We propose a correspondence between topological order in 2+1d and Seifert three-manifolds together with a choice of ADE gauge group G. Topological order in 2+1d is known to be characterised in terms of modular tensor categories (MTCs), and we thus propose a relation between MTCs and Seifert three-manifolds. The correspondence defines for every Seifert manifold and choice of G a fusion category, which we conjecture to be modular whenever the Seifert manifold has trivial first homology group with coefficients in the centre of G. The construction determines the spins of anyons and their S-matrix, and provides a constructive way to determine the R- and F-symbols from simple building blocks. We explore the possibility that this correspondence provides an alternative classification of MTCs, which is put to the test by realising all MTCs (unitary or non-unitary) with rank r<=5 in terms of Seifert manifolds and a choice of Lie group G.

I will discuss the integrability and wall-crossing properties of Kondo line defects in rational conformal field theories. It provides a large class of interesting defect RG flow starting from topological line defects. As a surprise, I will discuss new examples of the ODE/IM correspondence and our attempts towards its physical origin using 4d Chern Simons theory. This work is part of a multi-pronged exploration of studying 4D Chern-Simons theory as an overarching structure for integrable systems. ---- Part of London Integrability Journal Club. New participants can register using the form at integrability-london.weebly.com. The link will be emailed.