2022 CMI-HIMR Summer School on Unlikely Intersections in Diophantine Geometry23 Feb 2022, by Sponsored events in
22 – 26 August 2022
Mathematical Institute, University of Oxford, UK
Jointly funded by the Clay Mathematics Institute, the Heilbronn Institute for Mathematical Research and the Mathematical Institute at the University of Oxford
Unlikely intersection problems emerged around 25 years ago, with several different motivations. Bombieri, Masser and Zannier, Zilber, and Pink independently arrived at conjectures now known as the Zilber-Pink conjectures, which are still wide open in general. The Pila-Wilkie Theorem has become a key tool in the subject, and related developments in functional transcendence are now having an impact in other parts of diophantine geometry.
Key recent breakthroughs include Habegger and Pila’s proof of the Zilber-Pink conjecture for curves in abelian varieties, Tsimerman’s proof of the André-Oort conjecture for Ag, and work by Dimitrov, Gao, and Habegger on uniformities in Faltings’ Theorem. There have also been significant developments by Binyamini around the Pila-Wilkie Theorem towards effectivity and improved bounds.
This summer school will feature three short courses, each comprised of five lectures. The school is aimed at a wide audience of graduate students and early career researchers; the requisite background material from model theory and o-minimality will be covered at the start of the week. Daily afternoon tutorial sessions will allow students time to work on problems and to ask questions.
Paola D’Aquino (Caserta)
Lars Kühne (Copenhagen)
Jonathan Pila (Oxford)
Gareth Jones (Manchester)
Alex Wilkie (Manchester, Oxford)