Knot theory and its applications in analysis

This talk is divided into two parts. In the first part, we will study the Jones polynomial when it is evaluated at the sixth root of unity, with a particular focus on the sign that results from this evaluation. Besides getting familiar with the basic ideas of knot theory, we will also investigate the origin of the sign.

In the second part, we will focus on applications of knot theory in analysis. We will examine how the concept of linking can be used to demonstrate the existence of critical points of functionals defined on Banach spaces.