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| {{for|the violinist|Louis Kaufman}}
| | The author is known as Wilber Pegues. Credit authorising is where my main income arrives from. Her family members lives in Alaska but her husband desires them to transfer. She is truly fond of caving but she doesn't have the time lately.<br><br>Here is my webpage ... online psychic readings ([http://kpupf.com/xe/talk/735373 kpupf.com]) |
| [[File:Louis Kauffman.jpg|right|thumb|200px|Louis Kauffman]]
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| '''Louis Hirsch Kauffman''' (born February 3, 1945) is an American [[mathematician]], [[topology|topologist]], and professor of [[Mathematics]] in the Department of Mathematics, Statistics, and Computer science at the [[University of Illinois at Chicago]]. He is known for the introduction and development of the [[bracket polynomial]] and the [[Kauffman polynomial]].
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| == Biography ==
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| Kauffman was [[wiktionary:valedictorian|valedictorian]] of his graduating class at Norwood Norfolk Central High School in 1962. He received his [[B.S.]] at [[MIT]] in 1966 and his [[Ph.D.]] in [[mathematics]] from [[Princeton University]] in 1972.
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| Kauffman has worked at many places as a visiting professor and researcher, including the University of Zaragoza in Spain, the University of Iowa in Iowa City, the Institute Hautes Etudes Scientifiques in Bures Sur Yevette, France, the Institute Henri Poincaré in Paris, France, the Università di Bologna, Italy, the Universidade Federal de Pernambuco in Recife, Brasil, and the Newton Institute in Cambridge England.<ref name = "Knot Information"> http://www.math.uic.edu/~kauffman/569.html</ref>
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| He is the founding editor and one of the managing editors of the ''[[Journal of Knot Theory and Its Ramifications]]'', and editor of the ''World Scientific Book Series On Knots and Everything''. He writes a column entitled Virtual Logic for the journal ''Cybernetics and Human Knowing''
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| From 2005 to 2008 he was president of the [[American Society for Cybernetics]]. He plays
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| clarinet in the ChickenFat Klezmer Orchestra in Chicago.
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| == Work ==
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| Kauffman's research interests are in the fields of cybernetics, topology and foundations of mathematics and physics. His work is primarily in the topics of [[knot theory]] and connections with [[statistical mechanics]], [[Quantum field theory|quantum theory]], [[algebra]], [[combinatorics]] and foundations. <ref>[http://www.asci.org/artsci2002/artworks/Sunday/explorations.htm Presentation<!-- Bot generated title -->]</ref> In [[topology]] he introduced and developed the [[bracket polynomial]] and [[Kauffman polynomial]].
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| === Bracket polynomial ===
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| {{main|Bracket polynomial}}
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| In the mathematical field of [[knot theory]], the [[bracket polynomial]], also known as the ''Kauffman bracket'', is a [[polynomial]] invariant of [[framed link]]s. Although it is not an invariant of knots or links (as it is not invariant under type I [[Reidemeister move]]s), a suitably "normalized" version yields the famous [[knot invariant]] called the [[Jones polynomial]]. The bracket polynomial plays an important role in unifying the Jones polynomial with other [[quantum invariant]]s. In particular, Kauffman's interpretation of the Jones polynomial allows generalization to state sum invariants of [[3-manifold]]s. Recently the bracket polynomial formed the basis for Mikhail Khovanov's construction of a homology for knots and links, creating
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| a stronger invariant than the Jones polynomial and such that the graded Euler chacteristic of the [[Khovanov homology]] is equal to the original
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| Jones polynomial. The generators for the chain complex of the Khovanov homology are states of the bracket polynomial decorated with elements
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| of a [[Frobenius algebra]].
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| === Kauffman polynomial ===
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| {{main|Kauffman polynomial}}
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| The [[Kauffman polynomial]] is a 2-variable [[knot polynomial]] due to Louis Kauffman. It is defined as
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| :<math>F(K)(a,z)=a^{-w(K)}L(K)\,</math>
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| where <math>w(K)</math> is the [[writhe]] and <math>L(K)</math> is a [[regular isotopy]] invariant which generalizes the bracket polynomial.
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| === Discrete ordered calculus ===
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| In 1994, Kauffman and Tom Etter wrote a draft proposal for a non-commutative ''discrete ordered calculus'' (DOC), which they presented in revised form in 1996.<ref>T. Etter, L.H. Kauffman, ANPA West Journal, vol. 6, no. 1, pp. 3–5</ref> In the mean time, the theory was presented in a modified form by Kauffman and [[H. Pierre Noyes]] together with a presentation of a derivation of free space Maxwell equations on this basis.<ref>Louis H. Kauffman, H. Pierre Noyes, Discrete physics and the derivation of electromagnetism from the formalism of quantum mechanics, Proceedings of the Royal Society London A (1996), vol. 452, pp. 81–95</ref>
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| ==Awards and honors==
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| He is the 1993 recipient of the Warren McCulloch award of the American Society for Cybernetics and the 1996 award of the Alternative Natural Philosophy Association for his work in discrete physics.
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| In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-27.</ref>
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| == Publications ==
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| [[Louis H. Kauffman]] is author of several monographs on knot theory and mathematical physics. His publication list numbers over 170.<ref name = "Knot Information"/> Books:
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| * 1987, ''On Knots'', Princeton University Press 498 pp.
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| * 1993, ''Quantum Topology (Series on Knots & Everything)'', with Randy A. Baadhio, World Scientific Pub Co Inc, 394 pp.
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| * 1994, ''Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds'', with [[Sostenes Lins]], Princeton University Press, 312 pp.
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| * 1995, ''Knots and Applications (Series on Knots and Everything, Vol 6)''
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| * 1995, ''The Interface of Knots and Physics: American Mathematical Society Short Course January 2-3, 1995 San Francisco, California (Proceedings of Symposia in Applied Mathematics)'', with the American Mathematical Society.
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| * 1998, ''Knots at Hellas 98: Proceedings of the International Conference on Knot Theory and Its Ramifications'', with [[Cameron Gordon (mathematician)|Cameron McA. Gordon]], [[Vaughan F. R. Jones]] and [[Sofia Lambropoulou]],
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| * 1999, ''Ideal Knots'', with Andrzej Stasiak and Vsevolod Katritch, World Scientific Publishing Company, 414 pp.
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| * 2001, ''Knots and Physics (Series on Knots and Everything, Vol. 1)'', World Scientific Publishing Company, 788 pp.
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| * 2002, ''Hypercomplex Iterations: Distance Estimation and Higher Dimensional Fractals (Series on Knots and Everything , Vol 17)'', with Yumei Dang and Daniel Sandin.
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| * 2006, ''Formal Knot Theory'', Dover Publications, 272 pp.
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| * 2007, ''Intelligence of Low Dimensional Topology 2006'', with J. Scott Carter and Seiichi Kamada.
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| * 2012, ''Knots and Physics (Fourth Edition)'', World Scientific Publishing Company, ISBN 978-981-4383-00-4
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| Articles and papers, a selection:
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| * 2001, [http://www2.math.uic.edu/~kauffman/CHK.pdf The Mathematics of Charles Sanders Peirce], in: ''Cybernetics & Human Knowing'', Vol.8, no.1–2, 2001, pp. 79–110
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| == References ==
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| <references/>
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| == External links ==
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| * [http://www2.math.uic.edu/~kauffman/ Louis Kauffman] Homepage at uic.edu.
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| * [http://www.evl.uic.edu/hypercomplex/] Hypercomplex Fractals.
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| * [http://front.math.ucdavis.edu/search?a=louis+kauffman&t=&q=&c=&n=25&s=Listings] Arxiv Papers.
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| * {{MathGenealogy|id=1306}}
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| * [http://chickenfat.bandcamp.com/album/chickenfat-demos] ChickenFat Klezmer Orchestra.
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| {{Authority control|VIAF=33210027}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME =Kauffman, Louis
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = American mathematician
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| | DATE OF BIRTH = 1945
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| | PLACE OF BIRTH =
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| | DATE OF DEATH =
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| | PLACE OF DEATH =
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| }}
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| {{DEFAULTSORT:Kauffman, Louis}}
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| [[Category:1945 births]]
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| [[Category:Cyberneticists]]
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| [[Category:Living people]]
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| [[Category:Topologists]]
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| [[Category:University of Illinois at Chicago faculty]]
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| [[Category:Fellows of the American Mathematical Society]]
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The author is known as Wilber Pegues. Credit authorising is where my main income arrives from. Her family members lives in Alaska but her husband desires them to transfer. She is truly fond of caving but she doesn't have the time lately.
Here is my webpage ... online psychic readings (kpupf.com)