Multicrossing Knot Diagrams

：Prof.Jim Hoste
：2019-04-15 10:00
：实验楼105

       Speaker：Prof.Jim Hoste

                        Pitzer College，USA

Title: Multicrossing Knot Diagrams

       Time：15 April 2019,10:00

Location：实验楼105

Abstract:The mathematical study of knots began in the late 1800s by studying diagrams of knots, which are projections of knots into a plane where the only singularities aretransverse double points, that is, places where two strands of the knot project to  transversely intersecting arcs. By labeling which arc comes from the “higher” part of the knot, one obtains a diagram from which the knot can be reconstructed. It is possible to treat all of knot theory as the study of such diagrams with the understanding that different diagrams that represent the same knot must be considered as equivalent diagrams.While it is simpler to allow only double points in the projection,  there is no reason not to allow n-fold singularities where n strands cross at a single point in the projection for larger values of n. These multicrossing  diagrams provide a different vantage point on the theory of knots have been studied extensively in the last several years. In this talk I will describe much of what is known about multi crossing diagrams focus on the case of 3-crossing diagrams, where all singularities are transverse triple points. I will describe a set of diagrammatic “moves” similar to the classical Reidemeister moves for classical diagrams  that allow one to pass between any two 3-crossing diagrams of the same link. This is joint work with Colin Adams Martin Palmer.

Speaker Introduction：Hoste教授在University of California, Berkeley获学士和硕士学位， 在University of Utah获博士学位（1982年）。他主要研究低维拓扑，纽结理论以及计算机在二者的应用。已在BAMS, TAMS,  Math. Proc. Cambridge Philos. Soc. , Math. Comp.,  Math. Z.,  Algebr. Geom. Topol.等国际著名杂志发表论文近40篇。他是纽结理论中HOMFLY多项式的发现者之一（即HOMFLY中的“H”），该二元多项式推广了一元的Jones多项式（Jones因此曾在1990年获菲尔兹奖）。

 联系人：金贤安教授