Sergey Avvakumov: A subexponential size R P n

Description of video

Date: 2/12/21
Speaker :Avvakumov Sergey

Abstract: A practical way to encode a manifold is to triangulate it. Among all possible triangulations it makes sense to look for the minimal one, which for the purpose of this talk means using the least number of vertices. Consider now a family of manifolds such as SnRPnSOn, etc. A natural question is how the size of the minimal triangulation depends on n? Surprisingly, except for the trivial case of Sn, our best lower and upper bounds are very far apart. For RPn the current best lower and upper bounds are around n2 and ϕn, respectively, where ϕ is the golden ratio. In this talk I will present the first triangulation of RPn with a subexponential, nn, number of vertices. I will also state several open problems related to the topic. This is a joint work with Karim Adiprasito and Roman Karasev.