The University of Arizona

Rational numbers, rational functions, and rational points

Rational numbers, rational functions, and rational points

Series: Special Mathematics Colloquium
Location: ENR 2 s395
Presenter: Doug Ulmer, Georgia Tech

One of the central concerns of arithmetic geometry is the study of solutions of systems of polynomial equations where the solutions are required to lie in a "small" field such as the rational numbers.  I will explain the landscape of expectations and conjectures in this area, focusing on curves and their Jacobians over global fields (number fields and function fields), and then survey the significant progress made over the last decade in the function field case.  The talk is intended to be accessible to a very wide audience.

 

 

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