The extremal number of surfaces

Combinatorics Seminar
Friday, February 26, 2021 - 3:00pm for 1 hour (actually 50 minutes)
Location (To receive the password, please email Lutz Warnke
Andrey Kupavskii – CNRS and MIPT (Grenoble and Moscow)
Lutz Warnke

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, see