Professor Louis H. Kauffman

Louis H. Kauffman, Ph.D., FAMS is a mathematician, 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.
 
Louis 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. From 2005 to 2008 he was president of the American Society for Cybernetics. He coedited Cybernetics & Human Knowing, authored Formal Knot Theory, and coauthored Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds.
 
His 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 theory, algebra, combinatorics, and foundations.
 
In the mathematical field of knot theory, the bracket polynomial, also known as the Kauffman bracket, is a polynomial invariant of framed links. 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. The bracket polynomial plays an important role in unifying the Jones polynomial with other quantum invariants.
 
In particular, Louis’s interpretation of the Jones polynomial allows generalization to state sum invariants of 3-manifolds. Recently the bracket polynomial formed the basis for Mikhail Khovanov’s construction of a homology for knots and links, creating a stronger invariant than the Jones polynomial and such that the graded Euler characteristic of the Khovanov homology is equal to the original Jones polynomial. The generators for the chain complex of the Khovanov homology are states of the bracket polynomial decorated with elements of a Frobenius algebra.
 
The Kauffman polynomial is a 2-variable knot polynomial due to Louis Kauffman. It is defined as F(K)(a,z)=a^-w(K)L(K), where w(K) is the writhe and L(K) is a regular isotopy invariant which generalizes the bracket polynomial.
 
Louis earned his B.S. at MIT in 1966 and his Ph.D. in mathematics from Princeton University in 1972. In 2012 he became a fellow of the American Mathematical Society.
 
Watch LSU Mathematics Porcelli Lectures 1995: Louis H. Kauffman, Langenhop Lecture Louis H. Kauffman, Workshop on Reflexivity in Mathematics and Cybernetics (part 1/2) by Prof. Kauffman, and Workshop on Reflexivity in Mathematics and Cybernetics (part 2/2) by Prof. Kauffman. Read his Wikipedia profile.