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Explore an in-depth lecture on the Zilber-Pink conjecture and point-counting techniques in diophantine geometry. Delve into this far-reaching generalization of the Mordell-Lang and Andre-Oort conjectures, examining its significance in number theory. Discover the point-counting approach for definable sets in o-minimal structures and its successful application in proving the Andre-Oort conjecture. Investigate the specific case of a curve in a power of the modular curve, while gaining insights into the model-theoretic contexts and essential arithmetic ingredients underlying these conjectures and techniques. Join Jonathan Pila from the University of Oxford as he presents this advanced mathematical topic at the Institut des Hautes Etudes Scientifiques (IHES) in a comprehensive 1 hour and 52 minute session.
