Bence Csajbok: On sets of points with few odd secants

Let $S$ be a set of $q+2$ points in $PG(2,q)$, $q$ odd. An odd secant of $S$ is
a line incident with an odd number of points of $S$. A conjecture from
[1] states that the number of odd secants of $S$ is at least $2q-2$.
Observe that a conic, together with an external point is a set of $q+2$
points with  l2q-2$ odd secants. In this talk we prove asymptotically
this conjecture up to a constant, that is, we show
that there is a constant $c$ and a $K$ such that the number of odd secants
of $S$ is at least $2q-c$ for $q > K$. This is a joint work with Simeon
Ball.

[1] P. Balister, B. Bollobás, Z. Füredi and J. Thompson, Minimal
symmetric differences of lines in projective planes, J. Combin. Des.,
22 (2014) 435-451.