Курс лекций: Теория узлов

Профессор Луис Х. Кауффман (НГУ и Иллинойский Университет в Чикаго) прочитает курс лекций по теории узлов. Первая лекция: 24 сентября 2018 г. Лекции будут проходить в сентябре и октябре по понедельникам и средам c 16:00 в аудитории 4109 (НГУ). Приглашаются студенты и аспиранты.

This is a self-contained course in knot theory. It will be useful to have some familiarity with abstract algebra and the rudiments of point set topology. The course will begin with specific topics about graphs and map coloring, including the Penrose evaluation – counting colorings of trivalent graphs, the chromatic, dichromatic and Tutte polynomials and the relationship of these graph polynomials with the Potts model in statistical mechanics. We then introduce knot theory and virtual knot theory via knot and link diagrams and (generalized) Reidemeister moves. We first study writhe, odd writhe, linking numbers and then the bracket polynomial model for the Jones polynomial. We will show how the Jones polynomial is related to the Tutte and dichromatic polynomials and how it and the diagrammatic Temperley-Lieb algebra is related to the Potts model. We then branch out and study a number of topics in knot theory and virtual knot theory including, tangles and DNA replication, fundamental group and quandles, polynomial invariants of virtual knots and links, cobordism of classical and virtual knots, quantum link invariants via solutions to the Yang- Baxter equation. If there is time we will discuss Khovanov Homology as a generalization of the bracket model and Witten’s formulations of knot invariants in terms of a functional integral related to quantum field theory.

More information about the course will be posted at home-page

Фото лекции