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Stanislav Smirnov
Stanislav Konstantinovich Smirnov (russian: Станисла́в Константи́нович Cмирно́в; born 3 September 1970) is a Russian mathematician currently working at the University of Geneva. He was awarded the Fields Medal in 2010. His research involves complex analysis, dynamical systems and probability theory. Career Smirnov's Ph.D. was conducted at Caltech under advisor Nikolai Makarov. In 1998 he was employed as part of the faculty at the Royal Institute of Technology in Stockholm, after which he took up his second position as a professor in the Analysis, Mathematical Physics and Probability group at the University of Geneva in 2003. Research Smirnov has worked on percolation theory, where he proved Cardy's formula for critical site percolation on the triangular lattice, and deduced conformal invariance. The conjecture was proved in the special case of site percolation on the triangular lattice. Smirnov's theorem has led to a fairly complete theory for p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leningrad
Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), is the second-largest city in Russia. It is situated on the Neva River, at the head of the Gulf of Finland on the Baltic Sea, with a population of roughly 5.4 million residents. Saint Petersburg is the fourth-most populous city in Europe after Istanbul, Moscow and London, the most populous city on the Baltic Sea, and the world's northernmost city of more than 1 million residents. As Russia's Imperial capital, and a historically strategic port, it is governed as a federal city. The city was founded by Tsar Peter the Great on 27 May 1703 on the site of a captured Swedish fortress, and was named after apostle Saint Peter. In Russia, Saint Petersburg is historically and culturally associated with ... [...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] |
Oded Schramm
Oded Schramm ( he, עודד שרם; December 10, 1961 – September 1, 2008) was an Israeli-American mathematician known for the invention of the Schramm–Loewner evolution (SLE) and for working at the intersection of conformal field theory and probability theory. Biography Schramm was born in Jerusalem. His father, Michael Schramm, was a biochemistry professor at the Hebrew University of Jerusalem. He attended Hebrew University, where he received his bachelor's degree in mathematics and computer science in 1986 and his master's degree in 1987, under the supervision of Gil Kalai. He then received his PhD from Princeton University in 1990 under the supervision of William Thurston. After receiving his doctorate, he worked for two years at the University of California, San Diego, and then had a permanent position at the Weizmann Institute from 1992 to 1999. In 1999 he moved to the Theory Group at Microsoft Research in Redmond, Washington, where he remained for the rest of hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schramm–Loewner Evolution
In probability theory, the Schramm–Loewner evolution with parameter ''κ'', also known as stochastic Loewner evolution (SLE''κ''), is a family of random planar curves that have been proven to be the scaling limit of a variety of two-dimensional lattice models in statistical mechanics. Given a parameter ''κ'' and a domain in the complex plane ''U'', it gives a family of random curves in ''U'', with ''κ'' controlling how much the curve turns. There are two main variants of SLE, ''chordal SLE'' which gives a family of random curves from two fixed boundary points, and ''radial SLE'', which gives a family of random curves from a fixed boundary point to a fixed interior point. These curves are defined to satisfy conformal invariance and a domain Markov property. It was discovered by as a conjectured scaling limit of the planar uniform spanning tree (UST) and the planar loop-erased random walk (LERW) probabilistic processes, and developed by him together with Greg Lawler and Wendel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformally Invariant
In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed versions of the complex plane: locally near every point they look like patches of the complex plane, but the global topology can be quite different. For example, they can look like a sphere or a torus or several sheets glued together. The main interest in Riemann surfaces is that holomorphic functions may be defined between them. Riemann surfaces are nowadays considered the natural setting for studying the global behavior of these functions, especially multi-valued functions such as the square root and other algebraic functions, or the natural logarithm, logarithm. Every Riemann surface is a two-dimensional real analytic manifold (i.e., a Surface (topology), surface), but it contains more structure (specifically a Complex Manifold, complex stru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangular Lattice
The hexagonal lattice or triangular lattice is one of the five two-dimensional Bravais lattice types. The symmetry category of the lattice is wallpaper group p6m. The primitive translation vectors of the hexagonal lattice form an angle of 120° and are of equal lengths, : , \mathbf a_1, = , \mathbf a_2, = a. The reciprocal lattice of the hexagonal lattice is a hexagonal lattice in reciprocal space with orientation changed by 90° and primitive lattice vectors of length : g=\frac. Honeycomb point set The honeycomb point set is a special case of the hexagonal lattice with a two-atom basis. The centers of the hexagons of a honeycomb form a hexagonal lattice, and the honeycomb point set can be seen as the union of two offset triangular lattices. In nature, carbon atoms of the two-dimensional material graphene are arranged in a honeycomb point set. Crystal classes The ''hexagonal lattice'' class names, Schönflies notation, Hermann-Mauguin notation, orbifold notat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Cardy
John Lawrence Cardy FRS (born 19 March 1947, England)Guggenheim Foundation: Annual Report 1985. is a British-American theoretical physicist at the University of California, Berkeley. He is best known for his work in theoretical condensed matter physics and statistical mechanics, and in particular for research on critical phenomena and two-dimensional conformal field theory. He was an undergraduate and postgraduate student at Downing College, University of Cambridge, before moving to the University of California, Santa Barbara, where he joined the faculty in 1977. In 1993, he moved to the University of Oxford, where until 2014 he was a Fellow of All Souls College (now Emeritus) and a Professor of Physics in the Rudolf Peierls Centre for Theoretical Physics. He currently holds a Visiting Professorship at the University of California, Berkeley. He was elected as a Fellow of the Royal Society in 1991, received the Dirac Medal of the IoP in 2000, was awarded the Lars Onsager Prize ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Percolation Theory
In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters. The applications of percolation theory to materials science and in many other disciplines are discussed here and in the articles network theory and percolation. Introduction A representative question (and the source of the name) is as follows. Assume that some liquid is poured on top of some porous material. Will the liquid be able to make its way from hole to hole and reach the bottom? This physical question is modelled mathematically as a three-dimensional network of vertices, usually called "sites", in which the edge or "bonds" between each two neighbors may be open (allowing the liquid through) with probability , or closed with probability , and th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stockholm
Stockholm () is the Capital city, capital and List of urban areas in Sweden by population, largest city of Sweden as well as the List of urban areas in the Nordic countries, largest urban area in Scandinavia. Approximately 980,000 people live in the Stockholm Municipality, municipality, with 1.6 million in the Stockholm urban area, urban area, and 2.4 million in the Metropolitan Stockholm, metropolitan area. The city stretches across fourteen islands where Mälaren, Lake Mälaren flows into the Baltic Sea. Outside the city to the east, and along the coast, is the island chain of the Stockholm archipelago. The area has been settled since the Stone Age, in the 6th millennium BC, and was founded as a city in 1252 by Swedish statesman Birger Jarl. It is also the county seat of Stockholm County. For several hundred years, Stockholm was the capital of Finland as well (), which then was a part of Sweden. The population of the municipality of Stockholm is expected to reach o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thesis Advisor
A doctoral advisor (also dissertation director, dissertation advisor; or doctoral supervisor) is a member of a university faculty whose role is to guide graduate students who are candidates for a doctorate, helping them select coursework, as well as shaping, refining and directing the students' choice of sub-discipline in which they will be examined or on which they will write a dissertation. Students generally choose advisors based on their areas of interest within their discipline, their desire to work closely with particular graduate faculty, and the willingness and availability of those faculty to work with them. In some countries, the student's advisor serves as the chair of the dissertation committee or the examination committee. In some cases, though, the person who serves those roles may be different from the faculty member who has most closely advised the student. For instance, in the Dutch academic system, only full professors (''hoogleraren'') and associate professors ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Caltech
The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasionally referred to as "CIT", most notably in its alma mater, but this is uncommon. is a private university, private research university in Pasadena, California. Caltech is ranked among the best and most selective academic institutions in the world, and with an enrollment of approximately 2400 students (acceptance rate of only 5.7%), it is one of the world's most selective universities. The university is known for its strength in science and engineering, and is among a small group of Institute of Technology (United States), institutes of technology in the United States which is primarily devoted to the instruction of pure and applied sciences. The institution was founded as a preparatory and vocational school by Amos G. Throop in 1891 and began ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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