In Knot Theory, one of the main interests is understanding when two knots are equivalent: even if they look completely different, one could actually be continuously deformed into the other.
Our main tool for this purpose are the topological invariants associated to a knot. However, computing them is not in general an easy task: it boils down to make a sequence of choices, a rather difficult work for us human. This is why, in recent years, mathematicians have begun using AI-driven solutions to compute these invariants, hoping that machines can identify patterns within the apparent chaos of possibilities.
In this talk, we are going to see how to compute two fundamental invariants, namely Unknotting Number and Slice Genus, with the aid of a Reinforcement Learning (RL) agent. We will start with the basic definitions from Knot Theory and Deep Learning, focusing on concepts rather than technical details, with the ultimate goal of understanding what RL is and how we can exploit it.