Many problems in number theory can be phrased as counting problems. How many solutions are there to this Diophantine equation? How many values of this polynomial are perfect squares? How many of these exponential sums are large? We will give a taste of several, quite different, counting problems with connections and applications ranging from algebraic number theory to PDE’s. In each case, we will show how methods from analytic number theory can help us count. This talk aims to be accessible to mathematicians from all areas, and will also highlight open problems.
Lillian B. Pierce, Duke University
2023 AWM Research Symposium