Thematic Program on Arithmetic Geometry, Hyperbolic Geometry and Related Topic
July 1  December 31, 2008
Description
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 nonexistence of integer solutions of the Fermat polynomial x^{n} + y^{n} = z^{n} . 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


YumTong 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)

Workshops and Conferences
Seminars

July 1, 2008 to June 30, 2009
Special and Public Lectures

September 29  October 1, 2008

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 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.