# 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.