CRM: Centro De Giorgi
logo sns

Unlikely Intersections in Algebraic Groups and Shimura Varieties

Partially supported by AIM and NSF

28 March 2011 - 1 April 2011


This workshop, sponsored by AIM, Scuola Normale Superiore, and the NSF, will explore the recent conjectures on "unlikely intersections'' due to Zilber, Pink, and Bombieri-Masser-Zannier, and related or analogous problems in model theory, diophantine geometry, and arithmetic dynamics. A particular objective is to increase dialogue between some different interested communities whose interests centre on: (i) Shimura varieties/Andre-Oort conjecture, (ii) diophantine questions on multiplicative groups and abelian varieties, (iii) arithmetic dynamics, and (iv) mathematical logic.

Research Directions

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The lectures are open. However they shall be not of a "standard" nature, and could be organized at the last moment, depending on the mathematical issues which shall arise. In fact, this AIM meeting is mainly addressed to people who intend to develop detailed knowledge in the topics selected.