Old and new applications of the Combinatorial Nullstellensatz in geometry

Description of video

Date: 11/30/23
Speaker :Károlyi Gyula


    In previous talks at this seminar Zoltán Lóránt Nagy and Péter Maga
    discussed applications of the Combinatorial Nullstellensatz in graph theory
    and additive combinatorics. Here we mostly focus on applications in finite
    and discrete convex geometry. An almost cover of a discrete set of points
    is a collection of hyperplanes that cover all points except one. After showing
    the short proofs of some classical results, such as Jamison's theorem and
    the Alon-Füredi theorem, I will present some new results obtained with
    Gábor Hegedüs. Beacuse of its relevance, at some point I may make a short
    detour to additive combinatorics as well. I will also propose some open problems
    in the hope that some people visiting the Erdős Center will find them appealing.