Robin Neumayer will talk on 16th March at 1.45pm UK time, 2.45pm Belgian time. Robin’s title is *“d_p Convergence and epsilon-regularity theorems for entropy and scalar curvature lower bounds”* and her abstract is below.

#### d_p Convergence and epsilon-regularity theorems for entropy and scalar curvature lower bounds

*In this talk, we consider Riemannian manifolds with almost non-negative scalar curvature and Perelman entropy. We establish an epsilon-regularity theorem showing that such a space must be close to Euclidean space in a suitable sense. Interestingly, such a result is false with respect to the Gromov-Hausdorff and Intrinsic Flat distances, and more generally the metric space structure is not controlled under entropy and scalar lower bounds. Instead, we introduce the notion of the d_p distance between (in particular) Riemannian manifolds, which measures the distance between W^{1,p} Sobolev spaces, and it is with respect to this distance that the epsilon regularity theorem holds. We will discuss various applications to manifolds with scalar curvature and entropy lower bounds, including a compactness and limit structure theorem for sequences, a uniform L^infinity Sobolev embedding, and a priori L^p scalar curvature bounds for p<1 This is joint work with Man-Chun Lee and Aaron Nabe*r.