July 20, 2024

July-December, 2008

Organizing Committee:

John Bland (Toronto)
Caterina Consani (Johns Hopkins)
Stephen Kudla (Toronto)

Min Ru (Houston)
Paul Vojta (UC Berkeley)
Pit-Mann Wong (Notre Dame)
Colloquium Chair

Steven Lu (UQAM)



Grant no:

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

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Outline of Scientific Activities

The theory of diophantine geometry has a long rich history dating back all the way to the Greek schools and culminating in the great breakthrough in the 1980s by Faltings in the resolution of the Mordell Conjecture and the proof by Wiles of Fermat’s Last Theorem in 1994 concerning the non-existence of integer solutions of the Fermat polynomial xn + yn = zn . A natural next step is to study analogous questions in higher dimension, namely, solutions of polynomials of more variables. Analogous questions are also investigated by algebraic geometers, searching for solutions over function fields; by complex geometers, searching for meromorphic solutions. Techniques and theories developed in various different branches of mathematics can be brought together to solve these and other problems. One of the goals of this program is to provide a platform of communication by bringing together researchers from different fields.

Clay Mathematics Institute Senior Scholar

Henri Gillet, Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago

The Clay Mathematics Institute Senior Scholars program aim is to foster mathematical research and the exchange of ideas by providing support for senior mathematicians who will play a central role in a topical program at an institute or university. Senior Scholars will be in residence for a substantial fraction of the program and are expected to interact extensively with the other participants.

University of Toronto, Faculty of Arts and Science, Dean's Distinguished Visiting Professor

Yum-Tong Siu, Mathematics Department, Harvard

The University of Toronto, Faculty of Arts and Science Dean's Distinguished Visiting Professor/ Fields Senior Scholar program is designed to intensify the mathematical research and interaction at Fields by enabling distinguished senior mathematicians to visit for one to two semesters each year, and be active participants in the program activities at the Fields Institute during their tenure. During his residency at Fields Professor Siu will teach a semester long course at the graduate level on a topic related to the thematic program.
(See the course timetable for the schedule)

Coxeter Lecture Series

September 29-October 1, 2008
Shou-Wu Zhang, Columbia University
Periods, Heights, L-values

Distinguished Lecture Series

Week of November 12-14, 2008
Yum-Tong Siu, Mathematics Department, Harvard

Workshops, Mini-workshops and Colloquiums

September 17, 2008
Joint Colloquium with Department of Mathematics, 3:30 p.m, Room 230 Fields
Speaker: Paul Vojta (UC Berkeley)

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)

The workshop will be centered around the topics in arithmetic geometry of current interest such as Arithmetic of higher dimensional algebraic varieties, Arithmetic Riemann-Roch and applications, Galois theory and fundamental groups, Arc spaces and related problems, p-adic Arakelov theory.

October 27-28, 2008
Mini-workshop on p-adic dynamics

Organizer: Joseph Silverman
Speakers: Rob Benedetto, Robert Rumely and Joseph Silverman

Affiliated Activity
November 8- 9, 2008 Workshop on Arithmetic and Hyperbolic Geometry
To be held in UQAM, Montreal
Organizing Committee: A. Granville, S. Lu, P. Russell, N. Yui
Scientific Committee: H. Gillet, K.-F. Liu, M. McQuillan, J. Noguchi, M. Ru, Y.T. Siu, P. Vojta, P.-M. Wong
.One of its aims is to bring together people who may be interested in the program at the Fields Institute but who are unable to attend the part that may be of interest to them. Another is to explore the possible connections of recent advances in our understanding of the geometry of complex algebraic varieties that would be of relevance to the program.

November 10 - 14, 2008
Mini-workshop on complex dynamics

Organizers: Jeff Diller, Eric Bedford
Speakers: Nessim Sibony, Mattias Jonsson, Henri De Thelin, Jeff Diller, Eric Bedford

November 17-21, 2008
Workshop on Complex Hyperbolic Geometry and Related Topics
Organizing Committee: Jean-Pierre Demailly (Grenoble I), Junjiro Noguchi (Tokyo), Min Ru (Houston)
Bernard Shiffman-(Chair) (Johns Hopkins University), Yum-Tong Siu (Harvard), Paul Vojta (UC Berkeley)

The workshop will be centered around the topics in hyperbolic geometry, particularly topics that are linked to diophantine approximations:

  • Problems related to complex hyperbolicity,
  • Jets, multiplier ideal sheaves and applications,
  • Diophantine approximations over function fields,
  • Correspondence between hyperbolic geometry and diophantine approximation,
  • Nevanlinna theory and distributions of zeros

November 25, 2008 -- 4pm,
Clay Mathematics Institute Public Lecture
Henri Gillet, Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago
What is infinity factorial (and why might we care)?
held in Fields, Room 230

Graduate courses

  • Arakelov Geometry
  • Nevanlinna theory and Diophantine approximation
  • Jet spaces and motivic integration.


Weekly seminars are planned and will involve survey and expository talks by experts.

Apply to the Program:
All scientific events are open to the mathematical sciences community. Visitors who are interested in office space or funding are requested to apply by filling out the application form. Additional support is available (pending NSF funding) to support junior US visitors to this program. Fields scientific programs are devoted to research in the mathematical sciences, and enhanced graduate and post-doctoral training opportunities. Part of the mandate of the Institute is to broaden and enlarge the community, and to encourage the participation of women and members of visible minority groups in our scientific programs.

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