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Lada Peksová – How to Recognize Different Types of Knots From Quite a Long Way Away

Kdy: 23/10/2019 12:20 - 23/10/2019 13:50
Kde: Seminární místnost MUUK (3. patro)
Although various loops and knots have been around us for thousands of years, mathematicians were not interested in them until the late 18th century. Motivated by Kelvin's idea that each atom corresponds to a certain type of knot, the Scottish mathematician Tait decided to classify all possible knots. And he encountered a problem: how can one tell if a given knot can be unknotted or transformed to another by just twisting or pulling the strings? There is still no complete answer to this simple question.

It was not until the 20th century that tools were found to answer this question for at least some specific knots. The main tools are functions that assign to every knot an element from some set such that if we only twist the knot, the value of this function remains the same - in other words we have determined the invariant of the knot. We will show several different knot invariants - tricolorability, linking number, Jones polynomial and more.