Workshop on Arithmetic Geometry: Diophantine Approximation and Arakelov theory
Description
The workshop will be centered around topics in arithmetic geometry, particularly topics that are linked to diophantine approximation and Arakelov theory:
- Arakelov theory, including p-adic and "infinity-adic"
- Generalized rings and schemes
- Arithmetic of higher dimensional algebraic varieties
- Arc spaces and related problems
- Arithmetic Riemann-Roch theorem and applications
- Polylogarithms, regulators, and Arakelov motivic complexe
Confirmed Speakers: (speaker abstracts)
| Amnon Besser (Ben Gurion University) Enrico Bombieri (Institute for Advanced Study) Jean-Benoit Bost (CNRS)) José Ignacio Burgos (Barcelona) Antoine Chambert-Loir (IRMAR / UFR Math�matiques) Jean-Louis Colliot-Thélène (CNRS/Université Paris-Sud) Caterina Consani (Johns Hopkins) Pietro Corvaja (Udine) Jan-Hendrik Evertse (University of Leiden) Kálmán Gyõry (University of Debrecen) Eugene Ha (Johns Hopkins University) |
Philipp Habegger (ETH Zurich) |
Schedule
| 09:00 to 09:30 |
Welcome and Introductions
Paul Vojta, University of California Berkeley |
| 09:30 to 10:30 |
Linear projections and successive minima
Christophe Soul |
| 10:30 to 11:00 |
Coffee Break
|
| 11:00 to 12:00 |
Lefschetz theorems on arithmetic schemes
Jean-Benoit Bost |
| 12:00 to 13:30 |
Lunch Break
|
| 13:30 to 14:30 |
Rationality of formal functions on arithmetic surfaces
Antoine Chambert-Loir |
| 14:30 to 15:30 |
Gross-Schoen cycles, dualising sheaves, and tautological classes
Shouwu Zhang |
| 16:00 to 17:00 |
Selmer varieties
Minhyong Kim |
| 17:00 to 18:30 |
Reception
|
| 09:00 to 10:00 |
Algebraic Dynamics
Lucien Szpiro |
| 10:00 to 11:00 |
Roots of polynomial in subgroups of F*p and applications to congruences
Enrico Bombieri |
| 11:00 to 11:30 |
Coffee Break
|
| 11:30 to 12:30 |
Runge’s method and the effective computation of integral points
Aaron Levin |
| 12:30 to 14:00 |
Lunch Break
|
| 14:00 to 15:00 |
Heights of Jacobians and rational points
Gaël Rémond |
| 15:00 to 15:30 |
Coffee Break
|
| 15:30 to 16:30 |
Panel Discussion
|
| 10:00 to 11:00 |
Integral points, divisibility between values of polynomials and entire curves on surfaces
Pietro Corvaja |
| 11:00 to 11:30 |
Coffee Break
|
| 11:30 to 12:30 |
On Vojta’s Conjecture
Yu Yasufuku |
| 12:30 to 14:00 |
Lunch Break
|
| 14:00 to 15:00 |
Unit equations having few solutions
Noriko Hirata-Kohno |
| 15:00 to 15:30 |
Coffee Break
|
| 15:30 to 16:30 |
S-unit equations in number fields: effective results, generalizations, applications, abc conjecture
Kálmán Gyõry |
| 09:00 to 10:00 |
On the notion of geometry over F1
Caterina Consani, Johns Hopkins University |
| 10:00 to 11:00 |
On vector bundles and the adele-class space
Eugene Ha |
| 11:00 to 11:30 |
Coffee Break
|
| 11:30 to 12:30 |
Line bundles with connections on projective varieties over function fields and number fields
Klaus Künnemann |
| 12:30 to 14:00 |
Lunch Break
|
| 14:00 to 15:00 |
The height of toric subvarieties
José Ignacio Burgos |
| 15:00 to 15:30 |
Coffee Break
|
| 15:30 to 16:30 |
On the p-adic analogue of hermitian line bundles
Annon Besser |
| 09:00 to 10:00 |
Integral Brauer-Manin obstruction for homogeneous spaces
Jean-Louis Colliot-Thélène |
| 10:00 to 11:00 |
On the Quantitative Subspace Theorem
Jan-Hendrik Evertse |
| 11:00 to 11:30 |
Coffee Break
|
| 11:30 to 12:30 |
Height Upper Bounds on Abelian Varieties and Algebraic Tori
Philipp Habegger |
