|
Knots In Washington
Knots in Washington is an international conference on knot theory and its ramifications held twice a year since 1995. The main organizers are Józef Przytycki, Alexander Shumakovitch, Yongwu Rong and Valentina Harizanov, all of whom are at George Washington University. This conference has become an important topological event in the Washington Metropolitan Area and regularly attracts well-known topologists from other areas of the US and from other countries. For example, Knots in Washington XVIII, held in May 2004, was the first conference fully devoted to the Khovanov homology, with Mikhail Khovanov giving a series of talks and leading experts Dror Bar-Natan, Lev Rozansky, Oleg Viro, and Ciprian Manolescu giving plenary talks. Knots in Washington XX was dedicated to the 60th birthday of Louis H. Kauffman. Other related conferences include Knots in Poland (1995, 2003), and Knots in Hellas in 1998, where Fields Medal winner Vaughan Jones spoke about his work on knot invariant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knot Theory
In topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, \mathbb^3. Two mathematical knots are equivalent if one can be transformed into the other via a deformation of \mathbb^3 upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing it through itself. Knots can be described in various ways. Using different description methods, there may be more than one description of the same knot. For example, a common method of describing a knot is a planar diagram called a knot diagram, in which any knot can be drawn in many different ways. Therefore, a fundamental p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Józef Przytycki
Józef Henryk Przytycki (, ; born 14 October 1953 in Warsaw, Poland), is a Polish mathematician specializing in the fields of knot theory and topology. Academic background Przytycki received a Master of Science degree in mathematics from University of Warsaw in 1977 and a PhD in mathematics from Columbia University (1981) advised by Joan Birman. Przytycki then returned to Poland, where he became an assistant professor at the University of Warsaw. From 1986 to 1995 he held visiting positions at the University of British Columbia, the University of Toronto, Michigan State University, the Institute for Advanced Study in Princeton, New Jersey, the University of California, Riverside, Odense University, and the University of California, Berkeley. In 1995 he joined the Mathematics Department at George Washington University in Washington, D.C., where he became a professor in 1999. According to the Mathematics Genealogy Project The Mathematics Genealogy Project (MGP) is a web-ba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Valentina Harizanov
Valentina Harizanov is a Serbian-American mathematician and professor of mathematics at The George Washington University. Her main research contributions are in computable structure theory (roughly at the intersection of computability theory and model theory), where she introduced the notion of degree spectra of relations on computable structures and obtained the first significant results concerning uncountable, countable, and finite Turing degree spectra. Her recent interests include algorithmic learning theory and spaces of orders on groups. Education She obtained her Bachelor of Science in mathematics in 1978 at the University of Belgrade and her Ph.D. in mathematics in 1987 at the University of Wisconsin–Madison under the direction of Terry Millar. Career At The George Washington University, Harizanov was an assistant professor of mathematics from 1987 to 1993, an associate professor of mathematics from 1994 to 2002, and a professor of mathematics from 2003 to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Washington University
The George Washington University (GW or GWU) is a Private university, private University charter#Federal, federally-chartered research university in Washington, D.C., United States. Originally named Columbian College, it was chartered in 1821 by the United States Congress and is the first university founded under Washington, D.C.'s jurisdiction. It is one of the nation's six University charter#Federal, federally chartered universities. GW is Carnegie Classification of Institutions of Higher Education, classified among List of research universities in the United States#Universities classified as "R1: Doctoral Universities – Very high research activity", "R1: Doctoral Universities – Very High Research Activity." It is a member of the Association of American Universities. The university offers degree programs in seventy-one disciplines, enrolling around 11,500 Undergraduate education, undergraduate and 15,000 Graduate school, graduate students. The school's athletic teams, the G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Washington Post
''The Washington Post'', locally known as ''The'' ''Post'' and, informally, ''WaPo'' or ''WP'', is an American daily newspaper published in Washington, D.C., the national capital. It is the most widely circulated newspaper in the Washington metropolitan area and has a national audience. As of 2023, the ''Post'' had 130,000 print subscribers and 2.5 million digital subscribers, both of which were the List of newspapers in the United States, third-largest among U.S. newspapers after ''The New York Times'' and ''The Wall Street Journal''. The ''Post'' was founded in 1877. In its early years, it went through several owners and struggled both financially and editorially. In 1933, financier Eugene Meyer (financier), Eugene Meyer purchased it out of bankruptcy and revived its health and reputation; this work was continued by his successors Katharine Graham, Katharine and Phil Graham, Meyer's daughter and son-in-law, respectively, who bought out several rival publications. The ''Post ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Torsion (mechanics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a Set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of List of continuity-related mathematical topics, continuity. Euclidean spaces, and, more generally, metric spaces are examples of topological spaces, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and Homotopy, homotopies. A property that is invariant under such deformations is a to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Washington Metropolitan Area
The Washington metropolitan area, also referred to as the National Capital Region, Greater Washington, or locally as the DMV (short for Washington, D.C., District of Columbia, Maryland, and Virginia), is the metropolitan area comprising Washington, D.C., the federal capital of the United States, and its surroundings. The metropolitan area includes all of Washington, D.C., and parts of Maryland and Virginia. It anchors the southern end of the densely populated Northeast megalopolis and is part of the Washington–Baltimore combined statistical area, the country's third-largest. The area's estimated total population of 6,304,975 (as of 2023) makes it the country's List of Metropolitan Statistical Areas#United States, seventh-most populous metropolitan area It is one of the country's most educated and affluent metropolitan areas. Nomenclature The U.S. Office of Management and Budget defines the area as the Washington–Arlington–Alexandria, DC–VA–MD–WV metropolitan statisti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Khovanov Homology
In mathematics, Khovanov homology is an oriented link invariant that arises as the cohomology of a cochain complex. It may be regarded as a categorification of the Jones polynomial. It was developed in the late 1990s by Mikhail Khovanov. Overview To any link diagram D representing a link L, we assign the Khovanov bracket \left D \right/math>, a cochain complex of graded vector spaces. This is the analogue of the Kauffman bracket in the construction of the Jones polynomial. Next, we normalise \left D \right/math> by a series of degree shifts (in the graded vector spaces) and height shifts (in the cochain complex) to obtain a new cochain complex C(D). The cohomology of this cochain complex turns out to be an invariant of L, and its graded Euler characteristic is the Jones polynomial of L. Definition This definition follows the formalism given in Dror Bar-Natan's 2002 paper. Let denote the ''degree shift'' operation on graded vector spaces—that is, the homogeneous comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mikhail Khovanov
Mikhail Khovanov (; born 13 January 1972) is a Russian professor of mathematics at Johns Hopkins University who works on representation theory, knot theory, and algebraic topology. He is known for introducing Khovanov homology for links, which was one of the first examples of categorification. Education and career Khovanov graduated from Moscow State School 57 mathematical class in 1988. He earned a PhD in mathematics from Yale University in 1997, where he studied under Igor Frenkel. Khovanov was a faculty member at UC Davis The University of California, Davis (UC Davis, UCD, or Davis) is a Public university, public Land-grant university, land-grant research university in Davis, California, United States. It is the northernmost of the ten campuses of the University ... before moving to Columbia University. 4 April 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dror Bar-Natan
Dror Bar-Natan (; born January 30, 1966) is a professor at the University of Toronto Department of Mathematics, Canada. His main research interests include knot theory, finite type invariants, and Khovanov homology. Education Bar-Natan earned his B.Sc. in mathematics at Tel Aviv University in 1984. After performing his military service as a teacher, he went to study at Princeton University in 1987. He obtained his Ph.D. in mathematics from Princeton in 1991, under the direction of physicist Edward Witten. Professorship After holding a Benjamin Peirce Assistant Professorship at Harvard University for four years from 1991 to 1995, he returned to Israel, and became Associate Professor at the Hebrew University of Jerusalem. He moved to the University of Toronto in 2002, and was promoted to Full Professor in 2006. Personal life Bar-Natan holds US, Israeli, and Canadian citizenship, and currently resides in Canada. Bar-Natan originally refused to take the Canadian citizenship oath b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oleg Viro
Oleg Yanovich Viro () (b. 13 May 1948, Leningrad, USSR) is a Russian mathematician in the fields of topology and algebraic geometry, most notably real algebraic geometry, tropical geometry and knot theory. Contributions Viro developed a "patchworking" technique in algebraic geometry, which allows real algebraic varieties to be constructed by a "cut and paste" method. Using this technique, Viro completed the isotopy classification of non-singular plane projective curves of degree 7. The patchworking technique was one of the fundamental ideas which motivated the development of tropical geometry. In topology, Viro is most known for his joint work with Vladimir Turaev, in which the Turaev–Viro invariants (relatives of the Reshetikhin-Turaev invariants) and related topological quantum field theory notions were introduced. Education and career Viro studied at the Leningrad State University where he received his Ph.D. degree in 1974; his advisor was Vladimir Rokhlin. Viro taught f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ciprian Manolescu
Ciprian Manolescu (; born December 24, 1978) is a Romanian-American mathematician, working in gauge theory, symplectic geometry, and low-dimensional topology. He is currently a professor of mathematics at Stanford University. Biography Manolescu completed his first eight classes at Pitești, School no. 11 Mihai Eminescu and his secondary education at Ion Brătianu National College (Pitești), Ion Brătianu High School in Pitești. He completed his undergraduate studies and PhD at Harvard University under the direction of Peter B. Kronheimer. He was the winner of the Morgan Prize, awarded jointly by AMS-MAA-SIAM, in 2002. His undergraduate thesis was on ''Finite dimensional approximation in Seiberg–Witten gauge theory, Seiberg–Witten theory'', and his PhD thesis topic was ''A spectrum valued TQFT from the Seiberg–Witten equations''. In early 2013, he released a paper detailing a disproof of the Triangulation (topology), triangulation conjecture for manifolds of dimension 5 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
