The extremal number of surfaces

Abstract: In 1973, Brown, Erdős and Sós proved that if H is a 3-uniform hypergraph on n vertices which contains no triangulation of the sphere, then H has at most $O(n^{5/2})$ edges, and this bound is the best possible up to a constant factor. Resolving a conjecture of Linial, also reiterated by Keevash, Long, Narayanan, and Scott, we show that the same result holds for triangulations of the torus. Furthermore, we extend our result to every closed orientable surface S. Joint work with Alexandr Polyanskii, István Tomon and Dmitriy Zakharov

combinatoricsprobability

Audience: researchers in the topic

Extremal and probabilistic combinatorics webinar

Series comments: We've added a password: concatenate the 6 first prime numbers (hence obtaining an 8-digit password).