Counting arcs in F_q^2


Venue/Location: Online

Speaker: Oliver Roche-Newton (Johannes Kepler Universität in Linz, Austria)


An arc is a set of points in F_q^2 which does not contain any collinear triples. This talk will discuss how the method of hypergraph containers can be used to prove various counting results concerning the number of arcs in F_q^2. For instance, I will discuss a recent result which shows that there are 2^{(1+o(1))q} arcs in F_q^2. This bound is optimal up to the o(1) factor, as can be seen by considering any arc of size q and all of its subsets.

The talk is based on joint work with Audie Warren and Krishnendu Bhowmick.

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