|
Ezra Getzler
Ezra Getzler (born 9 February 1962 in Melbourne) is an Australian mathematician and mathematical physicist. Education and career Getzler studied from 1979 to 1982 at the Australian National University in Canberra (bachelor's degree with honours in 1982). In 1982 he moved to Harvard University with a Fulbright Scholarship; he received his PhD in 1986 under Arthur Jaffe, with a thesis entitled ''Degree theory for Wiener maps and supersymmetric quantum mechanics''. From 1986 to 1989 he was a Junior Fellow at Harvard. He then moved to the Massachusetts Institute of Technology, where he became assistant professor in 1989 and associate professor in 1993. In 1997 he became associate professor at Northwestern University and since 1999 he is full professor. He was a guest professor at several universities, including the Max-Planck-Institut für Mathematik in Bonn (1996), the École Normale Supérieure (1992), the Institut Henri Poincaré (2007), the University of Nice Sophia Antipoli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Melbourne
Melbourne ( ; Boonwurrung/Woiwurrung: ''Narrm'' or ''Naarm'') is the capital and most populous city of the Australian state of Victoria, and the second-most populous city in both Australia and Oceania. Its name generally refers to a metropolitan area known as Greater Melbourne, comprising an urban agglomeration of 31 local municipalities, although the name is also used specifically for the local municipality of City of Melbourne based around its central business area. The metropolis occupies much of the northern and eastern coastlines of Port Phillip Bay and spreads into the Mornington Peninsula, part of West Gippsland, as well as the hinterlands towards the Yarra Valley, the Dandenong and Macedon Ranges. It has a population over 5 million (19% of the population of Australia, as per 2021 census), mostly residing to the east side of the city centre, and its inhabitants are commonly referred to as "Melburnians". The area of Melbourne has been home to Aboriginal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Paris VI
Pierre and Marie Curie University (french: link=no, Université Pierre-et-Marie-Curie, UPMC), also known as Paris 6, was a public research university in Paris, France, from 1971 to 2017. The university was located on the Jussieu Campus in the Latin Quarter of the 5th arrondissement of Paris, France. UPMC merged with Paris-Sorbonne University into a new combined Sorbonne University. It was ranked as the best university in France in medicine and health sciences by ''Times Higher Education'' in 2018. History Paris VI was one of the inheritors of the faculty of Sciences of the University of Paris, which was divided into several universities in 1970 after the student protests of May 1968. In 1971, the five faculties of the former University of Paris (Paris VI as the Faculty of Sciences) were split and then re-formed into thirteen universities by the Faure Law. The campus of Paris VI was built in the 1950s and 1960s, on a site previously occupied by wine storehouses. The Dean, Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicole Berline
Nicole Berline (born 1944) is a French mathematician. Life and work Berline studied from 1963 to 1966 at the and she was as an exchange student at the Moscow State University in Moscow in 1966/67. In 1967, she taught at the ENS de Jeunes filles and in 1971, she worked for the CNRS (Attachée de recherches). In 1974 she received her doctorate at the University of Paris under the supervision of Jacques Dixmier (). In 1976/77 she was a visiting professor at the University of California, Berkeley. In 1977 she became a professor at the University of Rennes 1 and she has taught at the Ecole Polytechnique since 1984. She worked in the index theory of elliptic differential operators along the lines of the Atiyah-Singer index theorem and symplectic geometry. Publications *With Ezra Getzler, Michèle Vergne Michèle Vergne (born August 29, 1943, in L’Isle-Adam, Val d´Oise) is a French mathematician, specializing in analysis and representation theory. Life and work Michèle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up to homeomorphism, though usually most classify up to Homotopy#Homotopy equivalence and null-homotopy, homotopy equivalence. Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group. Main branches of algebraic topology Below are some of the main areas studied in algebraic topology: Homotopy groups In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, which records information about loops in a space. Intuitively, homotopy gro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Category Theory
Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, category theory is used in almost all areas of mathematics, and in some areas of computer science. In particular, many constructions of new mathematical objects from previous ones, that appear similarly in several contexts are conveniently expressed and unified in terms of categories. Examples include quotient spaces, direct products, completion, and duality. A category is formed by two sorts of objects: the objects of the category, and the morphisms, which relate two objects called the ''source'' and the ''target'' of the morphism. One often says that a morphism is an ''arrow'' that ''maps'' its source to its target. Morphisms can be ''composed'' if the target of the first morphism equals the source of the second one, and morphism compos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of the points of special interest like the singular points, the inflection points and the points at infinity. More advanced questions involve the topology of the ... [...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] |
Edward Witten
Edward Witten (born August 26, 1951) is an American mathematical and theoretical physicist. He is a Professor Emeritus in the School of Natural Sciences at the Institute for Advanced Study in Princeton. Witten is a researcher in string theory, quantum gravity, supersymmetric quantum field theories, and other areas of mathematical physics. Witten's work has also significantly impacted pure mathematics. In 1990, he became the first physicist to be awarded a Fields Medal by the International Mathematical Union, for his mathematical insights in physics, such as his 1981 proof of the positive energy theorem in general relativity, and his interpretation of the Jones invariants of knots as Feynman integrals. He is considered the practical founder of M-theory.Duff 1998, p. 65 Early life and education Witten was born on August 26, 1951, in Baltimore, Maryland, to a Jewish family. He is the son of Lorraine (née Wollach) Witten and Louis Witten, a theoretical physicist specializing in gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luis Álvarez-Gaumé
Luis Álvarez-Gaumé (born 1955 in Madrid) is a Spanish theoretical physicist who works on string theory and quantum gravity. Luis Álvarez-Gaumé obtained his PhD in 1981 from Stony Brook University and worked from 1981 to 1984 at Harvard University as a Junior Fellow, before he moved to Boston University to work as a professor. From 1986 until 2016, Álvarez-Gaumé was a permanent member of the CERN Theoretical Physics unit. In 2016, he became the director of the Simons Center for Geometry and Physics at Stony Brook. In the 1980s, Álvarez-Gaumé had various important contributions to the field of string theory and its mathematical framework. Together with Edward Witten he showed in 1983 that quantum field theories generally have gravitational anomalies. Shortly after this, Michael Green and John Schwarz showed that such anomalies are avoided in various realizations of superstring theory. Álvarez-Gaumé is also known for a physical proof of the Atiyah–Singer theorem using s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supersymmetry
In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories exist. Supersymmetry is a spacetime symmetry between two basic classes of particles: bosons, which have an integer-valued spin and follow Bose–Einstein statistics, and fermions, which have a half-integer-valued spin and follow Fermi–Dirac statistics. In supersymmetry, each particle from one class would have an associated particle in the other, known as its superpartner, the spin of which differs by a half-integer. For example, if the electron exists in a supersymmetric theory, then there would be a particle called a ''"selectron"'' (superpartner electron), a bosonic partner of the electron. In the simplest supersymmetry theories, with perfectly " unbroken" supersymmetry, each pair of superpartners would share the same mass and intern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atiyah–Singer Index Theorem
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data). It includes many other theorems, such as the Chern–Gauss–Bonnet theorem and Riemann–Roch theorem, as special cases, and has applications to theoretical physics. History The index problem for elliptic differential operators was posed by Israel Gel'fand. He noticed the homotopy invariance of the index, and asked for a formula for it by means of topological invariants. Some of the motivating examples included the Riemann–Roch theorem and its generalization the Hirzebruch–Riemann–Roch theorem, and the Hirzebruch signature theorem. Friedrich Hirzebruch and Armand Borel had proved the integrality of the  genus of a spin manifold, and At ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
