LMS-EPSRC Short Instructional Course - O-Minimality and Diophantine Geometry,
The last five years seen a surprising and fruitful interaction between o-minimality, a branch of model thoery, and diophantine geometry. The most spectacular outcome of this interaction is Pila's proof of the André-Oort conjecture for products of modular curves (Annals of Math., 2011). There have been further important developments by several mathematicians including Masser, Zannier, Ullmo, Yafaev, Habegger, and Pila.
The aim of the LMS-EPSRC Short Course is to introduce students in both model theory and number theory to these recent developments. The strategy underlying the diophantine applications will be introduced through a simple example accessible to first-year graduate students, and the key ingredients will each be discussed.