Point-Counting and the Zilber-Pink Conjecture - Lecture 1

Explore the Zilber-Pink conjecture and its point-counting approach in this comprehensive lecture. Delve into this diophantine finiteness conjecture that unifies and generalizes the classical Mordell-Lang and Andre-Oort conjectures. Examine the strategy of using point-counting results for definable sets in o-minimal structures to prove specific cases, including its successful application in proving the Andre-Oort conjecture. Focus on the case of a curve in a power of the modular curve while investigating the model-theoretic contexts and essential arithmetic ingredients of the conjectures and techniques. Presented by Jonathan Pila from the University of Oxford, this 1 hour and 51 minute talk offers an in-depth look at this wide-open area of mathematical research.