Quantum invariants via Hopf algebras and solutions to the Yang-Baxter equation

The fundamental problem of knot theory is to know whether two knots are equivalent or not. As a tool to prove that two knots are different, mathematicians have developed various invariants. Knots invariants are just functions that can be computed from the knot and depend only on the topology of the knot. Here we describe quantum invariants, a powerful family of invariants related to the celebrated Yang-Baxter equation.