Generalized Riemann Hypothesis and Brownian Motion

Event Date: 
September 28, 2022
Giuseppe Mussardo

Number Theory is arguably one of the most fascinating subjects in mathematics, while theoretical physics has helped us to shape our understanding of the laws of Nature. Both are characterized by the standards of clarity, beauty and depth. Sometimes the two subjects converge in a miraculous way, providing one of those vital, wonderful and superb narratives that are occasionally found in science.

Our story concerns the Riemann Hypothesis, certainly the most famous open problem in mathematics, but one that is not usually seen as being connected to physics. It states that the zeros of the Riemann zeta function lie on the critical line Re(s)=1/2.
Professor Mussardo will interpret and lend support to this hypothesis from the point of view of statistical physics, which suggests that the truth of the Riemann Hypothesis being a kind of arithmetical analogue of Brownian motion. He will present the probabilistic arguments which lead to this conclusion, and also discuss a battery of highly non-trivial tests which support the validity of this result with an extremely high confidence.

Speaker Bio: 
Giuseppe Mussardo is Professor of Theoretical Physics at SISSA in Trieste, where he founded and directed the Statistical Physics group for several years. He is the Editorial Director of the "Journal of Statistical Physics and Applications" (JSTAT) and author of various scientific monographs, such as "Statistical Field Theory," published by Oxford University Press. He has promoted research in quantum integrable models and opened the study of quantum field theories out of equilibrium. Among his recent research fields, there is the relation between Number Theory and Quantum Statistical Physics: in this field he has proposed and determined exactly a quantum potential having prime numbers as all and only eigenvalues, and promoted the study of the Riemann conjecture with the methods of statistical mechanics. He is the writer of several scientific documentaries, such as "Maksimovic. The Story of Bruno Pontecorvo” and “Galois. A revolutionary mathematician”. Among his awards are the Prize of the Italian Physical Society for Scientific Outreach (2013) and the Kramers Chair at the University of Utrecht (2017).