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Gabriele Nebe
Gabriele Nebe (born 1967) is a German mathematician with contributions in the theory of lattices, modular forms, spherical designs, and error-correcting codes. With Neil Sloane, she maintains the Online Catalogue of Lattices. She is a professor in the department of mathematics at RWTH Aachen University. Education Nebe earned a doctorate ( Dr. rer. nat.) in 1995 from RWTH Aachen University. Her dissertation, ''Endliche Rationale Matrixgruppen vom Grad 24'' concerned the theory of finite matrix groups and was supervised by Wilhelm Plesken. Research Nebe is known for using integral representations of finite groups to construct explicit examples of discrete mathematical structures using computer algebra systems. Her constructions include extremal even unimodular lattices in 48, 56, and 72 dimensions and an extremal 3-modular lattice in 64 dimensions. These lattices represent the densest known sphere packings and the highest known kissing numbers in these dimensions. Her discovery ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Research Institute Of Oberwolfach
The Oberwolfach Research Institute for Mathematics (german: Mathematisches Forschungsinstitut Oberwolfach) is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekly workshops on diverse topics where mathematicians and scientists from all over the world come to do collaborative research. The Institute is a member of the Leibniz Association, funded mainly by the German Federal Ministry of Education and Research and by the state of Baden-Württemberg. It also receives substantial funding from the ''Friends of Oberwolfach'' foundation, from the ''Oberwolfach Foundation'' and from numerous donors. History The Oberwolfach Research Institute for Mathematics (MFO) was founded as the ''Reich Institute of Mathematics'' (German: ''Reichsinstitut für Mathematik'') on 1 September 1944. It was one of several research institutes founded by the Nazis in order to further the German war effort, which at that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unimodular Lattice
In geometry and mathematical group theory, a unimodular lattice is an integral lattice of determinant 1 or −1. For a lattice in ''n''-dimensional Euclidean space, this is equivalent to requiring that the volume of any fundamental domain for the lattice be 1. The ''E''8 lattice and the Leech lattice are two famous examples. Definitions * A lattice is a free abelian group of finite rank with a symmetric bilinear form (·, ·). * The lattice is integral if (·,·) takes integer values. * The dimension of a lattice is the same as its rank (as a Z-module). * The norm of a lattice element ''a'' is (''a'', ''a''). * A lattice is positive definite if the norm of all nonzero elements is positive. * The determinant of a lattice is the determinant of the Gram matrix, a matrix with entries (''ai'', ''aj''), where the elements ''ai'' form a basis for the lattice. * An integral lattice is unimodular if its determinant is 1 or −1. * A unimodular lattice is ev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century German Mathematicians
The 1st century was the century spanning AD 1 ( I) through AD 100 ( C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or historical period. The 1st century also saw the appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius ( AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and instability, which was finally brought to an end by Vespasian, ninth Roman em ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1967 Births
Events January * January 1 – Canada begins a year-long celebration of the 100th anniversary of Confederation, featuring the Expo 67 World's Fair. * January 5 ** Spain and Romania sign an agreement in Paris, establishing full consular and commercial relations (not diplomatic ones). ** Charlie Chaplin launches his last film, ''A Countess from Hong Kong'', in the UK. * January 6 – Vietnam War: United States Marine Corps, USMC and Army of the Republic of Vietnam, ARVN troops launch ''Operation Deckhouse Five'' in the Mekong Delta. * January 8 – Vietnam War: Operation Cedar Falls starts. * January 13 – A military coup occurs in Togo under the leadership of Étienne Eyadema. * January 14 – The Human Be-In takes place in Golden Gate Park, San Francisco; the event sets the stage for the Summer of Love. * January 15 ** Louis Leakey announces the discovery of pre-human fossils in Kenya; he names the species ''Proconsul nyanzae, Kenyapithecus africanus''. ** American footbal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher learning in the United States and one of the most prestigious and highly ranked universities in the world. The university is composed of ten academic faculties plus Harvard Radcliffe Institute. The Faculty of Arts and Sciences offers study in a wide range of undergraduate and graduate academic disciplines, and other faculties offer only graduate degrees, including professional degrees. Harvard has three main campuses: the Cambridge campus centered on Harvard Yard; an adjoining campus immediately across Charles River in the Allston neighborhood of Boston; and the medical campus in Boston's Longwood Medical Area. Harvard's endowment is valued at $50.9 billion, making it the wealthiest academic institution in the world. Endowment inco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radcliffe Institute
The Radcliffe Institute for Advanced Study at Harvard University—also known as the Harvard Radcliffe Institute—is a part of Harvard University that fosters interdisciplinary research across the humanities, sciences, social sciences, arts, and professions. It is the successor institution to the former Radcliffe College, originally a women's college connected with Harvard. The institute comprises three programs: * The Radcliffe Institute Fellowship Program is a highly selective fellowship that supports the work of 50 artists and scholars each year. * The Academic Ventures program is for collaborative research projects and hosts lectures and conferences. * The Arthur and Elizabeth Schlesinger Library on the History of Women in America documents the lives of American women of the past and present for the future. The Radcliffe Institute often hosts public events, many of which can be watched online. It is a member of the Some Institutes for Advanced Study consortium. Prof. To ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kissing Number
In geometry, the kissing number of a mathematical space is defined as the greatest number of non-overlapping unit spheres that can be arranged in that space such that they each touch a common unit sphere. For a given sphere packing (arrangement of spheres) in a given space, a kissing number can also be defined for each individual sphere as the number of spheres it touches. For a lattice packing the kissing number is the same for every sphere, but for an arbitrary sphere packing the kissing number may vary from one sphere to another. Other names for kissing number that have been used are Newton number (after the originator of the problem), and contact number. In general, the kissing number problem seeks the maximum possible kissing number for ''n''-dimensional spheres in (''n'' + 1)-dimensional Euclidean space. Ordinary spheres correspond to two-dimensional closed surfaces in three-dimensional space. Finding the kissing number when centers of spheres are confined to a line (the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sphere Packing
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic space. A typical sphere packing problem is to find an arrangement in which the spheres fill as much of the space as possible. The proportion of space filled by the spheres is called the ''packing density'' of the arrangement. As the local density of a packing in an infinite space can vary depending on the volume over which it is measured, the problem is usually to maximise the average or asymptotic density, measured over a large enough volume. For equal spheres in three dimensions, the densest packing uses ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Packing Density
A packing density or packing fraction of a packing in some space is the fraction of the space filled by the figures making up the packing. In simplest terms, this is the ratio of the volume of bodies in a space to the volume of the space itself. In packing problems, the objective is usually to obtain a packing of the greatest possible density. In compact spaces If are measurable subsets of a compact measure space and their interiors pairwise do not intersect, then the collection is a packing in and its packing density is :\eta = \frac. In Euclidean space If the space being packed is infinite in measure, such as Euclidean space, it is customary to define the density as the limit of densities exhibited in balls of larger and larger radii. If is the ball of radius centered at the origin, then the density of a packing is :\eta = \lim_\frac. Since this limit does not always exist, it is also useful to define the upper and lower densities as the limit superior and limit i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Algebra System
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "computer algebra" or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials. Computer algebra systems may be divided into two classes: specialized and general-purpose. The specialized ones are devoted to a specific part of mathematics, such as number theory, group theory, or teaching of elementary mathematics. General-purpose computer algebra systems aim to be useful to a user working in any scientific field that requires manipulation of mathematical expressions. To be useful, a general-purpose computer algebra system must include various features such as: *a user interface allo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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