Alice Merz (Université de Lille): An overview on strongly invertible knots

Strongly invertible knots are knots with a special kind of symmetry. While they are a classical object of study, they have recently sparked new interest for their connection with the study of some 4-dimensional properties of knots, and for their importance for studying involutions on 3- and 4-manifolds. In this talk I will give an introduction to classical knot theory and to the class of strongly invertible knots, motivating the importance of their study. Time permitting, I will discuss some results that show that strongly invertible knots can be seen as closures of special kinds of braids endowed with a symmetry, giving an equivariant version of classical results due to Alexander and Markov.