O-minimality, Effectivity, and the André-Oort Conjecture

Explore the intersection of o-minimality theory and the André-Oort conjecture in this 53-minute conference talk delivered at the Fields Institute's Workshop on Model Theory, Algebraic Dynamics, and Differential-Algebraic Geometry. Delve into the mathematical connections between o-minimal structures and effectivity questions as they relate to one of the most significant open problems in arithmetic geometry. Examine how o-minimality techniques can be applied to understand special points on Shimura varieties and their distribution, while investigating the computational and algorithmic aspects that arise in this context. Learn about recent developments in model theory that provide new tools for approaching the André-Oort conjecture, which concerns the Zariski closure of sets of special points in mixed Shimura varieties. Discover the role of effective bounds and decidability questions in this area of research, and understand how these theoretical frameworks contribute to our understanding of the geometric and arithmetic properties of these fundamental mathematical objects.