Abstract:

Abstract: Since the late 70s, o-minimal theories have been developed as a generalization of the semi-algebraic setting. In this talk, I will give an historical overview of the main results in o-minimality, say a few words about techniques used to get these results and try to show how they can be useful for studying classical problems. In a second time, I will talk about some of my personal contribution to the subject. Namely, I will discuss the question of the control of o-minimal structures by the function they define in few variables, in the spirit of the Hilbert 13th problem.