Please join us for the Mathematics Colloquium on Monday, Sept. 22, 4 pm in Science Center 356.Prof. Louis Kauffman from the
University of Illinois, Chicago, will speak on “Introduction to Quantum Link Invariants.”
Title: Introduction to Quantum Link Invariants
Speaker: Louis Kauffman, University of Illinois, Chicago
Date & Time: Monday, September 22, 2025, 4:00-5:00 p.m.
Location: Science Center 356
Abstract: This talk is a self-contained introduction to quantum invariants of knots and links. We consider mathematical models of knotted rope in space. We begin with closed curves embedded in three-space. For links, there can be many curves. It is useful to use diagrams to represent the knots and links in terms of their projected shadows to a plane. A classical theorem of Reidemeister lets us handle the topology in terms of these graphs. Methods first developed in the 1980s allow us to obtain topological information by thinking of knots and links as particular patterns of particle creation, interaction, and annihilation from the vacuum to the vacuum. In this form, a special link diagram associated with the link is assigned the analogue of a quantum amplitude associated with the creation and annihilation process.
One can adjust this amplitude so that it is topologically invariant. Such invariants are called quantum knot invariants. This talk will discuss such invariants, their formulation, and relationships with topology, physics, and quantum computing. We will discuss specific examples, including the Jones polynomial and the Kauffman bracket model of the Jones polynomial.
About the Speaker: Prof. Kauffman was valedictorian of his graduating class at Norwood Norfolk Central High School in 1962. He received his B.S. at the Massachusetts Institute of Technology in 1966 and his Ph.D. in mathematics from Princeton University in 1972. Kauffman’s research interests are in the fields of cybernetics, topology, and mathematical physics. His work is primarily on the topics of knot theory and its connections with statistical mechanics, quantum theory, algebra, combinatorics, and foundations. In topology, he introduced and developed the bracket polynomial and Kauffman polynomial.
Wikipedia: https://en.wikipedia.org/wiki/Louis_Kauffman