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Frederick J. Almgren, Jr.
Frederick Justin Almgren Jr. (July 3, 1933 – February 5, 1997) was an American mathematician working in geometric measure theory. He was born in Birmingham, Alabama. Almgren received a Guggenheim Fellowship in 1974. Between 1963 and 1992 he was a frequent visiting scholar at the Institute for Advanced Study in Princeton. Almgren wrote one of the longest papers in mathematics, proving what is now called the Almgren regularity theorem: the singular set of an ''m''-dimensional mass-minimizing surface has dimension at most ''m−2''. He also developed the concept of varifold, first defined by L. C. Young in ,Young calls these geometric objects ''generalized surfaces'': in his commemorative papers describing the research of Almgren, writes that these are "''essentially the same class of surfaces''". and proposed them as generalized solutions to Plateau's problem in order to deal with the problem even when a concept of orientation is missing. He played also an important role in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birmingham, Alabama
Birmingham ( ) is a city in the north central region of the U.S. state of Alabama. Birmingham is the seat of Jefferson County, Alabama's most populous county. As of the 2021 census estimates, Birmingham had a population of 197,575, down 1% from the 2020 Census, making it Alabama's third-most populous city after Huntsville and Montgomery. The broader Birmingham metropolitan area had a 2020 population of 1,115,289, and is the largest metropolitan area in Alabama as well as the 50th-most populous in the United States. Birmingham serves as an important regional hub and is associated with the Deep South, Piedmont, and Appalachian regions of the nation. Birmingham was founded in 1871, during the post- Civil War Reconstruction period, through the merger of three pre-existing farm towns, notably, Elyton. It grew from there, annexing many more of its smaller neighbors, into an industrial and railroad transportation center with a focus on mining, the iron and steel industry, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mimeograph
A mimeograph machine (often abbreviated to mimeo, sometimes called a stencil duplicator) is a low-cost duplicating machine that works by forcing ink through a stencil onto paper. The process is called mimeography, and a copy made by the process is a mimeograph. Mimeographs, along with spirit duplicators and hectographs, were common technologies for printing small quantities of a document, as in office work, classroom materials, and church bulletins. Early fanzines were printed by mimeograph because the machines and supplies were widely available and inexpensive. Beginning in the late 1960s and continuing into the 1970s, photocopying gradually displaced mimeographs, spirit duplicators, and hectographs. For even smaller quantities, up to about five, a typist would use carbon paper. Origins Use of stencils is an ancient art, butthrough chemistry, papers, and pressestechniques advanced rapidly in the late nineteenth century: Papyrograph A description of the Papyrograph meth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Almgren
Robert F. Almgren is an applied mathematician, academic, and businessman focused on market microstructure and order execution. He is the son of Princeton mathematician Frederick J. Almgren, Jr. Frederick Justin Almgren Jr. (July 3, 1933 – February 5, 1997) was an American mathematician working in geometric measure theory. He was born in Birmingham, Alabama. Almgren received a Guggenheim Fellowship in 1974. Between 1963 and 1992 he wa ... With Neil Chriss, he wrote the seminal paper "Optimal execution of portfolio transactions,"R.Almgren and N.Chriss, "Optimal execution of portfolio transactions" J. Risk, 3 (Winter 2000/2001) pp.5–39 which Institutional Investor said "helped lay the groundwork for arrival-price algorithms being developed on Wall Street." In 2008 with Christian Hauff, he cofoundeQuantitative Brokers a financial technology company providing agency algorithmic execution in futures and interest rate markets. He is currently Chief Scientist at QB and a visiting p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ann S
Anne, alternatively spelled Ann, is a form of the Latin female given name Anna. This in turn is a representation of the Hebrew Hannah, which means 'favour' or 'grace'. Related names include Annie. Anne is sometimes used as a male name in the Netherlands, particularly in the Frisian speaking part (for example, author Anne de Vries). In this incarnation, it is related to Germanic arn-names and means 'eagle'.See entry on "Anne" in th''Behind the Name'' databaseand th"Anne"an"Ane"entries (in Dutch) in the Nederlandse Voornamenbank (Dutch First Names Database) of the Meertens Instituut (23 October 2018). It has also been used for males in France (Anne de Montmorency) and Scotland (Lord Anne Hamilton). Anne is a common name and the following lists represent a small selection. For a comprehensive list, see instead: . As a feminine name Anne * Saint Anne, Mother of the Virgin Mary * Anne, Queen of Great Britain (1665–1714), Queen of England, Scotland, and Ireland (1702–07) and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Geometry Center
The Geometry Center was a mathematics research and education center at the University of Minnesota. It was established by the National Science Foundation in the late 1980s and closed in 1998. The focus of the center's work was the use of computer graphics and visualization for research and education in pure mathematics and geometry. The center's founding director was Al Marden. Richard McGehee directed the center during its final years. The center's governing board was chaired by David P. Dobkin. Geomview Much of the work done at the center was for the development of Geomview, a three-dimensional interactive geometry program. This focused on mathematical visualization with options to allow hyperbolic space to be visualised. It was originally written for Silicon Graphics workstations, and has been ported to run on Linux systems; it is available for installation in most Linux distributions through the package management system. ''Geomview'' can run under Windows using Cygwin and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orientation (geometry)
In geometry, the orientation, angular position, attitude, bearing, or direction of an object such as a line, plane or rigid body is part of the description of how it is placed in the space it occupies. More specifically, it refers to the imaginary rotation that is needed to move the object from a reference placement to its current placement. A rotation may not be enough to reach the current placement. It may be necessary to add an imaginary translation, called the object's location (or position, or linear position). The location and orientation together fully describe how the object is placed in space. The above-mentioned imaginary rotation and translation may be thought to occur in any order, as the orientation of an object does not change when it translates, and its location does not change when it rotates. Euler's rotation theorem shows that in three dimensions any orientation can be reached with a single rotation around a fixed axis. This gives one common way of representing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Solution
In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense. There are many different definitions of weak solution, appropriate for different classes of equations. One of the most important is based on the notion of distributions. Avoiding the language of distributions, one starts with a differential equation and rewrites it in such a way that no derivatives of the solution of the equation show up (the new form is called the weak formulation, and the solutions to it are called weak solutions). Somewhat surprisingly, a differential equation may have solutions which are not differentiable; and the weak formulation allows one to find such solutions. Weak solutions are important because many differential equations encountered in modelling real-world phenomena do not admit of suffici ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laurence Chisholm Young
Laurence Chisholm Young (14 July 1905 – 24 December 2000) was a British mathematician known for his contributions to measure theory, the calculus of variations, optimal control theory, and potential theory. He was the son of William Henry Young and Grace Chisholm Young, both prominent mathematicians. He moved to the US in 1949 but never sought American citizenship. The concept of Young measure is named after him: he also introduced the concept of the generalized curve and a concept of generalized surface which later evolved in the concept of varifold. The Young integral also is named after him and has now been generalised in the theory of rough paths. Life and academic career Laurence Chisholm Young was born in Göttingen,. the fifth of the six children of William Henry Young and Grace Chisholm Young.. He held positions of Professor at the University of Cape Town, South Africa, and at the University of Wisconsin-Madison. He was also a chess grandmaster. Selected publicat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Varifold
In mathematics, a varifold is, loosely speaking, a measure-theoretic generalization of the concept of a differentiable manifold, by replacing differentiability requirements with those provided by rectifiable sets, while maintaining the general algebraic structure usually seen in differential geometry. Varifolds generalize the idea of a rectifiable current, and are studied in geometric measure theory. Historical note Varifolds were first introduced by Laurence Chisholm Young in , under the name "''generalized surfaces''". Frederick J. Almgren Jr. slightly modified the definition in his mimeographed notes and coined the name ''varifold'': he wanted to emphasize that these objects are substitutes for ordinary manifolds in problems of the calculus of variations. The modern approach to the theory was based on Almgren's notesThe first widely circulated exposition of Almgren's ideas is the book : however, the first systematic exposition of the theory is contained in the mimeograph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Almgren Regularity Theorem
In geometric measure theory, a field of mathematics, the Almgren regularity theorem, proved by , states that the singular set of a mass-minimizing surface has codimension at least 2. Almgren's proof of this was 955 pages long. Within the proof many new ideas are introduced, such as monotonicity of a ''frequency function'' and the use of a ''center manifold'' to perform a more intricate blow-up procedure. A streamlined and more accessible proof of Almgren's regularity theorem, following the same ideas as Almgren, was given by Camillo De Lellis and Emanuele Spadaro Emanuele is the Italian form of Manuel (name), Manuel. People with the name include: * Carlo Emanuele Buscaglia (1915–1944), Italian aviator * Emanuele Basile (1949–1980), captain of Carabinieri * Emanuele Belardi (born 1977), Italian football ... in a series of three papers.De Lellis, Camillo; Spadaro, Emanuele Regularity of area minimizing currents III: blow-up. Ann. of Math. (2) 183 (2016), no. 2, 577–617. Refer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
