Профессор Луис Х. Кауффман прочитает курс лекций «Комбинаторная теория узлов»

Профессор Луис Х. Кауффман (НГУ и Иллинойский Университет в Чикаго) прочитает курс лекций Комбинаторная теория узлов. Первая лекция состоится 7 октября 2019 г. Лекции будут проходить в октябре и ноябре по понедельникам и средам в 16:20 в аудитории 4109 (НГУ). Приглашаются студенты и аспиранты.

Summary: This is an introductory course on combinatorial knot theory with an emphasis on virtual knot theory and knotoids and on relationships between graph theory and knot theory. Virtual knot theory is a generalization of classical knot theory that includes the study of knots in thickened surfaces, and a diagrammatic approach to this structure. Knotoids are generalizations of classical knots to knotted intervals whose endpoints can be in any regions of the diagram. Knotoids have applications to the study of open-ended interval embeddings in space, and so to the embeddings of long molecules. One of the key topics in this study is cobordism of knots, and we shall discuss the relationship of knot and link cobordism with vortex reconnection for knotted vortices. The polynomial invariants of knots and links such as the Jones polynomial and its companion, the bracket polynomial, extend to virtual links and to knotoids. The same is true for Khovanov Homology and we will study at least one of these extensions. It is not known how to extend the Heegaard Floer Knot Homology to virtual knots and we shall discuss the combinatorics of this problem!

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