M-theory on spaces with codimension 11-d singularities gives rise to a rich class of d-dimensional field theories. I will discuss how (d+1)-dimensional topological field theories (TFTs) encode the higher symmetries and anomalies of these d-dimensional theories, and how these TFTs can be extracted from the geometry of the singular space. I will illustrate the discussion by analysing some simple examples explicitly. [for zoom link please contact jung-wook(dot)kim(at)qmul(dot)ac(dot)uk]

I will show how to construct the familiar heterotic NS5 brane as a topological soliton in a supercritical version of heterotic string theory. Closed string tachyon condensation removes the extra dimensions, leaving the NS5 in 10d, in a process highly reminiscent of the K-theoretical description of type II D-branes, but linking non-trivial gauge bundles and geometry. The construction requires a modification of the anomalous Bianchi identity for H_3 in supercritical heterotic string theory. I will give various proofs for the existence of this modification.