[ 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 (Hermann-Weyl Room).
| Umberto Zannier | On rational curves on affine subsets of ${\bf P}_2$ and conjectures of Vojta |
| Andrei Yafaev | On the André-Oort conjecture |
| Dinner |
| Ariane Mézard | Introduction to p-adic Langlands programm |
| Henri Darmon | On the ranks of Mordell-Weil groups over towers of Kummer exensions |
| Lunch break | |
| Philippe Michel | On some problems of Linnik |
How to reach the ETH Zurich.
Christina Buchmann (Secretary):
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Umberto Zannier (Scuola Normale Superiore di Pisa) |
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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.
|
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Andrei Yafaev (University College London) |
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On the André-Oort conjecture |
Abstract: |
This is a
joint work with Bruno Klingler. |
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Ariane Mézard (École normale supérieure) |
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Introduction to p-adic Langlands programm |
Abstract: |
We present an introduction to the p-adic Langlands program, which was intiated by C. Breuil. We expect that it will be a correspondence between certain p-adic Galois representations of Gal(\overline{{\bf Q}}_p/{\bf Q}_p) in dimension 2 and certain p-adic representations of Gl2({\bf Q}_p). |
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Henri Darmon (McGill Mathematics and Statistics) |
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On the ranks of Mordell-Weil 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. |
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Philippe Michel (Institut de Mathématiques et de Modélisation de Montpellier) |
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On some problems of Linnik |
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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 L-functions 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. |