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Jürgen Jost
Jürgen Jost (born 9 June 1956) is a German mathematician specializing in geometry. He has been a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 1996. Life and work In 1975, he began studying mathematics, physics, economics and philosophy. In 1980 he received a Dr. rer. nat. from the University of Bonn under the supervision of Stefan Hildebrandt. In 1984 he was at the University of Bonn for the habilitation. After his habilitation, he was at the Ruhr University Bochum, the chair of Mathematics X, Analysis. During this time he was the coordinator of the project "Stochastic Analysis and systems with infinitely many degrees of freedom" July 1987 to December 1996. For this work he received the 1993 Gottfried Wilhelm Leibniz Prize, awarded by the Deutsche Forschungsgemeinschaft. Since 1996, he has been director and scientific member at the Max Planck Institute for Mathematics in the Sciences in Leipzig. After more than 10 years of work in Boch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yum-Tong Siu
Yum-Tong Siu (; born May 6, 1943 in Guangzhou, China) is the William Elwood Byerly Professor of Mathematics at Harvard University. Siu is a prominent figure in the study of functions of several complex variables. His research interests involve the intersection of complex variables, differential geometry, and algebraic geometry. He has resolved various conjectures by applying estimates of the complex Neumann problem and the theory of multiplier ideal sheaves to algebraic geometry. Education and career Siu obtained his B.A. in mathematics from the University of Hong Kong in 1963, his M.A. from the University of Minnesota, and his Ph.D. from Princeton University in 1966. Siu completed his doctoral dissertation, titled "Coherent Noether-Lasker decomposition of subsheaves and sheaf cohomology", under the supervision of Robert C. Gunning. Before joining Harvard, he taught at Purdue University, the University of Notre Dame, Yale, and Stanford. In 1982 he joined Harvard as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Dynamical System
Complex dynamics is the study of dynamical systems defined by iteration of functions on complex number spaces. Complex analytic dynamics is the study of the dynamics of specifically analytic functions. Techniques *General **Montel's theorem **Poincaré metric **Schwarz lemma **Riemann mapping theorem **Carathéodory's theorem (conformal mapping) **Böttcher's equation *Combinatorial ** Hubbard trees ** Spider algorithm ** Tuning ** Laminations ** Devil's Staircase algorithm (Cantor function) ** Orbit portraits ** Yoccoz puzzles Parts * Holomorphic dynamics (dynamics of holomorphic functions) ** in one complex variable ** in several complex variables * Conformal dynamics unites holomorphic dynamics in one complex variable with differentiable dynamics in one real variable. See also *Arithmetic dynamics * Chaos theory * Complex analysis *Complex quadratic polynomial *Fatou set *Infinite compositions of analytic functions *Julia set *Mandelbrot set *Symbolic dynamics Notes Re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variational Analysts
Variational may refer to: *Calculus of variations, a field of mathematical analysis that deals with maximizing or minimizing functionals *Variational method (quantum mechanics), a way of finding approximations to the lowest energy eigenstate or ground state in quantum physics *Variational Bayesian methods, a family of techniques for approximating integrals in Bayesian inference and machine learning *Variational properties, properties of an organism relating to the production of variation among its offspring in evolutionary biology *Variationist sociolinguistics or variational sociolinguistics, the study of variation in language use among speakers or groups of speakers See also *List of variational topics in mathematics and physics *Variation (other) Variation or Variations may refer to: Science and mathematics * Variation (astronomy), any perturbation of the mean motion or orbit of a planet or satellite, particularly of the moon * Genetic variation, the difference in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysts
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fellows Of The American Mathematical Society
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Fellows may refer to Fellow, 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) Justice Fellows may refer to: * Grant Fellows (1865–1929), associate justice of the Michigan Supreme Court * Raymond Fellows (1885–1957), associate justice of the Maine Supreme Judicial Court {{disambiguation, tndis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Physics
Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics (also known as physical mathematics). Scope There are several distinct branches of mathematical physics, and these roughly correspond to particular historical periods. Classical mechanics The rigorous, abstract and advanced reformulation of Newtonian mechanics adopting the Lagrangian mechanics and the Hamiltonian mechanics even in the presence of constraints. Both formulations are embodied in analytical mechanics and lead to understanding the deep interplay of the notions of symmetry (physics), symmetry and conservation law, con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to Numerical methods for partial differential equations, numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematics, 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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Of Variation
The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of 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: light follows the path of shortest optical length connecting two points, which depends u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemannian Geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a ''Riemannian metric'', i.e. with an inner product on the tangent space at each point that varies smoothly from point to point. This gives, in particular, local notions of angle, length of curves, surface area and volume. From those, some other global quantities can be derived by integrating local contributions. Riemannian geometry originated with the vision of Bernhard Riemann expressed in his inaugural lecture "''Ueber die Hypothesen, welche der Geometrie zu Grunde liegen''" ("On the Hypotheses on which Geometry is Based.") It is a very broad and abstract generalization of the differential geometry of surfaces in R3. Development of Riemannian geometry resulted in synthesis of diverse results concerning the geometry of surfaces and the behavior of geodesics on them, with techniques that can be applied to the study of differentiable manifolds of higher dim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Biology
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side. Theoretical biology focuses more on the development of theoretical principles for biology while mathematical biology focuses on the use of mathematical tools to study biological systems, even though the two terms are sometimes interchanged. Mathematical biology aims at the mathematical representation and modeling of biological processes, using techniques and tools of applied mathematics. It can be useful in both theoretical and prac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
