Estimates for L-functions

L-functions are mathematical objects that help us understand the prime numbers and their distribution. Though studied for centuries, they remain the subject of fundamental open problems, such as the famous Riemann Hypothesis. A related problem is to determine how quickly L-functions grow.  Surprisingly, this connects to many other basic questions in number theory (such as the distribution of integral points on spheres) and quantum chaos (such as the distribution of certain high energy quantum particles). Recent advances on this problem draw from a range of mathematical fields. We will bring together experts to develop new methods for rigorously analyzing L-functions, with the goal of gaining deeper insights into these mysterious objects and tackling outstanding open problems.