Vahagn Aslanyan (University of Leeds)

Combining Manin-Mumford and weak Zilber-Pink

I will introduce some classical notions and problems in Diophantine geometry, including the Manin-Mumford and Zilber-Pink conjectures, and explain how model-theoretic tools are used to approach them. I will then talk about one of my recent theorems establishing a new partial result towards Zilber-Pink by combining Manin-Mumford and a weak version of Zilber-Pink (both are theorems). I am going to start with very basic things, give quite a few examples and define/explain all concepts that I am going to use, so I hope that most of the talk will be accessible to a wide range of people including those who have not heard about Diophantine geometry before.