Abstract: I will give an overview of connections between Random Matrix Theory and Number Theory, in particular connections with the theory of the Riemann zeta-function and zeta functions defined in function fields. I will then discuss recent developments in which integrability plays an important role. These include the statistics of extreme values and connections with the theory of log-correlated Gaussian fields.

Recording during the Jean-Morlet chair Research school "Coulomb gas, integrability and Painlevé equations" the March 11, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France)

Filmmaker: Luca Recanzone

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