Combinatorics Seminar

Solymosi’s conjecture on rich lines in grids

Brendan Murphy (Heilbronn Institute, UK)

Friday, October 20th, 2017
10:30 AM - 11:30 AM
Hylan 1106A

We give an explicit construction that disproves a conjecture of Solymosi on the number of lines in general position that contain a near maximal number of points of a Cartesian product set. We will explain how this problem is connected to the sum-product problem, and show why Solymosi’s conjecture is plausible. The counter-example we give is motivated by related questions in group theory, and is rather different from the usual examples in arithmetic combinatorics.

Event contact: hazel dot mcknight at rochester dot edu