Counting integral points in thin sets

by Prof. Lilian B. Pierce (Duke University)

Friday May 23, 2025, 10:00 AM → 11:00 AM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Many problems in number theory can be framed as questions about counting integral solutions to a Diophantine equation (say, within a certain “box”). If there are very few, or very many variables, certain methods gain an advantage, but sometimes there is extra structure that can be exploited as well. For example: let f be a given polynomial with integer coefficients in n variables. How many values of f are a perfect square? A perfect cube? These questions arise in a variety of specific applications, and also in the context of a general conjecture of Serre on counting points in thin sets. We will survey recently developed sieve methods that can exploit this type of structure to bound the number of integral points in affine thin sets.