## LOUIS KAUFFMAN

Louis Kauffman was born in Potsdam, New York on Feb. 3, 1945. In high school he developed interests in Boolean algebra, circuits and diagrammatic methods, the mathematics and practice of non-linear pendulum oscillations. He graduated from Norwood-Norfolk Central High School in 1962 as valedictorian and went to Cambridge, Massachusetts to study for an undergraduate degree at the Massachusetts Institute of Technology. He received the degree of B.S. in Mathematics from MIT in 1966 and went to Princeton University for graduate school. At Princeton he studied with William Browder and became fascinated with knots and with singularities of complex hypersurfaces through conversations with the knot theorist Ralph Fox and through the lectures of F. Hirzebruch and J. Milnor. He was particularly influenced by a fateful summer spent in Berkeley in 1968 where he heard lectures by M. Atiyah and F. Hirzebruch. Other events of this kind were an encounter with the book Laws of Form by G. Spencer-Brown in 1973, a lecture at the University of Illinois at Chicago by John Conway in 1978, and a research announcement in the post by Ken Millett and Ray Lickorish in 1984. Kauffman was awarded a PhD. in Mathematics by Princeton University in 1972. He has been teaching at the University of Illinois at Chicago since January 1971, with visiting appointments at the University of Michigan, Universidad de Zaragoza, Spain, Universita di Bologna, Bologna, Italy and the Institute des Hautes Etudes Scientifiques in Bures Sur Yvette, France, to name a few.

Kauffman's research expertise lies in algebraic topology and particularly in low dimensional topology (knot theory) and its relationships with algorithms, logic, combinatorics, mathematical physics and natural science. He is particularly interested in the structure of formal diagrammatic systems such as the system of knot diagrams that is one of the foundational pillars of knot theory. He discovered a significant state summation model for the Conway polynomial in 1980 and the bracket polynomial state model for the Jones polynomial in 1985. These state models constitute the first direct application of partition functions to the construction of knot invariants. In the case of the bracket polynomial model, Kauffman showed that this state summation is a version of the Potts model in statistical mechanics - translated to knot diagrams. He discovered a two variable generalization of the original Jones polynomial that is called the semi-oriented or Kauffman polynomial. Since these discoveries his work has been primarily directed to the structure of the new invariants of knots and links. The bracket model led Kauffman, Murasugi and (independently) Thistlethwaite to proofs of the Tait conjectures about the topological invariance of number of crossings for reduced alternating link projections. His recent research in Virtual Knot Theory has opened up a new field of knot theory and has resulted in the discovery of many new invariants of knots and links.

Kauffman is the author of four books on knot theory (three in Princeton University Press and one in World Scientific Press), a book on map coloring and the reformulation of mathematical problems, Map Reformulation (Princelet Editions; London and Zurich (1986)) and is the editor of the World-Scientific 'Book Series On Knots and Everything'. He is the Editor in Chief and founding editor of the Journal of Knot Theory and Its Ramifications. He is the co-editor of the review volume (with R. Baadhio) Quantum Topology and editor of the review volume Knots and Applications, both published by World Scientific Press. Kauffman is the recipient of a 1993 University Scholar Award by the University of Illinois at Chicago and he is the 1993 recipient of the 1993 Warren McCulloch Memorial Award of the American Society for Cybernetics for significant contributions to the field of Cybernetics and the 1996 award of the Alternative Natural Philosophy Association for his contribution to the understanding of discrete physics.