报告题目：Knot Theory: a Mathematical Art
摘要：The mathematical studies of knots began in 19th century with Gauss whereas knot tying dates back to as early as prehistoric times. A great many forms of it appear in Chinese artwork (especially中国结). Moreover, it made repeated appearances in different cultures as the symbol of strength in unity. Knot can be described in various ways. A fundamental problem in knot theory is determining when two descriptions represent the same knot. The first knot tables for complete classification of non-isotopic (i.e. non-equivalent) knots was created in 1860s by Tait. In practice, knots are often distinguished by using a knot invariant, from Alexander polynomials in the early part of the 20th century, to Jones polynomial motivated by Thurston via hyperbolic geometry in 1980s, and then to the more sophisticated tools including quantum groups and Floer homology. Recently knot theory are being used to understand knotting phenomena in nature, including DNA, tangles. It is also crucial in the construction of quantum computers. In the talk we will appreciate knots represented in different forms and use various knot invariants to judge the equivalence between them.