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.

computational geometrydiscrete mathematicsdata structures and algorithmscombinatorics

Audience: researchers in the discipline

( paper )

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Discrete and Computational Geometry Seminar in Paris

Series comments: Language is English if anyone in the audience prefers it (otherwise French).

Links and passwords for the talks are on the seminar homepage: monge.univ-mlv.fr/~hubard/GAC/

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