Finiteness of Kauffman bracket skein modules

Skein modules are algebraic objects that somehow "encode" links in a 3-dimensional manifold, in a way reminiscent of homology; they have many interesting connections to physics, representation theory, knot theory (via the Jones polynomial) and non-commutative algebra. In this talk I will give a broad introduction and overview of the topic and then discuss a new, elementary proof (due to myself and Renaud Detcherry) of finite dimensionality of the Kauffman bracket skein modules, originally done by Gunningham-Jordan-Safronov.