Hi all! I finally decided to have some blog with mathematical notes (I do not want to publish anything not concerning mathematics here, in particular this is why everything is assumed to be in “English”). I would continue on rus4.livejournal.com, but unfortunately livejournal does not support formulae and the easiest way to fix it seems… Read more

Some time ago Victor Kleptsyn explain the sense of an enigmatic operator occuring in the Huang’s sensitivity proof, which appears in a previous exposition in this blog post. UPDATE Arseny Akopyan reminded me that this explanation of Huang’s argument was observed before by Roman Karasev https://arxiv.org/pdf/1907.11175.pdf but for what it worth I keep my exposition… Read more

Let be an origin-symmetric symmetric convex body in , What is the optimal upper bound for the number of vertices of the convex polytope satisfying ? Here we may consider both large and small . As far as I understand, in full generality the 2-parametric asymptotic is still open, see some recent results and a… Read more