October 21, 2019
Dolgoprudny
MIPT

# Lecture by prof. Rom Pinchasi "Point sets in general position that determine lines with a small piercing set"

At the invitation of the Laboratory of Combinatorial and Geometric Structures and the PhysTech School of Applied Mathematics and Computer Science, Rom Pinchasi will visit the Moscow Institute of Physics and Technology on October, 21.

Rom Pinchasi will give the lecture on October 21 from 18.35 to 20.00 in the lecture auditorium 2.35 on the Cifra building.

"Point sets in general position that determine lines with a small piercing set"

"Let $P$ be a set of $n$ points in general position (no three on a line) in the plane. Assume $R$ is another set of $n$ points disjoint from $P$ such that every line through two points in $P$ passes through a point in $R$. It is conjectured that in such a case $P$ is contained in a cubic curve in the plane. In a joint work with Chaya Keller we prove this conjecture under additional assumption that the point in $R$ collinear with two points $a$ and $b$ in $P$ is not contained in the straight line segment delimited by $a$ and $b$. This already generalizes a result of Jamison from 1978 about point sets that determine minimum number of distinct directions.

We will discuss related results and open problems."

Everyone is invited to attend the lecture course. The language of the lectures is English. The course is aimed at master and graduate students, as well as researchers in the field of combinatorics.