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Joel Spruck
Joel Spruck (born 1946) is a mathematician, J. J. Sylvester Professor of Mathematics at Johns Hopkins University, whose research concerns geometric analysis and elliptic partial differential equations. He obtained his PhD from Stanford University with the supervision of Robert S. Finn in 1971. Mathematical contributions Spruck is well known in the field of elliptic partial differential equations for his series of papers "The Dirichlet problem for nonlinear second-order elliptic equations," written in collaboration with Luis Caffarelli, Joseph J. Kohn, and Louis Nirenberg. These papers were among the first to develop a general theory of second-order elliptic differential equations which are fully nonlinear, with a regularity theory that extends to the boundary. Caffarelli, Nirenberg & Spruck (1985) has been particularly influential in the field of geometric analysis since many geometric partial differential equations are amenable to its methods. With Basilis Gidas, Spruck studie ... [...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] |
Leon Simon
Leon Melvyn Simon , born in 1945, is a Leroy P. Steele PrizeSee announcemen retrieved 15 September 2017. and Bôcher Memorial Prize, Bôcher Prize-winningSee . mathematician, known for deep contributions to the fields of geometric analysis, geometric measure theory, and partial differential equations. He is currently Professor Emeritus in the Mathematics Department at Stanford University. Biography Academic career Leon Simon, born 6 July 1945, received his BSc from the University of Adelaide in 1967, and his PhD in 1971 from the same institution, under the direction of James H. Michael. His doctoral thesis was titled ''Interior Gradient Bounds for Non-Uniformly Elliptic Equations''. He was employed from 1968 to 1971 as a Tutor in Mathematics by the university. Simon has since held a variety of academic positions. He worked first at Flinders University as a lecturer, then at Australian National University as a professor, at the University of Melbourne, the University of Minn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tom Ilmanen
Tom Ilmanen (born 1961) is an American mathematician specializing in differential geometry and the calculus of variations. He is a professor at ETH Zurich ETH Zurich (; ) is a public university in Zurich, Switzerland. Founded in 1854 with the stated mission to educate engineers and scientists, the university focuses primarily on science, technology, engineering, and mathematics. ETH Zurich ran .... He obtained his PhD in 1991 at the University of California, Berkeley with Lawrence Craig Evans as supervisor. Ilmanen and Gerhard Huisken used inverse mean curvature flow to prove the Riemannian Penrose inequality, Riemannian Penrose conjecture, which is the fifteenth problem in Shing-Tung Yau, Yau's list of open problems, and was resolved at the same time in greater generality by Hubert Bray using alternative methods. In their 2001 paper, Huisken and Ilmanen made a conjecture on the mathematics of general relativity, about the curvature in spaces with very little mass: as the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yoshikazu Giga
Yoshikazu is a masculine Japanese given name. Written forms Yoshikazu can be written using different combinations of kanji characters. Here are some examples: *義一, "justice, 1" *義和, "justice, harmony" *吉一, "good luck, 1" *吉和, "good luck, harmony" *善一, "virtuous, 1" *善和, "virtuous, harmony" *芳一, "virtuous/fragrant, 1" *芳和, "virtuous/fragrant, harmony" *良一, "good, 1" *良和, "good, harmony" *喜和, "rejoice, harmony" *慶和, "congratulate, harmony" *能一, "capacity, 1" *嘉一, "excellent, 1" The name can also be written in hiragana よしかず or katakana is a Japanese syllabary, one component of the Japanese writing system along with hiragana, kanji and in some cases the Latin script (known as rōmaji). The word ''katakana'' means "fragmentary kana", as the katakana characters are derived fr ... ヨシカズ. Notable people with the name *, Japanese shōgun *, Japanese cyclist *, Japanese rugby union player *, Japanese conducto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lawrence C
Lawrence may refer to: Education Colleges and universities * Lawrence Technological University, a university in Southfield, Michigan, United States * Lawrence University, a liberal arts university in Appleton, Wisconsin, United States Preparatory & high schools * Lawrence Academy at Groton, a preparatory school in Groton, Massachusetts, United States * Lawrence College, Ghora Gali, a high school in Pakistan * Lawrence School, Lovedale, a high school in India * The Lawrence School, Sanawar, a high school in India Research laboratories * Lawrence Berkeley National Laboratory, United States * Lawrence Livermore National Laboratory, United States People * Lawrence (given name), including a list of people with the name * Lawrence (surname), including a list of people with the name * Lawrence (band), an American soul-pop group * Lawrence (judge royal) (died after 1180), Hungarian nobleman, Judge royal 1164–1172 * Lawrence (musician), Lawrence Hayward (born 1961), British musician * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Sethian
James Albert Sethian is a professor of mathematics at the University of California, Berkeley and the head of the Mathematics Grouat the United States Department of Energy, United States Department of Energy's Lawrence Berkeley National Laboratory. Sethian was born in Washington, D.C., on May 10, 1954. He received a B.A. (1976) from Princeton and a M.A. (1978) and Ph.D (1982) from Berkeley under the direction of Alexandre Chorin. Beginning in 1983, he was a National Science Foundation postdoctoral fellow, lastly at the Courant Institute under Peter Lax. In 1985, he returned to Berkeley to join the mathematics faculty, where he is currently a full professor. Sethian was elected member of the National Academy of Engineering in 2008 as well as the National Academy of Sciences in 2013. Sethian has acted as Interim Director Research at Thinking Machines Corporation and held visiting positions at the National Center for Atmospheric Research and the National Institute of Standards a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanley Osher
Stanley Osher (born April 24, 1942) is an American mathematician, known for his many contributions in shock capturing, level-set methods, and PDE-based methods in computer vision and image processing. Osher is a professor at the University of California, Los Angeles (UCLA), Director of Special Projects in the Institute for Pure and Applied Mathematics (IPAM) and member of the California NanoSystems Institute (CNSI) at UCLA. Education and career Osher received a bachelor's degree from Brooklyn College in 1962. He continued his studies at New York University, where he received a master's degree in 1964 and completed his Ph.D. in 1966. After two years working at the Brookhaven National Laboratories, he joined the University of California, Berkeley as an assistant professor of mathematics in 1968. He moved to Stony Brook University as an associate professor in 1970, and there was promoted to full professor in 1975. He moved again to the University of California, Los Angeles Dep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General theory of relativity, relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time in physics, time, or four-dimensional spacetime. In particular, the ''curvature of spacetime'' is directly related to the energy and momentum of whatever is present, including matter and radiation. The relation is specified by the Einstein field equations, a system of second-order partial differential equations. Newton's law of universal gravitation, which describes gravity in classical mechanics, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shing-Tung Yau
Shing-Tung Yau (; ; born April 4, 1949) is a Chinese-American mathematician. He is the director of the Yau Mathematical Sciences Center at Tsinghua University and professor emeritus at Harvard University. Until 2022, Yau was the William Caspar Graustein Professor of Mathematics at Harvard, at which point he moved to Tsinghua. Yau was born in Shantou in 1949, moved to British Hong Kong at a young age, and then moved to the United States in 1969. He was awarded the Fields Medal in 1982, in recognition of his contributions to partial differential equations, the Calabi conjecture, the positive energy theorem, and the Monge–Ampère equation. Yau is considered one of the major contributors to the development of modern differential geometry and geometric analysis. The impact of Yau's work are also seen in the mathematical and physical fields of convex geometry, algebraic geometry, enumerative geometry, mirror symmetry, general relativity, and string theory, while his work h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Schoen
Richard Melvin Schoen (born October 23, 1950) is an American mathematician known for his work in differential geometry and geometric analysis. He is best known for the resolution of the Yamabe problem in 1984 and his works on harmonic maps. Early life and education Schoen was born in Celina, Ohio, on October 23, 1950. In 1968, he graduated from Fort Recovery High School. He received his B.S. from the University of Dayton in mathematics. He then received his PhD in 1977 from Stanford University with Leon Simon and Shing-Tung Yau as advisors. Career After faculty positions at the Courant Institute, NYU, University of California, Berkeley, and University of California, San Diego, he was Professor at Stanford University from 1987 to 2014, as Bass Professor of Humanities and Sciences since 1992. He is currently Distinguished Professor and Excellence in Teaching Chair at the University of California, Irvine. His surname is pronounced "Shane." Schoen received an NSF Graduate Resear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
