CMI Workshop: Rational Curves and Diophantine Problems over Function Fields

Workshop Outline: Rational Points and Rational Curves

There is a well-known and very strong analogy between the existence and properties of rational points on varieties defined over number fields (or over finite fields, p-adic fields, etc.) and the existence and properties of rational curves on complex varieties. One example of this is the Lang conjecture together with its conjectural converse. Historically "rational curve" results have been far simpler than the analogous "rational point" results. This workshop will bring together experts in both types of results to discuss what has been proved on the rational points side of the picture, and possible directions for future research on rational curves inspired by questions about rational points.

A second purpose is to bring together experts to investigate a very focused question. more....

Schedule

Friday, November 2

9:30-10:00 Registration
10:00-11:00 Bjorn Poonen, Speculations about Rational Curves on Varieties over Countable Fields
11:30-12:30 Kirsten Eisentraeger, Hilbert's Tenth Problem for Function Fields of Varieties over C
12:30-2:30 Lunch
2:30-3:30 Max Lieblich, Some Basic Arithmetic Questions about Moduli Spaces of Vector Bundles on Curves
4:00-5:00 TBA

Saturday, November 3

9:30-10:30 János Kollár, Diophantine Subsets of Function Fields of Curves
11:00-12:00 James McKernan, On the Sarkisov Program
12:00-2:00 Lunch
2:00-3:00 Chenyang Xu, Congruence for Rational Points over Finite Fields and Coniveau over Local Fields
3:30-5:00 Problem Session

Sunday, November 4

9:30-10:30 Jason Starr, Rational Points of Varieties over Function Fields beyond Rational (higher) Connectedness
11:00-12:00 Izzet Coskun, Vanishing of Quantum Cohomology
12:00-2:00 Lunch
2:00-3:00 Tom Graber, Restriction of Sections for Families of Abelian Varieties
3:30-4:30 Group discussion on future developments

Abstracts

Visitor Information

Organizers

Participants