[ Speakers  Schedule  Travel information  Contacts  Abstracts ]
The Number Theory Days are organised for the third time by Eva Bayer Fluckiger (EPFL) and Richard Pink (ETHZ) , and will be held this year in Zurich.
To announce your participation and for any related questions please contact Christina Buchmann.
The talk on Thursday will take place in ... to be announced.
On Friday the lectures will take place in
room HG G43 (HermannWeyl Room).
 Umberto Zannier  On rational curves on affine subsets of ${\bf P}_2$ and conjectures of Vojta 
 Andrei Yafaev  On the AndréOort conjecture 
 Dinner 
 Ariane Mézard  Introduction to padic Langlands programm 
 Henri Darmon  On the ranks of MordellWeil groups over towers of Kummer exensions 
 Lunch break  
 Philippe Michel  On some problems of Linnik 
How to reach the ETH Zurich.
Christina Buchmann (Secretary):

Umberto Zannier (Scuola Normale Superiore di Pisa) 

On rational curves on affine subsets of {\bf P}_2 and conjectures of Vojta 
Abstract: 
In recent
joint work with P. Corvaja we investigate the regular morphism f: P_1\setminus
S\to P_2\setminus D, where S is a finite subset and D is the sum of two
lines and a conic. This case is special but significant, since it lies at
the boundary of what is known concerning a conjecture of Vojta for integral
points on affine subsets of P_2.


Andrei Yafaev (University College London) 

On the AndréOort conjecture 
Abstract: 
This is a
joint work with Bruno Klingler. 

Ariane Mézard (École normale supérieure) 

Introduction to padic Langlands programm 
Abstract: 
We present an introduction to the padic Langlands program, which was intiated by C. Breuil. We expect that it will be a correspondence between certain padic Galois representations of Gal(\overline{{\bf Q}}_p/{\bf Q}_p) in dimension 2 and certain padic representations of Gl2({\bf Q}_p). 

Henri Darmon (McGill Mathematics and Statistics) 

On the ranks of MordellWeil groups over towers of Kummer exensions 
Abstract: 
Let E be an elliptic curve over the rationals. I will discuss some results inspired by a question of Coates concerning the growth of the rank of E over certain towers of Kummer extensions of the form {\bf Q}(\zeta_{p^n}, q^{1/p^n}). As a numerical illustration of this result in a special case, the rank of X_0(11) over {\bf Q}(11^{1/3^n}) is shown to be equal to n. This is part of a joint work, in progress, with Ye Tian. 

Philippe Michel (Institut de Mathématiques et de Modélisation de Montpellier) 

On some problems of Linnik 

The problems of Linnik alluded to in the title ask for the distribution properties of the set of representations of a large integer by various ternary quadratic forms. By now, these problems can be approached by various methods: via harmonic analysis, modular forms and Lfunctions or, as Linnik did originally, via ergodic theory. In this talk, we survey some recent developments and generalizations of Linnik’s problems which follow either of the above approaches or which combine them. These are joint works with Elon Lindenstrauss, Manfred Einsiedler and Akshay Venkatesh. 