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Kevin Costello
Kevin Joseph Costello FRS is an Irish mathematician, since 2014 the Krembil Foundation's William Rowan Hamilton chair of theoretical physics at the Perimeter Institute in Waterloo, Ontario, Canada. Education Costello was educated at the University of Cambridge where he was awarded a PhD in 2003 for research on Gromov–Witten invariants supervised by Ian Grojnowski. Career and research Costello works in the field of mathematical physics, particularly in the mathematical foundations of perturbative quantum field theory and the applications of topological and conformal field theories to other areas of mathematics. In the book ''Renormalization and Effective Field Theory''Kevin Costello, ''Renormalization and Effective Field Theory'', Mathematical Surveys and Monographs Volume 170, American Mathematical Society, 2011, he introduced a rigorous mathematical formalism for the renormalization group flow formalism of Kenneth Wilson and proved the renormalizability of Yan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cork (city)
Cork ( , from , meaning 'marsh') is the second largest city in Ireland and third largest city by population on the island of Ireland. It is located in the south-west of Ireland, in the province of Munster. Following an extension to the city's boundary in 2019, its population is over 222,000. The city centre is an island positioned between two channels of the River Lee which meet downstream at the eastern end of the city centre, where the quays and docks along the river lead outwards towards Lough Mahon and Cork Harbour, one of the largest natural harbours in the world. Originally a monastic settlement, Cork was expanded by Viking invaders around 915. Its charter was granted by Prince John in 1185. Cork city was once fully walled, and the remnants of the old medieval town centre can be found around South and North Main streets. The city's cognomen of "the rebel city" originates in its support for the Yorkist cause in the Wars of the Roses. Corkonians sometimes r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory in quantum mechanics. History Quantum field theory emerged from the work of generations of theoretical physicists spanning much of the 20th century. Its devel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields. The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been described as the Nobel Prize of Mathematics, although there are several major differences, including frequency of award, number of awards, age limits, monetary value, and award criteria. According to the annual Academic Excellence Survey by ARWU, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG in 2013–14, the Fields Medal came closely after the Abel Prize as the second most prestigious international award in mathematics. The prize includes a monetary award which, since 2006, has bee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Davide Gaiotto
Davide Silvano Achille Gaiotto (born 11 March 1977) is an Italian mathematical physicist who deals with quantum field theories and string theory. He received the Gribov Medal in 2011 and the New Horizons in Physics Prize in 2013. Biography Gaiotto won 1996 the silver medal as Italian participants in the International Mathematical Olympiad and 1995 gold medal at the International Physics Olympiad in Canberra. He was an undergraduate student at Scuola Normale Superiore in Pisa from 1996 to 2000. From 2004 to 2007 he was a post-doctoral researcher at Harvard University and then to 2011 the Institute for Advanced Study. Since 2011 he has been working at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario. He introduced new techniques in the study and design of four-dimensional (N = 2) supersymmetric conformal field theories. He constructed from M5-branes, which are wound around Riemann surfaces with punctures. This led to new insights into the dynamics of four-d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chern–Simons Theory
The Chern–Simons theory is a 3-dimensional topological quantum field theory of Schwarz type developed by Edward Witten. It was discovered first by mathematical physicist Albert Schwarz. It is named after mathematicians Shiing-Shen Chern and James Harris Simons, who introduced the Chern–Simons 3-form. In the Chern–Simons theory, the action is proportional to the integral of the Chern–Simons 3-form. In condensed-matter physics, Chern–Simons theory describes the topological order in fractional quantum Hall effect states. In mathematics, it has been used to calculate knot invariants and three-manifold invariants such as the Jones polynomial. Particularly, Chern–Simons theory is specified by a choice of simple Lie group G known as the gauge group of the theory and also a number referred to as the ''level'' of the theory, which is a constant that multiplies the action. The action is gauge dependent, however the partition function of the quantum theory is well-define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Cohomology
In mathematics, elliptic cohomology is a cohomology theory in the sense of algebraic topology. It is related to elliptic curves and modular forms. History and motivation Historically, elliptic cohomology arose from the study of elliptic genera. It was known by Atiyah and Hirzebruch that if S^1 acts smoothly and non-trivially on a spin manifold, then the index of the Dirac operator vanishes. In 1983, Witten conjectured that in this situation the equivariant index of a certain twisted Dirac operator is at least constant. This led to certain other problems concerning S^1-actions on manifolds, which could be solved by Ochanine by the introduction of elliptic genera. In turn, Witten related these to (conjectural) index theory on free loop spaces. Elliptic cohomology, invented in its original form by Landweber, Stong and Ravenel in the late 1980s, was introduced to clarify certain issues with elliptic genera and provide a context for (conjectural) index theory of families of differenti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Witten Genus
In mathematics, a genus of a multiplicative sequence is a ring homomorphism from the ring of smooth compact manifolds up to the equivalence of bounding a smooth manifold with boundary (i.e., up to suitable cobordism) to another ring, usually the rational numbers, having the property that they are constructed from a sequence of polynomials in characteristic classes that arise as coefficients in formal power series with good multiplicative properties. Definition A genus \varphi assigns a number \Phi(X) to each manifold ''X'' such that # \Phi(X \sqcup Y) = \Phi(X) + \Phi(Y) (where \sqcup is the disjoint union); # \Phi(X \times Y) = \Phi(X)\Phi(Y); # \Phi(X) = 0 if ''X'' is the boundary of a manifold with boundary. The manifolds and manifolds with boundary may be required to have additional structure; for example, they might be oriented, spin, stably complex, and so on (see list of cobordism theories for many more examples). The value \Phi(X) is in some ring, often the ring of rat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator Product Expansion
In quantum field theory, the operator product expansion (OPE) is used as an axiom to define the product of fields as a sum over the same fields. As an axiom, it offers a non-perturbative approach to quantum field theory. One example is the vertex operator algebra, which has been used to construct two-dimensional conformal field theories. Whether this result can be extended to QFT in general, thus resolving many of the difficulties of a perturbative approach, remains an open research question. In practical calculations, such as those needed for scattering amplitudes in various collider experiments, the operator product expansion is used in QCD sum rules to combine results from both perturbative and non-perturbative (condensate) calculations. 2D Euclidean quantum field theory In 2D Euclidean field theory, the operator product expansion is a Laurent series expansion associated to two operators. A Laurent series is a generalization of the Taylor series in that finitely many pow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Observable
In physics, an observable is a physical quantity that can be measured. Examples include position and momentum. In systems governed by classical mechanics, it is a real-valued "function" on the set of all possible system states. In quantum physics, it is an operator, or gauge, where the property of the quantum state can be determined by some sequence of operations. For example, these operations might involve submitting the system to various electromagnetic fields and eventually reading a value. Physically meaningful observables must also satisfy transformation laws that relate observations performed by different observers in different frames of reference. These transformation laws are automorphisms of the state space, that is bijective transformations that preserve certain mathematical properties of the space in question. Quantum mechanics In quantum physics, observables manifest as linear operators on a Hilbert space representing the state space of quantum states. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chiral Algebra
In mathematics, a chiral algebra is an algebraic structure introduced by as a rigorous version of the rather vague concept of a chiral algebra in physics. In Chiral Algebras, Beilinson and Drinfeld introduced the notion of chiral algebra, which based on the pseudo-tensor category of D-modules. On the other hand, There is already a notion of vertex algebras based on formal power series. Chiral algebras on curves are essentially conformal vertex algebras. See also * Chiral homology *Chiral Lie algebra In algebra, a chiral Lie algebra is a D-module on a curve with a certain structure of Lie algebra. It is related to an \mathcal_2-algebra via the Riemann–Hilbert correspondence In mathematics, the term Riemann–Hilbert correspondence refers to t ... References * Further reading * Conformal field theory Representation theory {{algebra-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yang–Mills Theory
In mathematical physics, Yang–Mills theory is a gauge theory based on a special unitary group SU(''N''), or more generally any compact, reductive Lie algebra. Yang–Mills theory seeks to describe the behavior of elementary particles using these non-abelian Lie groups and is at the core of the unification of the electromagnetic force and weak forces (i.e. U(1) × SU(2)) as well as quantum chromodynamics, the theory of the strong force (based on SU(3)). Thus it forms the basis of our understanding of the Standard Model of particle physics. History and theoretical description In 1953, in a private correspondence, Wolfgang Pauli formulated a six-dimensional theory of Einstein's field equations of general relativity, extending the five-dimensional theory of Kaluza, Klein, Fock and others to a higher-dimensional internal space. However, there is no evidence that Pauli developed the Lagrangian of a gauge field or the quantization of it. Because Pauli found that his theor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kenneth G
Kenneth Geoffrey Oudejans (born Amsterdam, Netherlands ), better known by his stage name Kenneth G, is a Dutch DJ and record producer. He became known in 2013 with his releases on the Dutch label Hysteria Records before joining Revealed Recordings the following year. Discography Charting singles Singles * 2008: ''Wobble'' lub Generation* 2009: ''Konichiwa Bitches!'' (with Nicky Romero) ade In NL (Spinnin')* 2010: ''Are U Serious'' elekted Music* 2011: ''Tjoppings'' ade In NL (Spinnin')* 2012: ''Bazinga'' ysteria Recs* 2012: ''Wobble'' ig Boss Records* 2013: ''Duckface'' (with Bassjackers) ysteria Recs* 2013: ''Basskikker'' nes To Watch Records (Mixmash)* 2013: ''Stay Weird'' ysteria Recs* 2013: ''Rage-Aholics'' evealed Recordings* 2014: ''RAVE-OLUTION'' (with AudioTwinz) ysteria Recs* 2014: ''97'' (with FTampa) evealed Recordings* 2014: ''Rampage'' (with Bassjackers) evealed Recordings* 2014: ''Blowfish'' (with Quintino) ly Eye Records LY or ly may refer to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
