Knot theory studies embeddings of the circle into the three dimensional space and the first knot invariant was the Alexander polynomial. The world of quantum invariants started with the milestone discovery of the Jones polynomial and was expanded by Reshetikhin and Turaev’s algebraic construction which starts from a quantum group and leads to link invariants.

Oxford Mathematician Lukas Brantner explains how generalised Lie algebras lead to new insights in Galois theory, deformation theory, and the theory of configuration spaces. Lukas has just been awarded a Royal Society University Research Fellowship.