June 11 - 14, 2018

Lipschitz-Saal, Endenicher Allee 60

Organizers: Gaëtan Borot (Bonn), Anton Bovier (Bonn), Margherita Disertori (Bonn), Patrik Ferrari (Bonn)

Description: Log-correlated fields, and in particular their extreme values, have rich properties due to their multiscale nature. They form a universality class with many realizations in physics and mathematics – the twodimensional Gaussian free field being the simplest example. Results of the past ten years exhibit properties similar to log-correlated fields in

• branching Brownian motions,
• the logarithm of a characteristic polynomial of a random matrix
• the values of Riemann zeta on the critical line

The study of these problems is often interrelated, importing ideas from random matrix theory, analytic number theory, and stochastic processes, and benefits from physical arguments like the replica trick and the study of random energy landscapes, sometimes leading to far-reaching conjectures. This summer school aims at giving a unified introduction of these topics in light of the recent advances. It consists of three mini-courses, completed by a small number of research talks, and short talks by young researchers.

Lecture Series by: 

• Paul Bourgade (NYU): Random matrices and logarithmically correlated fields
• Lisa Hartung (NYU): Extreme level sets of branching Brownian motion
• Jon Keating (Bristol): Riemann zeta function and log-correlated fields

 Speakers:

• Louis-Pierre Arguin (CUNY): Freezing transition for the Riemann zeta function on a short interval
• Reda Chhaibi: A conjecture relating the Gaussian Multiplicative Chaos and Random matrices, on the circle
• Alexander Drewitz (Köln): The maximum particle of branching random walk in spatially random branching environment
• Oren Louidor (Technion): On the extreme and large-value landscape of the discrete Gaussian free field and friends
• Bastien Mallein (Paris 13): Infinitely ramified point measure and branching Lévy process
• Joseph Najnudel (Cincinnati): On the extreme values of the Riemann zeta function on random intervals of the critical line
• Sasha Sodin (Queen Mary): Gaussian fluctuations of interlacing sequences

Short Talks:

• Guillaume Baverez: First order asymptotic of Liouville four-point correlation function and the conformal bootstrap
• Maximilian Fels: Extreme values of the scale-dependent discrete Gaussian Free Field
• Anton Klimovsky: Complex random energy models
• Stephen Muirhead: The phase transition for level sets of smooth planar Gaussian fields
• Guillaume Remy: The Fyodorov-Bouchaud formula and Liouville conformal field theory
• Santiago Saglietti: A strong law of large numbers for supercritical BBM with absorption

 The deadline for applications was 30th March 2018.