The Square of the Riemann Zeta Function Gives Rise to Critical Multiplicative Chaos

Explore the fascinating intersection of multiplicative chaos and number theory in this mathematical lecture that examines how the square of the Riemann zeta function connects to critical multiplicative chaos. Delve into the recent discoveries showing strong connections between multiplicative chaos—a class of random measures—and number theoretic objects including L-functions, character sums, and the phenomenon of "better than square-root cancellation." Learn about the Saksman-Webb conjecture proposing that integrating test functions against absolute powers of the Riemann zeta function should give rise to multiplicative chaos measures, with particular focus on zeta squared corresponding to critical chaos. Discover the proof of this conjecture for the square case through joint work with Saksman and Webb, presented with a gentle introduction to these complex problems and insights into the main proof techniques that may have broader mathematical applications. Gain understanding of how this research advances our knowledge of the deep relationships between random processes and fundamental number theoretic functions.