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Georgia Benkart
Georgia McClure Benkart (December 30, 1947 – April 29, 2022) was an American mathematician who was known for her work in the structure and representation theory of Lie algebras and related algebraic structures. She published over 130 journal articles and co-authored three American Mathematical Society memoirs in four broad categories: modular Lie algebras; combinatorics of Lie algebra representations; graded algebras and superalgebras; and quantum groups and related structures. Education and career Benkart received her BS degree summa cum laude from the Ohio State University in 1970 and an MPhil in mathematics from Yale University in 1973. She completed her doctoral work at Yale under Nathan Jacobson and wrote a dissertation entitled ''Inner Ideals and the Structure of Lie Algebras.'' She was awarded a PhD in mathematics from the Yale University in 1974. Upon completing her doctoral degree, Benkart began her long career at the University of Wisconsin–Madison, fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Youngstown, Ohio
Youngstown is a city in the U.S. state of Ohio, and the largest city and county seat of Mahoning County, Ohio, Mahoning County. At the 2020 United States census, 2020 census, Youngstown had a city population of 60,068. It is a principal city of the Mahoning Valley, Youngstown–Warren metropolitan area, which had a population of 541,243 in 2020, making it the List of metropolitan statistical areas, 107th-largest metropolitan area in the United States and Ohio statistical areas, seventh-largest metro area in Ohio. Youngstown is situated on the Mahoning River, southeast of Cleveland and northwest of Pittsburgh. In addition to having its own media market, Youngstown is also part of the larger Northeast Ohio region. Youngstown is midway between Chicago and New York City via Interstate 80. The city was named for John Young (pioneer), John Young, an early settler from Whitestown, New York, who established the community's first sawmill and gristmill. Youngstown is a midwestern city, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ''ad hoc'' solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proof
A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in ''all'' possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work. Proofs employ logic expressed in mathematical symbols ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pro-p Group
In mathematics, a pro-''p'' group (for some prime number ''p'') is a profinite group G such that for any open normal subgroup N\triangleleft G the quotient group G/N is a ''p''-group. Note that, as profinite groups are compact, the open subgroups are exactly the closed subgroups of finite index, so that the discrete quotient group is always finite. Alternatively, one can define a pro-''p'' group to be the inverse limit of an inverse system of discrete finite ''p''-groups. The best-understood (and historically most important) class of pro-''p'' groups is the ''p''-adic analytic groups: groups with the structure of an analytic manifold over \mathbb_p such that group multiplication and inversion are both analytic functions. The work of Lubotzky and Mann, combined with Michel Lazard's solution to Hilbert's fifth problem over the ''p''-adic numbers, shows that a pro-''p'' group is ''p''-adic analytic if and only if it has finite rank, i.e. there exists a positive integer r suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States Army Corps Of Engineers
, colors = , anniversaries = 16 June (Organization Day) , battles = , battles_label = Wars , website = , commander1 = LTG Scott A. Spellmon , commander1_label = Chief of Engineers and Commanding General of the U.S. Army Corps of Engineers , commander2 = MGbr>Richard J. Heitkamp, commander2_label = Deputy Chief of Engineers and Deputy Commanding General , commander3 = MGKimberly M. Colloton, commander3_label = Deputy Commanding General for Military and International Operations , commander4 = MGbr>William H. Graham, commander4_label = Deputy Commanding General for Civil and Emergency Operations , commander5 = COLbr>James J. Handura, commander5_label = Chief of Staff for the U.S. Army Corps of Engi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Virginia
The University of Virginia (UVA) is a Public university#United States, public research university in Charlottesville, Virginia. Founded in 1819 by Thomas Jefferson, the university is ranked among the top academic institutions in the United States, with College admissions in the United States, highly selective admission. Set within the The Lawn, Academical Village, a World Heritage Site, UNESCO World Heritage Site, the university is referred to as a "Public Ivy" for offering an academic experience similar to that of an Ivy League university. It is known in part for certain rare characteristics among public universities such as #1800s, its historic foundations, #Honor system, student-run academic honor code, honor code, and Secret societies at the University of Virginia, secret societies. The original governing Board of Visitors included three List of presidents of the United States, U.S. presidents: Thomas Jefferson, Jefferson, James Madison, and James Monroe. The latter as si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aspen Center For Physics
The Aspen Center for Physics is a non-profit Center for research in Physics based in Aspen, Colorado, United States. The Center organizes workshops and conferences to facilitate interactions among research physicists. The Center was founded in 1962 by Purdue University postdoctoral fellow George Stranahan (later known for owning-operating the Flying Dog cattle ranch and co-founding the Flying Dog Brewery), University of Pennsylvania professor Michael Cohen and Aspen Institute director Robert W. Craig. While working on his doctoral dissertation at the Carnegie Institute of Technology in 1957, Stranahan first moved to Aspen, where he enjoyed the mountainous surroundings and fishing. Following this experience, he was motivated to establish the center as a retreat for physicists. Program During the Summer Program, late–May through mid–September, the Center provides individual researchers and small working groups with double offices and campus activities for over 500 leading scie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton, New Jersey
Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of which are now defunct. Centrally located within the Raritan Valley region, Princeton is a regional commercial hub for the Central New Jersey region and a commuter town in the New York metropolitan area.New York-Newark, NY-NJ-CT-PA Combined Statistical Area . Accessed December 5, 2020. As of the |
Institute For Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholars, including J. Robert Oppenheimer, Albert Einstein, Hermann Weyl, John von Neumann, and Kurt Gödel, many of whom had emigrated from Europe to the United States. It was founded in 1930 by American educator Abraham Flexner, together with philanthropists Louis Bamberger and Caroline Bamberger Fuld. Despite collaborative ties and neighboring geographic location, the institute, being independent, has "no formal links" with Princeton University. The institute does not charge tuition or fees. Flexner's guiding principle in founding the institute was the pursuit of knowledge for its own sake.Jogalekar. The faculty have no classes to teach. There are no degree programs or experimental facilities at the institute. Research is never contracted or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berkeley, California
Berkeley ( ) is a city on the eastern shore of San Francisco Bay in northern Alameda County, California, United States. It is named after the 18th-century Irish bishop and philosopher George Berkeley. It borders the cities of Oakland and Emeryville to the south and the city of Albany and the unincorporated community of Kensington to the north. Its eastern border with Contra Costa County generally follows the ridge of the Berkeley Hills. The 2020 census recorded a population of 124,321. Berkeley is home to the oldest campus in the University of California System, the University of California, Berkeley, and the Lawrence Berkeley National Laboratory, which is managed and operated by the university. It also has the Graduate Theological Union, one of the largest religious studies institutions in the world. Berkeley is considered one of the most socially progressive cities in the United States. History Indigenous history The site of today's City of Berkeley was the territo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Sciences Research Institute
The Simons Laufer Mathematical Sciences Institute (SLMath), formerly the Mathematical Sciences Research Institute (MSRI), is an independent nonprofit mathematical research institution on the University of California campus in Berkeley, California. It is widely regarded as a world leading mathematical center for collaborative research, drawing thousands of leading researchers from around the world each year. The institute was founded in 1982, and its funding sources include the National Science Foundation, private foundations, corporations, and more than 90 universities and institutions. The institute is located at 17 Gauss Way on the Berkeley campus, close to Grizzly Peak in the Berkeley Hills. Because of its contribution to the nation's scientific potential, SLMath's activity is supported by the National Science Foundation and the National Security Agency. Private individuals, foundations, and nearly 100 Academic Sponsor Institutions, including the top mathematics departm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Group
In mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital separable C*-algebras), and bicrossproduct quantum groups. Despite their name, they do not themselves have a natural group structure, though they are in some sense 'close' to a group. The term "quantum group" first appeared in the theory of quantum integrable systems, which was then formalized by Vladimir Drinfeld and Michio Jimbo as a particular class of Hopf algebra. The same term is also used for other Hopf algebras that deform or are close to classical Lie groups or Lie algebras, such as a "bicrossproduct" class of quantum groups introduced by Shahn Majid a little after the work of Drinfeld and Jimbo. In Drinfeld's approach, quantum groups arise as Hopf algebras depe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
