Abstract:
The study of uniform distribution of sequences is more than a century old, with pioneering work by Hardy and Littlewood, Weyl, van der Corput and others. More recently, the focus of research has shifted to much finer quantities, such as the distribution of nearest neighbor gaps and the pair correlation function. Examples of interesting sequences for which these quantities have been studied include the zeros of the Riemann zeta function, energy levels of quantum systems, and more. In this expository talk, I will discuss what is known and discuss the many outstanding problems that this theory has to offer.

Biography:
Zeev Rudnick is the Cissie and Aaron Beare Chair in Number Theory at Tel Aviv University,  specializing in Number Theory and Quantum Chaos.
Prior to his appointment at Tel Aviv in 1995, he was an Assistant Professor at Princeton and in Stanford. He received his PhD from Yale in 1990.
He was awarded the Erdos prize of the Israel Mathematical Union (2001), appointed a Fellow of the American Mathematical Society, 2012-, and awarded  ERC Advanced Grants in 2013 and 2019.
He was a 45-minute Invited Speaker at ICM in Seoul (2014), the Aisenstadt Chair, CRM Montreal  (2014),   the David Rees Distinguished Visiting Fellow, University of Exeter, 2017, the Heilbronn Distinguished Visiting Professor, University of Bristol, 2019.
He is the Executive Editor of the journal International Mathematics Research Notices (IMRN), published by Oxford University Press.

Recording: https://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=Beyond_uniform_distribution.html