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Johannes Sjöstrand
Johannes Sjöstrand (born 1947) is a Swedish mathematician, specializing in partial differential equations and functional analysis. Sjöstrand received his doctorate in 1972 from Lund University under Lars Hörmander. Sjöstrand taught at the University of Paris XI and he is a professor at the University of Burgundy in Dijon. He is a member of the Royal Swedish Academy of Sciences and, since 2017, a member of the American Academy of Arts and Sciences. His research deals with microlocal analysis. He has investigated, ''inter alia'', the Schrödinger equation of an electron in a magnetic field (with a spectrum of the Hofstadter butterfly), Jean Bellissard ''Le papillon de Hofstadter, d'après B. Helffer et J. Sjöstrand'', Séminaire Bourbaki, Nr. 745, 1991/92Online resonances in the semiclassical limit, and quantum tunneling In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion t ... [...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] |
Jean Bellissard
Jean Vincent Bellissard (born 1 March 1946, Lyon) is a French theoretical physicist and mathematical physicist, known for his work on C*-algebras, K-theory, noncommutative geometry as applied to solid state physics, particularly, to quantum Hall effect. Bellissard worked as a teaching assistant at the ''École catholique des arts et métiers'' (E.C.A.M.) from 1965 to 1969. He graduated from the ''Université Claude Bernard Lyon'' 1 with bachelor's degree in 1967, ''Diplôme d'études approfondies'' (DEA) in wave mechanics in 1968, and DEA in theoretical physics in 1970. He qualified in 1969 with the ''Agrégation'' in physics. From 1969 to 1970 he taught at Lyon's ''Lycée La Martinière'', an engineering preparatory school, and was simultaneously enrolled as a graduate student in theoretical physics at the Aix-Marseille University. In 1974 he received his doctorate from the Aix-Marseille University with thesis ''Champs quantifiés dans un champ exterieur'' (Quantized fields in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lund University Alumni
Lund (, ;"Lund" (US) and ) is a city in the provinces of Sweden, province of Scania, southern Sweden. The town had 94,393 inhabitants out of a municipal total of 130,288 . It is the seat of Lund Municipality, Scania County. The Öresund Region, which includes ''Lund'', is home to more than 4.2 million people. Archeologists date the founding of Lund to around 990, when Scania was part of Denmark. From 1103 it was the seat of the Catholic Metropolitan Archdiocese of Lund, and the towering Lund Cathedral, built –1145, still stands at the centre of the town. Denmark ceded the city to Sweden in the Treaty of Roskilde in 1658. Lund University, established in 1666, is one of Scandinavia's oldest and largest institutions for education and research. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Swedish Mathematicians
Swedish or ' may refer to: Anything from or related to Sweden, a country in Northern Europe. Or, specifically: * Swedish language, a North Germanic language spoken primarily in Sweden and Finland ** Swedish alphabet, the official alphabet used by the Swedish language * Swedish people or Swedes, persons with a Swedish ancestral or ethnic identity ** A national or citizen of Sweden, see demographics of Sweden ** Culture of Sweden * Swedish cuisine See also * * Swedish Church (other) * Swedish Institute (other) * Swedish invasion (other) * Swedish Open (other) Swedish Open is a tennis tournament. Swedish Open may also refer to: * Swedish Open (badminton) * Swedish Open (table tennis) * Swedish Open (squash) * Swedish Open (darts) {{disambiguation ... {{disambig Language and nationality disambiguation pages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Purpose: Because living persons may suffer personal harm from inappropriate information, we should watch their articles carefully. By adding an article to this category, it marks them with a notice about sources whenever someone tries to edit them, to remind them of WP:BLP (biographies of living persons) policy that these articles must maintain a neutral point of view, maintain factual accuracy, and be properly sourced. Recent changes to these articles are listed on Special:RecentChangesLinked/Living people. Organization: This category should not be sub-categorized. Entries are generally sorted by family name In many societies, a surname, family name, or last name is the mostly hereditary portion of one's personal name that indicates one's family. It is typically combined with a given name to form the full name of a person, although several give .... Maintenance: Individuals of advanced age (over 90), for whom there has been no new documentation in the last ten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1947 Births
It was the first year of the Cold War, which would last until 1991, ending with the dissolution of the Soviet Union. Events January * January–February – Winter of 1946–47 in the United Kingdom: The worst snowfall in the country in the 20th century causes extensive disruption of travel. Given the low ratio of private vehicle ownership at the time, it is mainly remembered in terms of its effects on the railway network. * January 1 – The ''Canadian Citizenship Act, 1946, Canadian Citizenship Act'' comes into effect, providing a Canadian citizenship separate from British law. * January 4 – First issue of weekly magazine ''Der Spiegel'' published in Hanover, Germany, edited by Rudolf Augstein. * January 10 – The United Nations adopts a resolution to take control of the free city of Trieste. * January 15 – Elizabeth Short, an aspiring actress nicknamed the "Black Dahlia", is found brutally murdered in a vacant lot in Los Angeles; the mysterious case is never solv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maciej Zworski
Maciej Zworski is a Polish-Canadian mathematician, currently a professor of mathematics at the University of California, Berkeley. His mathematical interests include microlocal analysis, scattering theory, and partial differential equations. He was an invited speaker at International Congress of Mathematicians in Beijing in 2002, and a plenary speaker at the conference Dynamics, Equations and Applications in Kraków , officially the Royal Capital City of Kraków, is the List of cities and towns in Poland, second-largest and one of the oldest cities in Poland. Situated on the Vistula River in Lesser Poland Voivodeship, the city has a population of 804,237 ... in 2019. Selected publications Articles * * * * * * * * Books * with Richard Melrose and Antônio Sá Barreto: ''Semi-linear diffraction of conormal waves'', Astérisque, vol. 240, Societé Mathématique de France, 199abstract* Semiclassical analysis, American Mathematical Society 2012 * as editor with Plam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernard Helffer
Bernard Helffer (born 8 January 1949, Paris) is a French mathematician, specializing in partial differential equations, spectral theory, and mathematical physics. He is the son of the pianist Claude Helffer and the musicologist Mireille Helffer. Helffer studied from 1968 at the École Polytechnique and received in 1976 from the University of Paris-Sud his doctorate under Charles Goulaouic with dissertation ''Hypoellipticité pour des classes d'opérateurs pseudodifférentiels à caractéristiques multiples''. From 1971 to 1978 he did research at CNRS, from 1978 to 1989 he was a professor at the University of Nantes, and then he was a professor at the University Paris-Sud (and simultaneously taught for five years at the École Normale Superieure). His research in mathematical physics deals with statistical mechanics, liquid crystals, superconductivity, semiclassical approximation, and ground-state nodal lines in Laplace operators and Schrödinger operators. The French Academy o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Melrose
Richard Burt Melrose is an Australian mathematician and emeritus professor at the Massachusetts Institute of Technology who works on geometric analysis, partial differential equations, and differential geometry. Education Melrose received in 1974 his Ph.D. from Cambridge University under F. Gerard Friedlander with thesis ''Initial and Initial-Boundary Value Problems''. Career Melrose became a research fellow at St John's College, Cambridge. In 1977 he was a visiting scholar at the Institute for Advanced Study. Since 1976 he has been a professor at MIT, where since 2006 he has been the Simons Professor of Mathematics. From 1999 to 2002 he was the chair of the committee for pure mathematics at MIT. His doctoral students include Mark S. Joshi, John M. Lee, Rafe Mazzeo, András Vasy, and Maciej Zworski. Awards In 1984 Melrose received the Bôcher Memorial Prize for his work on scattering theory. Since 1986 he has been a Fellow of the American Academy of Arts and Sciences. For ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Tunneling
In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum. For example, a photon is a single quantum of light of a specific frequency (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom. Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of the fundamental framework for understanding and describing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hofstadter Butterfly
In condensed matter physics, Hofstadter's butterfly is a graph of the spectral properties of non-interacting two-dimensional electrons in a perpendicular magnetic field in a lattice. The fractal, self-similar nature of the spectrum was discovered in the 1976 Ph.D. work of Douglas Hofstadter and is one of the early examples of modern scientific data visualization. The name reflects the fact that, as Hofstadter wrote, "the large gaps n the graphform a very striking pattern somewhat resembling a butterfly." The Hofstadter butterfly plays an important role in the theory of the integer quantum Hall effect and the theory of topological quantum numbers. History The first mathematical description of electrons on a 2D lattice, acted on by a perpendicular homogeneous magnetic field, was studied by Rudolf Peierls and his student R. G. Harper in the 1950s. Hofstadter first described the structure in 1976 in an article on the energy levels of Bloch electrons in perpendicular magnetic fie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
