the areas of the philosophy of mind, and the philosophy of language. He is a professor of philosophy and neural science at New York University, as well as co-director of NYU's Center for Mind, Brain and Consciousness. In 2006, he was elected a Fellow of the Australian Academy of the Humanities. In 2013, he was elected a Fellow of the American Academy of Arts & Sciences.
In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type of C*-algebra.
In functional analysis and related areas of mathematics, the group algebra is any of various constructions to assign to a locally compact group an operator algebra, such that representations of the algebra are related to representations of the group. As such, they are similar to the group ring associated to a discrete group.
In mathematics, there are up to isomorphism exactly two separably acting hyperfinite type II factors; one infinite and one finite. Murray and von Neumann proved that up to isomorphism there is a unique von Neumann algebra that is a factor of type II1 and also hyperfinite; it is called the hyperfinite type II1 factor. There are an uncountable number of other factors of type II1. Connes proved that the infinite one is also unique.
Sir Vaughan Frederick Randal Jones was a New Zealand mathematician known for his work on von Neumann algebras and knot polynomials. He was awarded a Fields Medal in 1990.
In mathematics, a Borel equivalence relation on a Polish space X is an equivalence relation on X that is a Borel subset of X × X.
In mathematics, a crossed product is a basic method of constructing a new von Neumann algebra from a von Neumann algebra acted on by a group. It is related to the semidirect product construction for groups.
Dennis M. DeTurck is an American mathematician known for his work in partial differential equations and Riemannian geometry, in particular contributions to the theory of the Ricci flow and the prescribed Ricci curvature problem. He first used the DeTurck trick to give an alternative proof of the short time existence of the Ricci flow, which has found other uses since then.
Augustin Banyaga is a Rwandan-born American mathematician whose research fields include symplectic topology and contact geometry. He is currently a Professor of Mathematics at Pennsylvania State University.
In mathematics, an approximately finite-dimensional (AF) C*-algebra is a C*-algebra that is the inductive limit of a sequence of finite-dimensional C*-algebras. Approximate finite-dimensionality was first defined and described combinatorially by Ola Bratteli. Later, George A. Elliott gave a complete classification of AF algebras using the K0 functor whose range consists of ordered abelian groups with sufficiently nice order structure.
Alberto Bressan is an Italian mathematician at Penn State University. His primary field of research is mathematical analysis including hyperbolic systems of conservation laws, impulsive control of Lagrangian systems, and non-cooperative differential games.
Connes' embedding problem, formulated by Alain Connes in the 1970s, is a major problem in von Neumann algebra theory. During that time, the problem was reformulated in several different areas of mathematics. Dan Voiculescu developing his free entropy theory found that Connes' embedding problem is related to the existence of microstates. Some results of von Neumann algebra theory can be obtained assuming positive solution to the problem. The problem is connected to some basic questions in quantum theory, which led to the realization that it also has important implications in computer science.
Richard Vincent Kadison was an American mathematician known for his contributions to the study of operator algebras.
In mathematics, Jordan operator algebras are real or complex Jordan algebras with the compatible structure of a Banach space. When the coefficients are real numbers, the algebras are called Jordan Banach algebras. The theory has been extensively developed only for the subclass of JB algebras. The axioms for these algebras were devised by Alfsen, Shultz & Størmer (1978). Those that can be realised concretely as subalgebras of self-adjoint operators on a real or complex Hilbert space with the operator Jordan product and the operator norm are called JC algebras. The axioms for complex Jordan operator algebras, first suggested by Irving Kaplansky in 1976, require an involution and are called JB* algebras or Jordan C* algebras. By analogy with the abstract characterisation of von Neumann algebras as C* algebras for which the underlying Banach space is the dual of another, there is a corresponding definition of JBW algebras. Those that can be realised using ultraweakly closed Jordan algebras of self-adjoint operators with the operator Jordan product are called JW algebras. The JBW algebras with trivial center, so-called JBW factors, are classified in terms of von Neumann factors: apart from the exceptional 27 dimensional Albert algebra and the spin factors, all other JBW factors are isomorphic either to the self-adjoint part of a von Neumann factor or to its fixed point algebra under a period two *-anti-automorphism. Jordan operator algebras have been applied in quantum mechanics and in complex geometry, where Koecher's description of bounded symmetric domains using Jordan algebras has been extended to infinite dimensions.
Bryna Rebekah Kra is an American mathematician and Sarah Rebecca Roland Professor at Northwestern University who is on the board of trustees of the American Mathematical Society and was elected the president of the American Mathematical Society in 2021. As a member of the American Academy of Arts and Sciences and the National Academy of Sciences, Kra has made significant contributions to the structure theory of characteristic factors for multiple ergodic averages. Her academic work centered on dynamical systems and ergodic theory, and uses dynamical methods to address problems in number theory and combinatorics.
Joan M. Redwing is an American materials scientist known for research on electronic and optoelectronic materials, including the processing of semiconductor thin films and nanomaterials by metalorganic chemical vapor deposition (MOCVD). Redwing is a distinguished professor of materials science and engineering and electrical engineering at Pennsylvania State University and director of the university's 2D Crystal Consortium research facility. She is a fellow of the American Association for the Advancement of Science, the American Physical Society, and the Materials Research Society.