Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Since its release on the arXiv in 2017, the (so far unpublished) proof of the higher-dimensional Positive-Mass Theorem by Schoen & Yau has become notorious for being rather difficult to understand, especially if one is not intimately familiar with the relevant results from Geometric Measure Theory. I will therefore try to keep the prerequisites as low as possible and give a basic overview of Schoen & Yau's proof and the challenges they faced. If time permits, I will also talk about some of the details of constructing Yamabe-positive minimal hypersurfaces in the presence of singularities.