Triangulating real projective n-space

How many vertices do you need to triangulate the real projective n-space? From this blog post of Gil Kalai I learned about a recent preprint (arXiv:2009.02703) by Adiprasito-Avvakumov-Karasev where they construct triangulations with \[\exp\big((1/2 + \mathcal{o}(1))\sqrt{n}\log{n}\big)\text{-many}\] vertices, which is the first construction needing subexponentially-many vertices. More information, also about the history of this problem, may … Continue reading "Triangulating real projective n-space"

Blockseminar on Dirac operators and scalar curvature

In mid-October we gathered for one week in Bollmannsruh (somewhat west of Berlin) to work our way through the seminal paper Positive scalar curvature and the Dirac operator on complete Riemannian manifolds by Gromov and Lawson. The hotel we stayed in lies directly at the beautiful lake Beetzsee. It was the perfect place to do … Continue reading "Blockseminar on Dirac operators and scalar curvature"

Seminar on soap bubbles and positive scalar curvature

Together with Rudolf Zeidler I am organizing a reading seminar this winter on generalized soap bubbles and positive scalar curvature. The goal of it is to read the corresponding preprint by Chodosh-Li (arXiv:2008.11888). The two main results we want to understand are the following: No closed aspherical manifold of dimension 4 or 5 admits a … Continue reading "Seminar on soap bubbles and positive scalar curvature"

Preise auf der DMV-Jahrestagung 2020

Die Jahrestagung 2020 der DMV fand vor zwei Wochen statt. Hier könnt ihr einen Kurzbericht dazu lesen: link. An dieser Stelle möchte ich kurz von den zwei auf dieser Jahrestagung verliehenen Preisen berichten: Anlässlich ihres 130-jährigen Bestehens hat die DMV die Minkowski-Medaille für besondere mathematische Forschungsleistungen geschaffen. Mit der Minkowski-Medaille will die DMV Mathematikerinnen und Mathematiker … Continue reading "Preise auf der DMV-Jahrestagung 2020"