Studying knot diagrams has been one of the most important techniques of knot theory since the 19th century, and has expanded into considering new types of diagrams (called "virtual knots") in the last twenty years. This area of research hardly has any practical applications, but its attraction lies in visually pleasing and algebraically elegant constructions arising in it.
In this talk Dr Vernitski will present some directions of his current research. The seminar will mainly concentrate on showing you nice diagrams, but there will be also algebra (some groups and some matrices) in the talk.