Speaker: Lior Bary-Soroker, professor at Tel Aviv University.

Date: December 21, 2022

Time: 20:00-21:00

Location: Zoom

Sponsor: School of Mathematics, Shandong University

Abstract:

The talk aims to present recent progress in the area Hilbert's irreducibility theorem.

The theorem may be formulated as the statement there are "many" rational points on the *line* not coming from rational points on a given cover. If one replaces the line by other varieties, the situation becomes more complicated and, in particular, there are obstructions to the theorem coming from rational points of unramified covers (recall that the line is simply connected).

I will present recent two results: The first result, j/w Daniele Garzoni, deals with affine groups: We show that a random walk on a finitely generated Zariski dense subgroup almost surely misses rational points coming from a ramified cover. The second result, j/w Arno Fehm and Sebastian Petersen, deals with abelian varieties and with rational points over the maximal cyclotomic field (or more generally, the field obtained by adding the torsion points of an abelian variety).

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/173956.htm