TITLE/TITRE

The unknotting number
 

RÉSUMÉ / ABSTRACT

The unknotting number of a knot is one of the simplest classical knot invariants to define: it simply counts the minimum times a knot must pass through itself in order to become unknotted. Despite this simple definition, the unknotting number is often fiendishly difficult to compute. Beginning from the definition, I will discuss some of what is known about this invariant and highlight some of the many things that we still do not understand.