# Unlikely intersections in algebraic groups and Shimura varieties

March 28 to April 1, 2011

at the

American Institute of Mathematics, San Jose, California

organized by

Jonathan Pila and Umberto Zannier

## Original Announcement

This workshop will explore the recent conjectures onunlikely 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.

## Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:

Unlikely Intersections in Poincaré Biextensions over Elliptic Schemes
by  Daniel Bertrand,   Notre Dame Journal of Formal Logic 54(3-4), January 2013
Arithmetic Nullstellensatz and Nonstandard Methods
by  Haydar Göral
Relative Manin-Mumford for semi-abelian surfaces
by  Daniel Bertrand, David Masser, Anand Pillay, and Umberto Zannier
The Andre-Oort conjecture
by  Bruno Klingler and Andrei Yafaev,  Ann. of Math. (2) 180 (2014), no. 3, 867-925  MR3245009
Integer-valued definable functions
by  A. J. Wilkie, G. O. Jones, and M. E. M. Thomas,  Manchester Institute for Mathematical Sciences (MIMS)MIMS EPrint: 2012.1  MR3007661
Special points and Poincaré-extensions
by  Daniel Bertrand (with an Appendix by Bas Edixhoven)
On torsion anomalous intersections
by  Sara Checcoli, Francesco Veneziano, and Evelina Viada,  Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 25 (2014), no. 1, 1-36  MR3180478