Louis H. Kauffman (3 February 1945) is an American mathematician, topologist, and professor of Mathematics in the Department of Mathematics, Statistics, and Computer science at the University of Illinois at Chicago. Events 1112 - Ramon Berenguer III of Barcelona and Douce I of Provence marry uniting the fortunes of those two states Year 1945 ( MCMXLV) was a Common year starting on Monday (link will display the full calendar A mathematician is a person whose primary area of study and research is the field of Mathematics. Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and The University of Illinois at Chicago, or UIC, is a state-funded public research university located in Chicago. He is known for the introduction and development of the bracket polynomial and Kauffman polynomial. In the mathematical field of Knot theory, the bracket polynomial (also known as the Kauffman bracket) is a Polynomial invariant of Framed The Kauffman polynomial is a 2-variable Knot polynomial due to Louis Kauffman.
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Biography
Kauffman was born in 1945. He was 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. A Bachelor of Science ( BS, BSc or BSc in the UK; less commonly S "PhD" redirects here for other uses see PhD (disambiguation. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Princeton University is a private Coeducational research university located in Princeton, New Jersey.
Kaufmann 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 Univesidad de Pernambuco in Recife, Brasil, and the Newton Institute in Cambridge England. [1]
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
In 2007 he is president of the American Society for Cybernetics. The American Society for Cybernetics (ASC is an organization for interdisciplinary collaboration and synthesis of Cybernetics. He is the 1993 recipient of the Warren McCulloch award of the American Society for Cybernetics
Work
Kauffman's interests are in cybernetics, topology (knot theory and its ramifications) and foundations of mathematics and physics. His work is primarily in knot theory and connections with statistical mechanics, quantum theory, algebra, combinatorics and foundations. In Mathematics, knot theory is the area of Topology that studies mathematical knots While inspired by knots which appear in daily life in shoelaces Statistical mechanics is the application of Probability theory, which includes mathematical tools for dealing with large populations to the field of Mechanics In quantum field theory (QFT the forces between particles are mediated by other particles Algebra is a branch of Mathematics concerning the study of structure, relation, and Quantity. Combinatorics is a branch of Pure mathematics concerning the study of discrete (and usually finite) objects These fields include representation and exploration of topology, fractals and recursions using computers, logical and diagrammatic algebras, Hopf algebras, relations of topology with statistical mechanics and quantum field theory, foundations of discrete physics, quantum computing. [2] In topology he introduced and developed the bracket polynomial and Kauffman polynomial. Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of In the mathematical field of Knot theory, the bracket polynomial (also known as the Kauffman bracket) is a Polynomial invariant of Framed The Kauffman polynomial is a 2-variable Knot polynomial due to Louis Kauffman.
Kauffman has been a prominent leader in Knot Theory, one of the most active research areas in mathematics today. His discoveries include a state sum model for the Alexander-Conway Polynomial, the bracket state sum model for the Jones polynomial, the Kauffman polyomial and Virtual Knot Theory. [1]
Bracket polynomial
In the mathematical field of knot theory, the bracket polynomial, also known as the Kauffman bracket, is a polynomial invariant of framed links. In the mathematical field of Knot theory, the bracket polynomial (also known as the Kauffman bracket) is a Polynomial invariant of Framed In Mathematics, knot theory is the area of Topology that studies mathematical knots While inspired by knots which appear in daily life in shoelaces In the mathematical field of Knot theory, the bracket polynomial (also known as the Kauffman bracket) is a Polynomial invariant of Framed In Mathematics, a polynomial is an expression constructed from Variables (also known as indeterminates and Constants using the operations In the mathematical theory of knots, a framed knot is the extension of a tame knot to an embedding of the Solid torus D 2 × Although it is not an invariant of knots or links (as it is not invariant under type I Reidemeister moves), a suitably "normalized" version yields the famous knot invariant called the Jones polynomial. In the mathematical area of Knot theory, a Reidemeister move refers to one of three local moves on a Link diagram. In the mathematical field of Knot theory, a knot invariant is a quantity (in a broad sense defined for each knot which is the same for equivalent knots In the mathematical field of Knot theory, the Jones polynomial is a Knot polynomial discovered by Vaughan Jones in 1983 The bracket polynomial plays an important role in unifying the Jones polynomial with other quantum invariants. In particular, Kauffman's interpretation of the Jones polynomial allows generalization to invariants of 3-manifolds. In Mathematics, a 3-manifold is a 3-dimensional Manifold. The topological Piecewise-linear, and smooth categories are all equivalent in three dimensions
Kauffman polynomial
The Kauffman polynomial is a 2-variable knot polynomial due to Louis Kauffman. The Kauffman polynomial is a 2-variable Knot polynomial due to Louis Kauffman. The Kauffman polynomial is a 2-variable Knot polynomial due to Louis Kauffman. In the mathematical field of Knot theory, a knot polynomial is a Knot invariant in the form of a Polynomial whose coefficients encode some of It is defined as
where w(K) is the writhe and L(K) is a regular isotopy invariant which generalizes the bracket polynomial. In Knot theory, the writhe is a property of an oriented link diagram In the mathematical subject of Knot theory, a regular isotopy of a link diagram is the equivalence relation generated by using the 2nd and 3rd Reidemeister
Quantum topology
Quantum topology is the interdisciplinary study of a number of new invariants of manifolds, links, and related objects, as well as some possible frameworks for them. It has established many unexpected, exciting relations between low-dimensional topology and various areas of mathematics and theoretical physics. It was born through a few independent contributions in the early 1980s and quickly ramified into a wide variety of techniques at several levels of abstraction and generality. [3]
Publications
Louis H. Kauffman is author of several monographs on knot theory and mathematical physics. Louis H Kauffman ( 3 February, 1945) is an American Mathematician, topologist, and professor of Mathematics in the Department of Mathematics His publication list numbers over 170. [1] Books:
- 1987, On Knots, Princeton University Press 498 pp.
- 1993, Quantum Topology (Series on Knots & Everything), with Randy A. Baadhio, World Scientific Pub Co Inc, 394 pp.
- 1994, Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds, with Sostenes Lins, Princeton University Press, 312 pp.
- 1995, Knots and Applications (Series on Knots and Everything, Vol 6)
- 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.
- 1998, Knots at Hellas 98: Proceedings of the International Conference on Knot Theory and Its Ramifications, with Cameron Gordon, Vaughan F. R. Jones and Sofia Lambropoulou,
- 1999, Ideal Knots, with Andrzej Stasiak and Vsevolod Katritch, World Scientific Publishing Company, 414 pp. Vaughan Frederick Randal Jones DCNZM (born 31 December 1952) is a New Zealand Mathematician, known for his work on
- 2001, Knots and Physics (Series on Knots and Everything, Vol. 1), World Scientific Publishing Company, 788 pp.
- 2002, Hypercomplex Iterations: Distance Estimation and Higher Dimensional Fractals (Series on Knots and Everything , Vol 17), with Yumei Dang and Daniel Sandin.
- 2006, Formal Knot Theory, Dover Publications, 272 pp.
- 2007, Intelligence of Low Dimensional Topology 2006, with J. Scott Carter and Seiichi Kamada.
Articles and papers, a selection:
- 2001, The Mathematics of Charles Sanders Peirce, in: Cybernetics & Human Knowing, Vol. 8, no. 1–2, 2001, pp. 79–110
References
- ^ a b c http://www.math.usf.edu/Nagle/kauffman.html
- ^ Presentation
- ^ http://www.ams.org/notices/200410/2005-jsrc.pdf.
External links
- Louis Kauffman Homepage at uic. edu.
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