|
American Institute Of Mathematics
The American Institute of Mathematics (AIM) is one of eight mathematical institutes in the United States, funded by the National Science Foundation (NSF). It was founded in 1994 by John Fry, co-founder of Fry's Electronics, and originally located in the Fry's Electronics store in San Jose, California. It was privately funded by Fry at inception, and obtained NSF funding starting in 2002.. From 2023 onwards, the institute will be located on the campus of the California Institute of Technology in Pasadena, California. History The institute was founded with the primary goal of identifying and solving important mathematical problems. Originally very small groups of top mathematicians would be assembled to solve a major problem, such as the Birch and Swinnerton-Dyer conjecture. Later, the institute began running a program of week-long workshops on current topics in mathematical research. These workshops rely strongly on interactive problem sessions. Brian Conrey became the institute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Science Foundation
The National Science Foundation (NSF) is an independent agency of the United States government that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health. With an annual budget of about $8.3 billion (fiscal year 2020), the NSF funds approximately 25% of all federally supported basic research conducted by the United States' colleges and universities. In some fields, such as mathematics, computer science, economics, and the social sciences, the NSF is the major source of federal backing. The NSF's director and deputy director are appointed by the President of the United States and confirmed by the United States Senate, whereas the 24 president-appointed members of the National Science Board (NSB) do not require Senate confirmation. The director and deputy director are responsible for administration, planning, budgeting and day-to-day operations of the foundation, whil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robin Thomas (mathematician)
Robin Thomas (August 22, 1962 – March 26, 2020) was a mathematician working in graph theory at the Georgia Institute of Technology. Thomas received his doctorate in 1985 from Charles University in Prague, Czechoslovakia (now the Czech Republic), under the supervision of Jaroslav Nešetřil. He joined the faculty at Georgia Tech in 1989, and became a Regents' Professor there, briefly serving as the department Chair. On March 26, 2020, he died of Amyotrophic Lateral Sclerosis at the age of 57 after 12 years of struggle with the illness. Awards Thomas was awarded the Fulkerson Prize for outstanding papers in discrete mathematics twice, in 1994 as co-author of a paper on the Hadwiger conjecture, and in 2009 for the proof of the strong perfect graph theorem. In 2011 he was awarded the Karel Janeček Foundation Neuron Prize for Lifetime Achievement in Mathematics. In 2012 he became a fellow of the American Mathematical Society. He was named a SIAM Fellow The SIAM Fellowship is an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Research Institutes Established In 1994
Research is "creative and systematic work undertaken to increase the stock of knowledge". It involves the collection, organization and analysis of evidence to increase understanding of a topic, characterized by a particular attentiveness to controlling sources of bias and error. These activities are characterized by accounting and controlling for biases. A research project may be an expansion on past work in the field. To test the validity of instruments, procedures, or experiments, research may replicate elements of prior projects or the project as a whole. The primary purposes of basic research (as opposed to applied research) are documentation, discovery, interpretation, and the research and development (R&D) of methods and systems for the advancement of human knowledge. Approaches to research depend on epistemologies, which vary considerably both within and between humanities and sciences. There are several forms of research: scientific, humanities, artistic, economic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Organizations Established In 1994
An organization or organisation (Commonwealth English; see spelling differences), is an entity—such as a company, an institution, or an association—comprising one or more people and having a particular purpose. The word is derived from the Greek word ''organon'', which means tool or instrument, musical instrument, and organ. Types There are a variety of legal types of organizations, including corporations, governments, non-governmental organization A non-governmental organization (NGO) or non-governmental organisation (see spelling differences) is an organization that generally is formed independent from government. They are typically nonprofit entities, and many of them are active in ...s, political organizations, international organizations, armed forces, charitable organization, charities, not-for-profit corporations, partnerships, cooperatives, and Types of educational institutions, educational institutions, etc. A hybrid organization is a body that ope ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Organizations Based In San Jose, California
An organization or organisation (Commonwealth English; see spelling differences), is an entity—such as a company, an institution, or an association—comprising one or more people and having a particular purpose. The word is derived from the Greek word ''organon'', which means tool or instrument, musical instrument, and organ. Types There are a variety of legal types of organizations, including corporations, governments, non-governmental organizations, political organizations, international organizations, armed forces, charities, not-for-profit corporations, partnerships, cooperatives, and educational institutions, etc. A hybrid organization is a body that operates in both the public sector and the private sector simultaneously, fulfilling public duties and developing commercial market activities. A voluntary association is an organization consisting of volunteers. Such organizations may be able to operate without legal formalities, depending on jurisdiction, incl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Science Foundation Mathematical Sciences Institutes
National may refer to: Common uses * Nation or country ** Nationality – a ''national'' is a person who is subject to a nation, regardless of whether the person has full rights as a citizen Places in the United States * National, Maryland, census-designated place * National, Nevada, ghost town * National, Utah, ghost town * National, West Virginia, unincorporated community Commerce * National (brand), a brand name of electronic goods from Panasonic * National Benzole (or simply known as National), former petrol station chain in the UK, merged with BP * National Car Rental, an American rental car company * National Energy Systems, a former name of Eco Marine Power * National Entertainment Commission, a former name of the Media Rating Council * National Motor Vehicle Company, Indianapolis, Indiana, USA 1900-1924 * National Supermarkets, a defunct American grocery store chain * National String Instrument Corporation, a guitar company formed to manufacture the first resonato ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Research Institutes In The San Francisco Bay Area
Research is "creative and systematic work undertaken to increase the stock of knowledge". It involves the collection, organization and analysis of evidence to increase understanding of a topic, characterized by a particular attentiveness to controlling sources of bias and error. These activities are characterized by accounting and controlling for biases. A research project may be an expansion on past work in the field. To test the validity of instruments, procedures, or experiments, research may replicate elements of prior projects or the project as a whole. The primary purposes of basic research (as opposed to applied research) are documentation, discovery, interpretation, and the research and development (R&D) of methods and systems for the advancement of human knowledge. Approaches to research depend on epistemologies, which vary considerably both within and between humanities and sciences. There are several forms of research: scientific, humanities, artistic, economic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
E8 (mathematics)
In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8. The designation E8 comes from the Cartan–Killing classification of the complex simple Lie algebras, which fall into four infinite series labeled A''n'', B''n'', C''n'', D''n'', and five exceptional cases labeled G2, F4, E6, E7, and E8. The E8 algebra is the largest and most complicated of these exceptional cases. Basic description The Lie group E8 has dimension 248. Its rank, which is the dimension of its maximal torus, is eight. Therefore, the vectors of the root system are in eight-dimensional Euclidean space: they are described explicitly later in this article. The Weyl group of E8, which is the group of symmetries of the maximal torus which are induced by conjugations in the whole group, has order 2357 = . The compact group E8 is unique ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lie Group
In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additional properties it must have to be thought of as a "transformation" in the abstract sense, for instance multiplication and the taking of inverses (division), or equivalently, the concept of addition and the taking of inverses (subtraction). Combining these two ideas, one obtains a continuous group where multiplying points and their inverses are continuous. If the multiplication and taking of inverses are smooth (differentiable) as well, one obtains a Lie group. Lie groups provide a natural model for the concept of continuous symmetry, a celebrated example of which is the rotational symmetry in three dimensions (given by the special orthogonal group \text(3)). Lie groups are widely used in many parts of modern mathematics and physics. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. The theory has been widely applied in quantum mechanics since the 1920s, particularly influenced by Hermann Weyl's 1928 book ''Gruppentheorie und Quantenmechanik''. One of the pioneers in constructing a general theory of unitary representations, for any group ''G'' rather than just for particular groups useful in applications, was George Mackey. Context in harmonic analysis The theory of unitary representations of topological groups is closely connected with harmonic analysis. In the case of an abelian group ''G'', a fairly complete picture of the representation theory of ''G'' is given by Pontryagin duality. In general, the unitary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atlas Of Lie Groups And Representations
The Atlas of Lie Groups and Representations is a mathematical project to solve the problem of the unitary dual for real reductive Lie groups. , the following mathematicians are listed as members: * Jeffrey Adams * Dan Barbasch * Birne Binegar *Bill Casselman * Dan Ciubotaru * Fokko du Cloux * Scott Crofts * Steve Jackson * Alfred Noël * Tatiana Howard * Alessandra Pantano * Annegret Paul * Patrick Polo * Siddhartha Sahi * Susana Salamanca * John Stembridge * Peter Trapa * Marc van Leeuwen * David Vogan * Wai-Ling Yee * Jiu-Kang Yu *Gregg Zuckerman Gregg Jay Zuckerman (born 1949) is a mathematician at Yale University who discovered Zuckerman functors and translation functors, and with Anthony W. Knapp classified the irreducible tempered representations of semisimple Lie groups. He recei ... External links Atlas web page Representation theory of groups {{mathpublication-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hadwiger Conjecture (graph Theory)
In graph theory, the Hadwiger conjecture states that if G is loopless and has no K_t minor then its chromatic number satisfies It is known to be true for The conjecture is a generalization of the four-color theorem and is considered to be one of the most important and challenging open problems in the field. In more detail, if all proper colorings of an undirected graph G use k or more colors, then one can find k disjoint connected subgraphs of G such that each subgraph is connected by an edge to each other subgraph. Contracting the edges within each of these subgraphs so that each subgraph collapses to a single vertex produces a complete graph K_k on k vertices as a minor This conjecture, a far-reaching generalization of the four-color problem, was made by Hugo Hadwiger in 1943 and is still unsolved. call it "one of the deepest unsolved problems in graph theory." Equivalent forms An equivalent form of the Hadwiger conjecture (the contrapositive of the form stated abo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
