HIGHER DIMENSIONAL VARIETIES AND RATIONAL POINTS

Alfréd Rényi Institute of Mathematics,

Budapest, Hungary, September 2 - September 22, 2001

The Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences which has recently been awarded the grant Centre of Excellence of the European Union, will host a 3 week programme in September 2001, in cooperation with The Erdős Summer Institute, and the European networks EAGER and Arithmetic Algebraic Geometry. This event is supported by the EU High Level Scientific Conferences Project (proposal HIGHARITHM, contract No. HPCF 2001-00062).

Co-chair:

Jean-Louis Colliot-Thélène (Orsay)
János Kollár (Princeton University).

Organizing Committee: Károly Böröczky, Jr., András Némethi and Tamás Szamuely.

List of participants

Accomodation information

Arrival information

Aim and scope

The programme is organized in order to encourage collaboration between specialists in higher dimensional complex geometry and those studying arithmetic/diophantine questions. In recent years it became apparent that the powerful geometric tools elaborated in connection with Mori's Minimal Model Program have applications over arithmetic ground fields as well. We hope that bringing together experts and graduate students specialising in higher dimensional geometry or arithmetic will induce further cross-fertilization between the two fields and give rise to new powerful results.

Main topics:

classification and minimal models of varieties

rationally connected varieties

rational and integral points

fundamental groups and Galois groups

Programme

Week 1 (3-7 September): Instructional Conference (Euro Summer School)

Schedule of lectures

Abstracts of lecture courses:

J.-L. Colliot-Thélène (Orsay, France): Rational points on fibrations"
O. Debarre (Strasbourg, France): "Fano varieties" For lecture notes, click here.
B. Hassett (Houston, USA): "Density of rational points on K3 surfaces and their symmetric products"
J. Kollár (Princeton, USA): "Rational curves on varieties"
S. Kovács (Seattle, USA):"Families of varieties of general type: the Shafarevich conjecture and related problems" For slides of the lecture, click here.
E. Peyre (Grenoble, France): "Points of bounded height and geometry of Fano varieties"
Weeks 2 & 3 (8-22 September):

Research Programme (Euro Workshop)

These two weeks (8-22 September) following the Instructional Conference are mainly devoted to research work and informal discussions of a limited number of participants. There is a research seminar featuring roughly two lectures a day, usually in the morning. These are complemented by informal seminars in the afternoon, for smaller groups of participants. Ample time is left for free discussions.
Programme of research seminar

Funding

The programme is supported by the EU Center of Excellence and High Level Scientific Conferences projects and by the Paul Erdös Centre. We can cover accomodation and travel costs for selected participants. The instructional conference is agreed by the TMR network on "Arithmetic Geometry"; participants coming from a node of this network and requiring travel support should contact their local coordinator.

Contact

For further inquiries send an email to
arithgeo@renyi.hu
or contact one of the local organizers by regular mail at the following address:

HIGHER DIMENSIONAL VARIETIES AND RATIONAL POINTS

Alfréd Rényi Institute of Mathematics,

Budapest, Hungary, September 2 - September 22, 2001

Aim and scope

Programme

Week 1 (3-7 September): Instructional Conference (Euro Summer School)

Weeks 2 & 3 (8-22 September):

Research Programme (Euro Workshop)

Funding

Contact