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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 the mathematical field of 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, Unknot, 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 (in topology, a circle is not bound to the classical geometric concept, but to all of its homeomorphisms). 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 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 descr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Józef Przytycki
Joseph is a common male given name, derived from the Hebrew Yosef (יוֹסֵף). "Joseph" is used, along with "Josef", mostly in English, French and partially German languages. This spelling is also found as a variant in the languages of the modern-day Nordic countries. In Portuguese and Spanish, the name is "José". In Arabic, including in the Quran, the name is spelled ''Yūsuf''. In Persian, the name is "Yousef". The name has enjoyed significant popularity in its many forms in numerous countries, and ''Joseph'' was one of the two names, along with ''Robert'', to have remained in the top 10 boys' names list in the US from 1925 to 1972. It is especially common in contemporary Israel, as either "Yossi" or "Yossef", and in Italy, where the name "Giuseppe" was the most common male name in the 20th century. In the first century CE, Joseph was the second most popular male name for Palestine Jews. In the Book of Genesis Joseph is Jacob's eleventh son and Rachel's first son, and kn ... [...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 the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Washington University
, mottoeng = "God is Our Trust" , established = , type = Private federally chartered research university , academic_affiliations = , endowment = $2.8 billion (2022) , president = Mark S. Wrighton , provost = Christopher Bracey , students = 27,159 (2016) , undergrad = 11,244 (2016) , postgrad = 15,486 (2016) , other = 429 (2016) , faculty = 2,663 , city = Washington, D.C. , country = U.S. , campus = Urban, , former_names = Columbian College (1821–1873)Columbian University (1873–1904) , sports_nickname = Colonials , mascot = George , colors = Buff & blue , sporting_affiliations = NCAA Division I – A-10 , website = , free_label = Newspaper , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Washington Post
''The Washington Post'' (also known as the ''Post'' and, informally, ''WaPo'') is an American daily newspaper published in Washington, D.C. It is the most widely circulated newspaper within the Washington metropolitan area and has a large national audience. Daily broadsheet editions are printed for D.C., Maryland, and Virginia. The ''Post'' was founded in 1877. In its early years, it went through several owners and struggled both financially and editorially. Financier Eugene Meyer purchased it out of bankruptcy in 1933 and revived its health and reputation, work continued by his successors Katharine and Phil Graham (Meyer's daughter and son-in-law), who bought out several rival publications. The ''Post'' 1971 printing of the Pentagon Papers helped spur opposition to the Vietnam War. Subsequently, in the best-known episode in the newspaper's history, reporters Bob Woodward and Carl Bernstein led the American press's investigation into what became known as the Watergate scandal, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
In mathematics, topology (from the Greek language, Greek words , and ) is 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, Twist (mathematics), 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 continuity (mathematics), continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, 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 topological property. Basic exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Washington Metropolitan Area
The Washington metropolitan area, also commonly referred to as the National Capital Region, is the metropolitan area centered on Washington, D.C. The metropolitan area includes all of Washington, D.C. and parts of the states of Maryland, Virginia, and West Virginia. It is part of the larger Baltimore–Washington metropolitan area. The Washington metropolitan area is one of the most educated and most affluent metropolitan areas in the U.S. The metro area anchors the southern end of the densely populated Northeast megalopolis with an estimated total population of 6,385,162 , making it the sixth-largest metropolitan area in the nation and the largest metropolitan area in the Census Bureau's South Atlantic division. Nomenclature The U.S. Office of Management and Budget defines the area as the Washington–Arlington–Alexandria, DC–VA–MD–WV metropolitan statistical area, a metropolitan statistical area used for statistical purposes by the United States Census Bureau and ot ... [...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, then at the University of California, Davis, now at Columbia University. Overview To any link diagram ''D'' representing a link ''L'', we assign the Khovanov bracket ''D''.html" ;"title="/nowiki>''D''">/nowiki>''D''/nowiki>, 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 ''D''.html" ;"title="/nowiki>''D''">/nowiki>''D''/nowiki> 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 defin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mikhail Khovanov
Mikhail Khovanov (russian: Михаил Гелиевич Хованов; born 1972) is a Russian-American professor of mathematics at Columbia 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 before moving to Columbia University. 4 April 2007. "Mikhail Khovanov was in the department when he developed the famous homology theory that bears his name."He is a half-brother of |
Dror Bar-Natan
Dror Bar-Natan ( he, דרוֹר בָר-נָתָן; 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 1991–95, 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 th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oleg Viro
Oleg Yanovich Viro (russian: Олег Янович Виро) (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 w ... [...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 School no. 11 Mihai Eminescu and his secondary education at Ion Brătianu High School in Piteşti. 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 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 conjecture for manifolds of dimension 5 and higher. For this paper he received the E. H. Moore Prize from the American Mathematical Society. Awards a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
