Lehmer’s conjecture via model theory

par Haydar Göral

lundi 10 juil. 2023, 14:00 → 15:00 Europe/Paris

112

Abstract: In this talk, we first introduce the height function and the Mahler measure on the field of algebraic numbers. We state and give a survey on Lehmer’s conjecture for the Mahler measure, which is still an open problem. Then, we consider the field of algebraic numbers with elements of small Mahler measures in terms of model theory, and we link this theory with Lehmer’s conjecture.  Our approach is based on van der Waerden's theorem from additive combinatorics.