The extremal number of surfaces
1st December 2020, 11:00 am – 12:00 pm
Virtual (online) Zoom seminar; a link will be sent to the Bristol Combinatorics Seminar mailing list, the week before the seminar.
In 1973, Brown, Erdos and Sos 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 A. Kupavskii, A. Polyanskii and D. Zakharov.