# Jozsef Solymosi "Directions in an affine Galois plane and the clique number of the Paley graph"

**Jozsef Solymosi ** from University of British Columbia will
give the talk "Directions in an affine Galois plane and the clique number of the Paley graph" on the labs' Big Seminar.

Password: first 6 decimal places of $\pi$ after the decimal point

You can also write to Alexander Polyanskii (alexander.polyanskii@yandex.ru) or to Maksim Zhukovskii (zhukmax@gmail.com) if you want to be added to mailing list.

**Abstract:**

We prove that the number of directions determined by a set of the form A × B ⊂ AG(2,p), where p is prime, is at least |A||B| − min{|A|,|B|} + 2. We are using the polynomial method: the Rédei polynomial with Szőnyi's extension + a simple variant of Stepanov's method. As an application of the result, we obtain an upper bound on the clique number of the Paley graph.

Based on joint work with Daniel Di Benedetto and Ethan White.

## Watch the video:

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