CMI-HIMR Summer School on Unlikely Intersections in Diophantine Geometry
Date: 22 - 26 August 2022
Location: University of Oxford
Event type: Research School
Organisers: Gareth Jones (Manchester) and Alex Wilkie (Manchester and 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.
Short Course Lecturers
Gal Binyamini (Weizmann), Counting rational points on transcendental sets
Laura Capuano (Roma Tre), Unlikely intersection problems
Gabriel Dill (Oxford), Functional transcendence in diophantine geometry
The summer school will also feature guest lectures from Paola D’Aquino (Caserta), Lars Kühne (Copenhagen), and Jonathan Pila (Oxford).
Registration: Please register your interest by completing the application form; your c.v. and a short supporting letter from your PhD supervisor will be required with your application. Closing date for registration is 31 May 2022. Successful applicants will be notified by 15 June 2022. Student places are offered with accommodation and meals.
This postgraduate mathematics summer school is jointly funded by the Clay Mathematics Institute, the Heilbronn Institute for Mathematical Research and the Mathematical Institute at the University of Oxford.
We are regularly reviewing the Covid-19 situation and our current intention is to run an in-person residential program. Should we find ourselves unable to run an in-person program, it would be our intention to move to an online program.