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 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.

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