For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions, and determine the fusion rule. We give an explicit realization of this duality defect in the free Maxwell theory. The duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides. [for zoom link please contact h(dot)jiang(at)qmul(dot)ac(dot)uk]

I will describe recent progress in computing Weyl anomalies in strongly-coupled six-dimensional field theories. Along the way we will prove an a-theorem quantifying the loss of degrees of freedom along renormalization group flows.