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Marc Rieffel
Marc Aristide Rieffel is a mathematician noted for his fundamental contributions to C*-algebraG Cortinas (2008) ''K-theory and Noncommutative Geometry'', European Mathematical Society. and quantum group theory. He is currently a professor in the department of mathematics at the University of California, Berkeley. In 2012, he was selected as one of the inaugural fellows of the American Mathematical Society. retrieved 2014-03-17. Contributions Rieffel earned his doctorate from in 1963 under |
New York City
New York, often called New York City or NYC, is the most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the most densely populated major city in the United States, and is more than twice as populous as second-place Los Angeles. New York City lies at the southern tip of New York State, and constitutes the geographical and demographic center of both the Northeast megalopolis and the New York metropolitan area, the largest metropolitan area in the world by urban landmass. With over 20.1 million people in its metropolitan statistical area and 23.5 million in its combined statistical area as of 2020, New York is one of the world's most populous megacities, and over 58 million people live within of the city. New York City is a global cultural, financial, entertainment, and media center with a significant influence on commerce, health care and life sciences, research, technology, educa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Morita Equivalence
In abstract algebra, Morita equivalence is a relationship defined between rings that preserves many ring-theoretic properties. More precisely two rings like ''R'', ''S'' are Morita equivalent (denoted by R\approx S) if their categories of modules are additively equivalent (denoted by _M\approx_M). It is named after Japanese mathematician Kiiti Morita who defined equivalence and a similar notion of duality in 1958. Motivation Rings are commonly studied in terms of their modules, as modules can be viewed as representations of rings. Every ring ''R'' has a natural ''R''-module structure on itself where the module action is defined as the multiplication in the ring, so the approach via modules is more general and gives useful information. Because of this, one often studies a ring by studying the category of modules over that ring. Morita equivalence takes this viewpoint to a natural conclusion by defining rings to be Morita equivalent if their module categories are equival ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fellows Of The American Mathematical Society
Fellows may refer to Fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ..., in plural form. Fellows or Fellowes may also refer to: Places * Fellows, California, USA * Fellows, Wisconsin, ghost town, USA Other uses * Fellows Auctioneers, established in 1876. * Fellowes, Inc., manufacturer of workspace products *Fellows, a partner in the firm of English canal carriers, Fellows Morton & Clayton * Fellows (surname) See also * North Fellows Historic District, listed on the National Register of Historic Places in Wapello County, Iowa * Justice Fellows (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Columbia Graduate School Of Arts And Sciences Alumni
Columbia may refer to: * Columbia (personification), the historical female national personification of the United States, and a poetic name for America Places North America Natural features * Columbia Plateau, a geologic and geographic region in the U.S. Pacific Northwest * Columbia River, in Canada and the United States ** Columbia Bar, a sandbar in the estuary of the Columbia River ** Columbia Country, the region of British Columbia encompassing the northern portion of that river's upper reaches ***Columbia Valley, a region within the Columbia Country ** Columbia Lake, a lake at the head of the Columbia River *** Columbia Wetlands, a protected area near Columbia Lake ** Columbia Slough, along the Columbia watercourse near Portland, Oregon * Glacial Lake Columbia, a proglacial lake in Washington state * Columbia Icefield, in the Canadian Rockies * Columbia Island (District of Columbia), in the Potomac River * Columbia Island (New York), in Long Island Sound Populated place ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century American Mathematicians
The 1st century was the century spanning AD 1 (Roman numerals, I) through AD 100 (Roman numerals, 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 History by period, historical period. The 1st century also saw the Christianity in the 1st century, 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 inst ... [...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] |
String Theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force. Thus, string theory is a theory of quantum gravity. String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. String theory has contributed a number of advances to mathematical physics, which have been applied to a variety of problems in black hole physics, early universe cosmology, nuclear physics, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metric Spaces
In mathematics, a metric space is a set together with a notion of ''distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane. A metric may correspond to a metaphorical, rather than physical, notion of distance: for example, the set of 100-character Unicode strings can be equipped with the Hamming distance, which measures the number of characters that need to be changed to get from one string to another. Since they are very general, metric spaces are a tool used in many different branches of mathematics. Many types of mathematical objects have a natural notion of distance an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compact Space
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space by making precise the idea of a space having no "punctures" or "missing endpoints", i.e. that the space not exclude any ''limiting values'' of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval ,1would be compact. Similarly, the space of rational numbers \mathbb is not compact, because it has infinitely many "punctures" corresponding to the irrational numbers, and the space of real numbers \mathbb is not compact either, because it excludes the two limiting values +\infty and -\infty. However, the ''extended'' real number line ''would'' be compact, since it contains both infinities. There are many ways to make this heuristic notion precise. These ways usually agree in a metric space, but may not be equivalent in other top ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractional Linear Transformations
In mathematics, a linear fractional transformation is, roughly speaking, a transformation of the form :z \mapsto \frac , which has an inverse. The precise definition depends on the nature of , and . In other words, a linear fractional transformation is a ''transformation'' that is represented by a ''fraction'' whose numerator and denominator are ''linear''. In the most basic setting, , and are complex numbers (in which case the transformation is also called a Möbius transformation), or more generally elements of a field. The invertibility condition is then . Over a field, a linear fractional transformation is the restriction to the field of a projective transformation or homography of the projective line. When are integer (or, more generally, belong to an integral domain), is supposed to be a rational number (or to belong to the field of fractions of the integral domain. In this case, the invertibility condition is that must be a unit of the domain (that is or in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
