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Andre Leclair - “New Perspectives on the Riemann Hypothesis”

Stanford University APPLIED PHYSICS/PHYSICS COLLOQUIUM Tuesday, February 26, 2019 4:30 p.m. on campus in Hewlett Teaching Center, Rm. 201 Andre Leclair Cornell University “New Perspectives on the Riemann Hypothesis” The Riemann Hypothesis is widely considered as the greatest unsolved problem in pure mathematics, conjectured nearly over 160 years ago. Its importance is for the many far-reaching implications for the distribution of prime numbers. In this colloquium, I will first review these well-known facts and history, with some emphasis on the appearance of Riemann’s zeta function in physics, in particular in quantum statistical mechanics. I will then outline some recent work that offers a clear strategy towards proving the Riemann Hypothesis. One such strategy is based on an analogy with random walks and stochastic time series. As a concrete application of these ideas, I will explain how I calculated the google-th Riemann zero. This lecture is dedicated to Shoucheng Zhang. In discussions with him in the last year I learned that he had a deep interest and knowledge of this problem, and some interesting ideas about it.