2025 - Sustainable Industrial Processing Summit
SIPS2025 Volume 3. Kauffman Intl. Symp. / Mathematics

Editors:F. Kongoli, A. Bountis, M. Johnson, S. Karam, P. Mandell, M. Mikalajunas, W. Miller, G. Ord, P. Rowlands, R.M. Santilli, E. Suhir, E. Trell, T. Vougiouklis
Publisher:Flogen Star OUTREACH
Publication Year:2025
Pages:214 pages
ISBN:978-1-998384-42-6 (CD)
ISSN:2291-1227 (Metals and Materials Processing in a Clean Environment Series)
CD-SIPS2025_Volume1
CD shopping page

    KNOTS AND APPLICATIONS – TALK NUMBER 2

    Louis Kauffman1;
    1UNIVERSITY OF ILLINOIS AT CHICAGO, Chicago, United States;
    Type of Paper: Regular
    Id Paper: 320
    Topic: 38

    Abstract:

    These talks are a short introduction to knot theory from a combinatorial point of view and with an eye towards applications to Natural Science.  The talks are self-contained and form a short introductory course in knot theory.

    2. Introduction to the Kauffman bracket polynomial, Many examples. Discussion of other knot polynomials. Relationships with graph theory and with statistical mechanics, state summation models, the Potts model, tensor networks and categories.

    Keywords:

    knot theory; knots; unknots; Reidemeister moves; linking numbers; tangles; rational tangles; writhe; DNA; Kauffman bracket polynomial; Khovanov Homology; Rasmussen invariant

    Cite this article as:

    Kauffman L. (2024). KNOTS AND APPLICATIONS – TALK NUMBER 2. In F. Kongoli, A. Bountis, M. Johnson, S. Karam, P. Mandell, M. Mikalajunas, W. Miller, G. Ord, P. Rowlands, R.M. Santilli, E. Suhir, E. Trell, T. Vougiouklis (Eds.), Sustainable Industrial Processing Summit Volume 3 Kauffman Intl. Symp. / Mathematics (pp. 133-134). Montreal, Canada: FLOGEN Star Outreach