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Guido De Philippis
Guido De Philippis (born August 16, 1985 at Fiesole) is an Italian mathematician. He works on the calculus of variations, partial differential equations and geometric measure theory. In 2016, he was awarded the EMS Prize, "for his outstanding contributions to the regularity of solutions of Monge–Ampère equation and optimal maps and for his deep work on quantitative stability inequalities for the first eigenvalue of the Laplacian and rigidity in some isoperimetric type inequalities.". In 2018 he was awarded the Stampacchia Medal. In 2021, he received the ISAAC award. De Philippis was a PhD student of Luigi Ambrosio and Luis Caffarelli Luis Ángel Caffarelli (; born December 8, 1948) is an Argentine-American mathematician. He studies partial differential equations and their applications. Caffarelli is a professor of mathematics at the University of Texas at Austin, and the win .... Selected publications * * * Regularity of optimal transport maps and applications Ed. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oberwolfach
Oberwolfach () is a town in the district of Ortenau (district), Ortenau in Baden-Württemberg, Germany. It is the site of the Oberwolfach Research Institute for Mathematics, or Mathematisches Forschungsinstitut Oberwolfach. Geography Geographical situation The town of Oberwolfach lies between 270 and 948 meters above sea level in the central Schwarzwald (Black Forest) on the river Wolf (Fluss), Wolf, a tributary of the Kinzig (Rhine), Kinzig. Neighbouring localities The district is neighboured by Bad Peterstal-Griesbach to the north, Bad Rippoldsau-Schapbach in Freudenstadt (district), Landkreis Freudenstadt to the east, by the towns of Wolfach and Hausach to the south, and by Oberharmersbach to the west. Demographics Population development: References External links Gemeinde Oberwolfach: Official Homepage (in German) [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fiesole
Fiesole () is a town and ''comune'' of the Metropolitan City of Florence in the Italian region of Tuscany, on a scenic height above Florence, 5 km (3 miles) northeast of that city. It has structures dating to Etruscan and Roman times. Founded in the seventh century BC as Vipsul, the city became one of the most important and earliest urban centres of the Etruscan civilisation. Since the fourteenth century, the city has always been considered a getaway for members of the upper class of Florence and, up to this day, Fiesole remains noted for its very expensive residential properties, just as well as its centuries-old villas and their formal gardens. The city is generally considered to be the wealthiest and most affluent suburb of Florence. In 2016, the city had the highest median family income in the whole of Tuscany. Fiesole is a centre of higher education. The campus of the European University Institute is situated in the suburb and uses several historical buildings in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1985 Births
The year 1985 was designated as the International Youth Year by the United Nations. Events January * January 1 ** The Internet's Domain Name System is created. ** Greenland withdraws from the European Economic Community as a result of a new agreement on fishing rights. * January 7 – Japan Aerospace Exploration Agency launches ''Sakigake'', Japan's first interplanetary spacecraft and the first deep space probe to be launched by any country other than the United States space exploration programs, United States or the Soviet space program, Soviet Union. * January 15 – Tancredo Neves is Brazilian presidential election, 1985, elected president of Brazil by the National Congress of Brazil, Congress, ending the Military dictatorship in Brazil, 21-year military rule. * January 27 – The Economic Cooperation Organization, Economic Cooperation Organization (ECO) is formed, in Tehran. * January 28 – The charity single record "We Are the World" is recorded by USA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century Italian Mathematicians
File:1st century collage.png, From top left, clockwise: Jesus is crucified by Roman authorities in Judaea (17th century painting). Four different men ( Galba, Otho, Vitellius, and Vespasian) claim the title of Emperor within the span of a year; The Great Fire of Rome (18th-century painting) sees the destruction of two-thirds of the city, precipitating the empire's first persecution against Christians, who are blamed for the disaster; The Roman Colosseum is built and holds its inaugural games; Roman forces besiege Jerusalem during the First Jewish–Roman War (19th-century painting); The Trưng sisters lead a rebellion against the Chinese Han dynasty (anachronistic depiction); Boudica, queen of the British Iceni leads a rebellion against Rome (19th-century statue); Knife-shaped coin of the Xin dynasty., 335px rect 30 30 737 1077 Crucifixion of Jesus rect 767 30 1815 1077 Year of the Four Emperors rect 1846 30 3223 1077 Great Fire of Rome rect 30 1108 1106 2155 Boudican ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isoperimetric Inequality
In mathematics, the isoperimetric inequality is a geometric inequality involving the square of the circumference of a closed curve in the plane and the area of a plane region it encloses, as well as its various generalizations. '' Isoperimetric'' literally means "having the same perimeter". Specifically, the isoperimetric inequality states, for the length ''L'' of a closed curve and the area ''A'' of the planar region that it encloses, that :4\pi A \le L^2, and that equality holds if and only if the curve is a circle. The isoperimetric problem is to determine a plane figure of the largest possible area whose boundary has a specified length. The closely related ''Dido's problem'' asks for a region of the maximal area bounded by a straight line and a curvilinear arc whose endpoints belong to that line. It is named after Dido, the legendary founder and first queen of Carthage. The solution to the isoperimetric problem is given by a circle and was known already in Ancient Greece. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimal Map
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. Optimization problems Optimization problems can be divided into two categories, depending on whether the variables a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monge–Ampère Equation
In mathematics, a (real) Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. A second-order equation for the unknown function ''u'' of two variables ''x'',''y'' is of Monge–Ampère type if it is linear in the determinant of the Hessian matrix of ''u'' and in the second-order partial derivatives of ''u''. The independent variables (''x'',''y'') vary over a given domain ''D'' of R2. The term also applies to analogous equations with ''n'' independent variables. The most complete results so far have been obtained when the equation is elliptic. Monge–Ampère equations frequently arise in differential geometry, for example, in the Weyl and Minkowski problems in differential geometry of surfaces. They were first studied by Gaspard Monge in 1784 and later by André-Marie Ampère in 1820. Important results in the theory of Monge–Ampère equations have been obtained by Sergei Bernstein, Aleksei Pogorelov, Charles Fefferman, and ... [...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] |
Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how is thought of as an unknown number solving, e.g., an algebraic equation like . However, it is usually impossible to write down explicit formulae for solutions of partial differential equations. There is correspondingly a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity and stability. Among the many open questions are the existence ... [...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] |
Caccioppoli Prize
The Caccioppoli Prize is awarded by the Italian Mathematical Union to an Italian mathematician not exceeding the age of 38 who established a wide international reputation. The prize is entitled to the memory of the Italian mathematician Renato Caccioppoli and is awarded on the occasion of the Italian Mathematical Union conference every four years. In its early stages the prize was awarded every two years. The recipient currently receives 10,000 euros. Further prizes of the Italian Mathematical Union are the Bartolozzi Prize, the Stampacchia Medal and the Vinti Prize. Prize winners SourceUnione Matematica ItalianaWinners and relative academic affiliations at the time of the awarding of the prize *1960 Ennio De Giorgi (Scuola Normale Superiore di Pisa) *1962 Edoardo Vesentini (University of Pisa) *1964 Emilio Gagliardo (University of Genova) *1966 Enrico Bombieri (University of Pisa) *1968 Mario Miranda (University of Pisa) *1970 Claudio Baiocchi (University of Pavia) *1974 Al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fiesole, Italy
Fiesole () is a town and ''comune'' of the Metropolitan City of Florence in the Italian region of Tuscany, on a scenic height above Florence, 5 km (3 miles) northeast of that city. It has structures dating to Etruscan and Roman times. Founded in the seventh century BC as Vipsul, the city became one of the most important and earliest urban centres of the Etruscan civilisation. Since the fourteenth century, the city has always been considered a getaway for members of the upper class of Florence and, up to this day, Fiesole remains noted for its very expensive residential properties, just as well as its centuries-old villas and their formal gardens. The city is generally considered to be the wealthiest and most affluent suburb of Florence. In 2016, the city had the highest median family income in the whole of Tuscany. Fiesole is a centre of higher education. The campus of the European University Institute is situated in the suburb and uses several historical buildings includi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
