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)
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    KNOTS AND APPLICATIONS – TALK NUMBER 4

    Louis Kauffman1;
    1UNIVERSITY OF ILLINOIS AT CHICAGO, Chicago, United States;
    Type of Paper: Regular
    Id Paper: 322
    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.

    4. Knot theory and quantum computing. This talk will discuss how quantum algorithms that compute the Jones polynomial can be constructed, how the Fibonacci model - based in knot theoretic recoupling theory - can be used to create universal quantum computation, and how this model is related to the Quantum Hall effect. We will also discuss the role of the Dirac equation and Majorana fermions in topological quantum computing.

    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 4. 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. 157-158). Montreal, Canada: FLOGEN Star Outreach