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Ennio De Giorgi
Ennio De Giorgi (8 February 1928 – 25 October 1996) was an Italian mathematician who worked on partial differential equations and the foundations of mathematics. Mathematical work De Giorgi's first work was in geometric measure theory, on the topic of the sets of finite perimeters which he called in 1958 Caccioppoli sets, after his mentor and friend. His definition applied some important analytic tools and De Giorgi's theorem for the sets established a new tool for set theory as well as his own works. This achievement not only brought Ennio immediate recognition but displayed his ability to attack problems using completely new and effective methods which, though conceived before, can be used with greater precision as shown in his research works. De Giorgi solved Bernstein's problem about minimal surfaces for 8 dimensions in 1969 with Enrico Bombieri and Enrico Giusti, for which Bombieri won the Fields Medal in 1974. De Giorgi's earliest work aimed to develop a regularity t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lecce
Lecce (; ) is a city in southern Italy and capital of the province of Lecce. It is on the Salentine Peninsula, at the heel of the Italian Peninsula, and is over two thousand years old. Because of its rich Baroque architecture, Lecce is nicknamed "The Florence of the South". "Lecce stone"—a particular kind of limestone—is one of the city's main exports, because it is very soft and workable, and thus suitable for sculptures. Lecce is also an important agricultural centre, chiefly for its olive oil and wine production, as well as an industrial centre specializing in ceramics. Lecce is home to the University of Salento. History According to legend, a city called ''Sybar'' existed at the time of the Trojan War, founded by the Messapii. It was conquered by the Romans in the 3rd century BC, receiving the new name of ''Lupiae''. Under the emperor Hadrian (2nd century AD) the city was moved to the northeast, taking the name of Licea or Litium. Lecce had a theater and an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of International Congresses Of Mathematicians Plenary And Invited Speakers
This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." The current list of Plenary and Invited Speakers presented here is based on the ICM's post-WW II terminology, in which the one-hour speakers in the morning sessions are called "Plenary Speakers" and the other speakers (in the afternoon sessions) whose talks are included in the ICM published proceedings are called "Invited Speakers". In the pre-WW II congresses the Plenary Speakers were called "Invited Speakers". By congress year 1897, Zürich *Jules Andrade *Léon Autonne *Émile Borel *Nikolai Bugaev *Francesco Brioschi *Hermann Brunn *Cesare Burali-Forti *Charles Jean de la Vallée Poussin *Gustaf Eneström *Federigo Enriques *Gino Fano *Zoel García de Galdeano *Francesco Gerbaldi *Paul Gordan *Jacques Hadamard *Adolf Hurwitz *Felix ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Analysis
Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of linear elliptic PDEs dates at least as far back as Hodge theory. More recently, it refers largely to the use of nonlinear partial differential equations to study geometric and topological properties of spaces, such as submanifolds of Euclidean space, Riemannian manifolds, and symplectic manifolds. This approach dates back to the work by Tibor Radó and Jesse Douglas on minimal surfaces, John Forbes Nash Jr. on isometric embeddings of Riemannian manifolds into Euclidean space, work by Louis Nirenberg on the Minkowski problem and the Weyl problem, and work by Aleksandr Danilovich Aleksandrov and Aleksei Pogorelov on convex hypersurfaces. In the 1980s fundamental contributions by Karen Uhlenbeck,Jackson, Allyn. (2019)Founder of geom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields. The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been list of prizes known as the Nobel or the highest honors of a field, described as the Nobel Prize of Mathematics, although there are several major differences, including frequency of award, number of awards, age limits, monetary value, and award criteria. According to the annual Academic Excellence Survey by Academic Ranking of World Universities, ARWU, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG Observatory on Academic Ranking and Excellence, IR ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Forbes Nash Jr
John Forbes Nash Jr. (June 13, 1928 – May 23, 2015), known and published as John Nash, was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations. Nash and fellow game theorists John Harsanyi and Reinhard Selten were awarded the 1994 Nobel Memorial Prize in Economic Sciences, Nobel Prize in Economics. In 2015, Louis Nirenberg and he were awarded the Abel Prize for their contributions to the field of partial differential equations. As a graduate student in the Princeton University Department of Mathematics, Nash introduced a number of concepts (including Nash equilibrium and the Nash bargaining solution), which are now considered central to game theory and its applications in various sciences. In the 1950s, Nash discovered and proved the Nash embedding theorems by solving a system of nonlinear partial differential equations arising in Riemannian geometry. This work, also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Partial Differential Equation
In mathematics, an elliptic partial differential equation is a type of partial differential equation (PDE). In mathematical modeling, elliptic PDEs are frequently used to model steady states, unlike parabolic PDE and hyperbolic PDE which generally model phenomena that change in time. The canonical examples of elliptic PDEs are Laplace's Equation and Poisson's Equation. Elliptic PDEs are also important in pure mathematics, where they are fundamental to various fields of research such as differential geometry and optimal transport. Definition Elliptic differential equations appear in many different contexts and levels of generality. First consider a second-order linear PDE for an unknown function of two variables u = u(x,y), written in the form Au_ + 2Bu_ + Cu_ + Du_x + Eu_y + Fu +G= 0, where , , , , , , and are functions of (x,y), using subscript notation for the partial derivatives. The PDE is called elliptic if B^2-AC 0 are hyperbolic. For a general linear second-order ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Of Variations
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of functionals: Map (mathematics), mappings from a set of Function (mathematics), functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as ''geodesics''. A related problem is posed by Fermat's principle: li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enrico Giusti
Enrico Giusti (28 October 1940 – 26 March 2024) was an Italian mathematician mainly known for his contributions to the fields of calculus of variations, regularity theory of partial differential equations, minimal surfaces and history of mathematics. He was professor of mathematics at the Università di Firenze; he also taught and conducted research at the Australian National University at Canberra, at the Stanford University and at the University of California, Berkeley. After retirement, he devoted himself to the managing of the "Giardino di Archimede", a museum entirely dedicated to mathematics and its applications. Giusti was also the editor-in-chief of the international journal dedicated to the history of mathematics ''Bollettino di storia delle scienze matematiche'' (''Bulletin of the history of the mathematical sciences''). One of Giusti's most famous results, obtained with Enrico Bombieri and Ennio De Giorgi, concerned the minimality of Simons' cones, and made it poss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enrico Bombieri
Enrico Bombieri (born 26 November 1940) is an Italian mathematician, known for his work in analytic number theory, Diophantine geometry, complex analysis, and group theory. Bombieri is currently professor emeritus in the School of Mathematics at the Institute for Advanced Study in Princeton, New Jersey. Bombieri won the Fields Medal in 1974 for his work on the large sieve and its application to the distribution of prime numbers. Career Bombieri published his first mathematical paper in 1957, when he was 16 years old. In 1963, at age 22, he earned his first degree (Laurea) in mathematics from the Università degli Studi di Milano under the supervision of Giovanni Ricci and then studied at Trinity College, Cambridge, with Harold Davenport. Bombieri was an assistant professor (1963–1965) and then a full professor (1965–1966) at the Università di Cagliari, at the Università di Pisa in 1966–1974, and then at the Scuola Normale Superiore di Pisa in 1974–1977. From Pi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimal Surface
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame. However, the term is used for more general surfaces that may self-intersect or do not have constraints. For a given constraint there may also exist several minimal surfaces with different areas (for example, see minimal surface of revolution): the standard definitions only relate to a local optimum, not a global optimum. Definitions Minimal surfaces can be defined in several equivalent ways in \R^3. The fact that they are equivalent serves to demonstrate how minimal surface theory lies at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Renato Caccioppoli
Renato Caccioppoli (; 20 January 1904 – 8 May 1959) was an Italian mathematician, known for his contributions to mathematical analysis, including the theory of functions of several complex variables, functional analysis, measure theory. Life and career Born in Naples, he was the son of Giuseppe Caccioppoli (1852–1947), a surgeon, and his second wife Sofia Bakunin (1870–1956), daughter of the Russian revolutionary Mikhail Bakunin. After earning his high-school diploma in 1921, he enrolled in the Department of engineering to swap to mathematics in November 1923. Immediately after earning his laurea in 1925, he became the assistant of Mauro Picone, who in that year was called to the University of Naples, where he remained until 1932. Picone immediately discovered Caccioppoli's brilliance and pointed him towards research in mathematical analysis. During the following five years, Caccioppoli published about 30 works on topics developed in the complete autonomy provided by a minis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Measure Theory
In mathematics, geometric measure theory (GMT) is the study of geometric properties of sets (typically in Euclidean space) through measure theory. It allows mathematicians to extend tools from differential geometry to a much larger class of surfaces that are not necessarily smooth. History Geometric measure theory was born out of the desire to solve Plateau's problem (named after Joseph Plateau) which asks if for every smooth closed curve in \mathbb^3 there exists a surface of least area among all surfaces whose boundary equals the given curve. Such surfaces mimic soap films. The problem had remained open since it was posed in 1760 by Lagrange. It was solved independently in the 1930s by Jesse Douglas and Tibor Radó under certain topological restrictions. In 1960 Herbert Federer and Wendell Fleming used the theory of currents with which they were able to solve the orientable Plateau's problem analytically without topological restrictions, thus sparking geometric measure th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
