Point-Counting and the Zilber-Pink Conjecture - Lecture 3

Explore the Zilber-Pink conjecture and its point-counting approach in this comprehensive lecture. Delve into this diophantine finiteness conjecture that 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. Gain insights from Jonathan Pila of the University of Oxford in this 1 hour 49 minute presentation at the Institut des Hautes Etudes Scientifiques (IHES).