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Planar Algebra
In mathematics, planar algebras first appeared in the work of Vaughan Jones on the standard invariant of a II1 subfactor. They also provide an appropriate algebraic framework for many knot invariants (in particular the Jones polynomial), and have been used in describing the properties of Khovanov homology with respect to tangle composition. Any subfactor planar algebra provides a family of unitary representations of Thompson groups. Any finite group (and quantum generalization) can be encoded as a planar algebra. Definition The idea of the planar algebra is to be a diagrammatic axiomatization of the standard invariant. Planar tangle A (shaded) planar tangle is the data of finitely many ''input'' disks, one ''output'' disk, non-intersecting strings giving an even number, say 2n , intervals per disk and one \star-marked interval per disk. 200px Here, the mark is shown as a \star-shape. On each input disk it is placed between two adjacent outgoing strings, and on the o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hopf Algebra
Hopf is a German surname. Notable people with the surname include: *Eberhard Hopf (1902–1983), Austrian mathematician *Hans Hopf (1916–1993), German tenor *Heinz Hopf (1894–1971), German mathematician *Heinz Hopf (actor) (1934–2001), Swedish actor *Ludwig Hopf (1884–1939), German physicist *Maria Hopf Maria Hopf (13 September 1913 – 24 August 2008) was a pioneering archaeobotanist, based at the RGZM, Mainz. Career Hopf studied botany from 1941–44, receiving her doctorate in 1947 on the subject of soil microbes. She then worked in phyto ... (1914-2008), German botanist and archaeologist {{surname, Hopf German-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trans
Trans- is a Latin prefix meaning "across", "beyond", or "on the other side of". Used alone, trans may refer to: Arts, entertainment, and media * Trans (festival), a former festival in Belfast, Northern Ireland, United Kingdom * ''Trans'' (film), a 1998 American film * Trans Corp, an Indonesian business unit of CT Corp in the fields of media, lifestyle, and entertainment ** Trans Media, a media subsidiary of Trans Corp *** Trans TV, an Indonesian television network *** Trans7, an Indonesian television network Literature * '' Trans: Gender and Race in an Age of Unsettled Identities'', a 2016 book by Rogers Brubaker * '' Trans: When Ideology Meets Reality'', a 2021 book by Helen Joyce Music * ''Trans'' (album), by Neil Young * ''Trans'' (Stockhausen), a 1971 orchestral composition Places * Trans, Mayenne, France, a commune * Trans, Switzerland, a village Science and technology * Trans effect in inorganic chemistry, the increased lability of ligands that are trans to certain o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stefaan Vaes
Stefaan Vaes (born February 29, 1976 in Herentals, Belgium) is a Belgian mathematician. Vaes studied mathematics at the KU Leuven with a diploma in 1998 and a PhD in 2001 with thesis advisor Alfons Van Daele and thesis Locally Compact Quantum Groups. As a postdoc he was from 1998 to 2002 at KU Leuven and from 1998 to 2002 in Paris, where he did research for CNRS. In 2002 he began part-time teaching at the KU Leuven, where he became an associate professor in 2006 and a full professor in 2009. He was a visiting professor in 2009 at Pierre and Marie Curie University (Paris VI) and in 2011 at Paris Diderot University (Paris VII) (where he habilitated in 2004). In 2005 he held the ''Peccot Chair'' at the Collège de France. His research deals with Von Neumann algebras and quantum groups. In 2010, Vaes was an Invited Speaker with talk ''Rigidity for von Neumann algebras and their invariants'' at the International Congress of Mathematicians in Hyderabad. In 2012 he was elected a Fellow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acta Mathematica
''Acta Mathematica'' is a peer-reviewed open-access scientific journal covering research in all fields of mathematics. According to Cédric Villani, this journal is "considered by many to be the most prestigious of all mathematical research journals".. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 4.273, ranking it 5th out of 330 journals in the category "Mathematics". Publication history The journal was established by Gösta Mittag-Leffler in 1882 and is published by Institut Mittag-Leffler, a research institute for mathematics belonging to the Royal Swedish Academy of Sciences. The journal was printed and distributed by Springer from 2006 to 2016. Since 2017, Acta Mathematica has been published electronically and in print by International Press. Its electronic version is open access without publishing fees. Poincaré episode The journal's "most famous episode" (according to Villani) concerns Henri Poincaré, who won a prize offered ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen Bigelow
Stephen John Bigelow is an Australian mathematician and professor of mathematics at the University of California, Santa Barbara.. He is known for his proof that braid groups are linear, concurrently with and independently of another proof by Daan Krammer. Bigelow earned bachelor's and master's degrees in 1992 and 1994 from the University of Melbourne. He completed his PhD in 2000 from the University of California, Berkeley under the joint supervision of Robion Kirby and Andrew Casson. He returned to Melbourne for two years as a research fellow before joining the UCSB faculty in 2002. Bigelow was an invited speaker at the International Congress of Mathematicians in 2002, speaking on representations of braid groups. He was a Sloan Research Fellow for 2002–2006. In 2012 he was designated as one of the inaugural fellows of the American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uffe Haagerup
Uffe Valentin Haagerup (19 December 1949 – 5 July 2015) was a mathematician from Denmark. Biography Uffe Haagerup was born in Kolding, but grew up on the island of Funen, in the small town of Fåborg. The field of mathematics had his interest from early on, encouraged and inspired by his older brother. In fourth grade Uffe was doing trigonometric and logarithmic calculations. He graduated as a student from Svendborg Gymnasium in 1968, whereupon he relocated to Copenhagen and immediately began his studies of mathematics and physics at the University of Copenhagen, again inspired by his older brother who also studied the same subjects at the same university. Early university studies in Einstein's general theory of relativity and quantum mechanics, sparked a lasting interest in the mathematical field of operator algebra, in particular Von Neumann algebra and Tomita–Takesaki theory. In 1974 he received his Candidate's degree ( cand. scient.) from the University of Copenhagen a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proc
Proc may refer to: * Proč, a village in eastern Slovakia * '' Proč?'', a 1987 Czech film * procfs or proc filesystem, a special file system (typically mounted to ) in Unix-like operating systems for accessing process information * Protein C (PROC) * Proc, a term in video game terminology * Procedures or process, in the programming language ALGOL 68 * People's Republic of China, the formal name of China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ... * the official acronym for the Canadian House of Commons Standing Committee on Procedure and House Affairs {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vaughan F
Vaughan () (2021 population 323,103) is a city in Ontario, Canada. It is located in the Regional Municipality of York, just north of Toronto. Vaughan was the fastest-growing municipality in Canada between 1996 and 2006 with its population increasing by 80.2% during this time period and having nearly doubled in population since 1991. It is the fifth-largest city in the Greater Toronto Area, and the List of the largest municipalities in Canada by population, 17th-largest city in Canada. Toponymy The township was named after Benjamin Vaughan, a Kingdom of Great Britain, British commissioner who signed a peace treaty with the United States in 1783. History In the late pre-contact period, the Wyandot people, Huron-Wendat people populated what is today Vaughan. The Skandatut ancestral Wendat village overlooked the east branch of the Humber River (Ontario), Humber River (Pine Valley Drive) and was once home to approximately 2,000 Huron in the sixteenth century. The site is close to a H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alice Guionnet
Alice Guionnet (born 24 May 1969) is a French mathematician known for her work in probability theory, in particular on large random matrices. Biography Guionnet entered the École Normale Supérieure (Paris) in 1989. She earned her PhD in 1995 under the supervision of Gérard Ben Arous at University of Paris-Sud. Focuses of her academic research can be viewed in her thesis, ''Dynamique de Langevin d'un verre de spins'' (Langevin Dynamics of spin glass). She has held positions at the Courant Institute, Berkeley, MIT, and ENS (Paris). She is currently a Director of Research at ENS de Lyon. Works Alice Guionnet is known for her work on large random matrices. In this context, she established principles of large deviations for the empirical measurements of the eigenvalues of large random matrices with Gérard Ben Arous and Ofer Zeitouni, applied the theory of concentration of measure, initiated the rigorous study of matrices with a heavy tail, and obtained the convergence of s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
