October  3, 2023


October 20-24, 2008
Workshop on Arithmetic Geometry: Diophantine Approximation and Arakelov theory

Organizing Committee:


Caterina Consani (Johns Hopkins)
Henri Gillet (Co-Chair) (UIC)
Yuri Manin (Northwestern)
Paul Vojta (Co-Chair) (UC Berkeley)
Umberto Zannier (SNS Pisa)

Supported partially by Grant-in-Aid for Scientific Research (S) 17104001,

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 Mathématiques)
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)
Noriko Hirata-Kohno (Nihon University)
Klaus Künnemann (Universität Regensburg)
Minhyong Kim (University College London)
Aaron Levin (Scuola Normale Superiore)
Gaël Rémond (Institut Fourier)
Christophe Soulé (IHES)
Lucien Szpiro (CUNY)
Gisbert Wüstholz (ETH-Zurich)
Yu Yasufuku (CUNY))
Shouwu Zhang (Columbia)

Workshop Schedule

Monday October 20, 2008
9:00-9:30 am Welcome and Introduction
Paul Vojta and Juris Steprans
9:30-10:30 am

Christophe Soulé
Linear projections and successive minima

10:30-11:00 am Coffee Break
11:00-12:00 pm Jean-Benoit Bost
Lefschetz theorems on arithmetic schemes
12:00-1:30 pm Lunch Break
1:30-2:30 pm Antoine Chambert-Loir
Rationality of formal functions on arithmetic surfaces
2:30-3:30 pm Shouwu Zhang
Gross-Schoen cycles, dualising sheaves, and tautological classes
3:30-4:00 pm Coffee Break
4:00-5:00 pm Minhyong Kim
Selmer varieties
5:00-6:30 pm Reception- cash bar
Fields Institute
Tuesday October 21, 2008
9:00-10:00 am Lucien Szpiro
Algebraic Dynamics
10:00-11:00 am Enrico Bombieri
Roots of polynomial in subgroups of F*p and applications to congruences
11:00-11:30 am Coffee Break
11:30-12:30 pm Aaron Levin
Runge’s method and the effective computation of integral points
12:30-2:00 pm Lunch Break
2:00-3:00 pm Gaël Rémond
Heights of Jacobians and rational points
3:00-3:30 pm Coffee Break
3:30-4:30 pm Panel Discussion
Wednesday October 22, 2008
10:00-11:00 am Pietro Corvaja
Integral points, divisibility between values of polynomials and entire curves on surfaces
11:00-11:30 am Coffee Break
11:30-12:30 pm Yu Yasufuku
On Vojta’s Conjecture
12:30-2:00 pm Lunch Break
2:00-3:00 pm Noriko Hirata-Kohno
Unit equations having few solutions
3:00-3:30 pm Coffee Break
3:30-4:30 pm Kálmán Gyõry
S-unit equations in number fields: effective results, generalizations, applications, abc conjecture
Thursday October 23, 2008
9:00-10:00 am Caterina Consani
On the notion of geometry over F1
10:00-11:00 am Eugene Ha
On vector bundles and the adele-class space
11:00-11:30 am Coffee Break
11:30-12:30 pm Klaus Künnemann
Line bundles with connections on projective varieties over function fields and number fields
12:30-2:00 pm Lunch Break
2:00-3:00 pm José Ignacio Burgos
The height of toric subvarieties
3:00-3:30 pm Coffee Break
3:30-4:30 pm Amnon Besser
On the p-adic analogue of hermitian line bundles
Friday October 24, 2008
9:00-10:00 am Jean-Louis Colliot-Thélène
Integral Brauer-Manin obstruction for homogeneous spaces
10:00-11:00 am Jan-Hendrik Evertse
On the Quantitative Subspace Theorem
11:00-11:30 am Coffee Break
11:30-12:30 pm Philipp Habegger
Height Upper Bounds on Abelian Varieties and Algebraic Tori


Confirmed Participants

Updated October 31, 2008

Fullname University/Affiliation
Akhtari, Shabnam University of British Columbia
An, Ta Thi Hoai Institute of Mathematics
Andrews, Rob (no affiliation)
Berczes, Attila University of Debrecen
Bertrand, Florian University of Provence
Besser, Amnon Ben-Gurion University of the Negev
Bland, John University of Toronto
Bombieri, Enrico Institute for Advanced Study
Bost, Jean-Benoit Université Paris-Sud 11
Burgos, José Ignacio Universidad de Barcelona
Chambert-Loir, Antoine IRMAR / UFR Mathématiques
Chung, Min In  
Colliot-Thélène, Jean-Louis CNRS/Université Paris-Sud
Consani, Caterina Johns Hopkins University
Corvaja, Pietro University of Udine
Curilla, Christian Universität Hamburg
Dalla Torre, Gabriele Scuola Normale Superiore
Delsinne, Emmanuel University of Ottawa
Desrochers-Guérin, Félix UQAM
Dethloff, Gerd Université de Brest
Dulock, Matthew University of Houston
Evertse, Jan-Hendrik University of Leiden
Faber, Xander McGill University
Gasbarri, Carlo Universita' di Roma "Tor Vergata"
Gillet, Henri University of Illinois at Chicago
Gotsbacher, Gerald University of Toronto
Graham, Ian University of Toronto
Gubler, Walter Humboldt Universität zu Berlin
Gyory, Kalman University of Debrecen
Ha, Eugene Johns Hopkins University
Habegger, Philipp ETH Zurich
Hirata-Kohno, Noriko Nihon University
Hoermann, Fritz Humboldt Universitaet zu Berlin
Holmstrom, Andreas University of Cambridge
Hsia, Liang-Chung National Central University
Hsu, Ho-ling National Tsing-hua University
Ih, Su-ion University of Colorado
Ingram, Patrick University of Waterloo
Jones, Nathan CRM, Universite de Montreal
Kamensky, Moshe University of Waterloo
Kawaguchi, Shu Osaka University
Kim, Kang-Tae Pohang University of Science and Technology
Kim, Minhyong University College London
Kramer, Jürg Humboldt-Universität zu Berlin
Künnemann, Klaus Universität Regensburg
Levin, Aaron Scuola Normale Superiore
Li, Chao University of Toronto
Lu, Hung Hawaii Pacific University
Lu, Steven Université du Québec à Montréal
Mahanta, Snigdhayan IHES
Mayer, Hartwig Humboldt University
McQuillan, Michael Institut des Hautes Etudes Scientifiques
Noguchi, Junjiro University of Tokyo
Petersen, Kathleen Queen's University
Posingies, Anna Universität Hamburg
Rémond, Gaël Univ. Grenoble I
Rojas, J. Maurice Texas A&M University
Rousseau, Erwan Université Louis Pasteur
Ru, Min University of Houston
Shahabi, Shahab McGill University
Shelestunova, Veronika University of Waterloo
Siu, Yum-Tong Harvard University
Soulé, Christophe IHES
Stewart, Cameron University of Waterloo
Szpiro, Lucien The CUNY Graduate Center
Takloo-Bighash, Ramin University of Illinois at Chicago
Tschinkel, Yuri Courant Institute of Mathematical Sciences
van Frankenhuijsen, Machiel Utah Valley University
Veneziano, Francesco Scuola Normale Superiore
Vojta, Paul University of California, Berkeley
von Pippich, Anna-Maria Humboldt University
Wong, Bun University of California, Riverside
Wong, Pit-Mann University of Notre Dame
Yan, Qiming Fudan University
Yao, Weihong Shanghai Jiaotong University
Yasufuku, Yu City University of New York
Yazdani, Soroosh McMaster University
Zannier, Umberto Scuola Normale Superiore di Pisa
Zhan, Cheng University of Houston
Zhang, Shou-Wu Columbia University
Zong, Ying University of Toronto


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