# Hausdorff School on Log-correlated Fields

Dates: June 11 - 13, 2018

Venue: Lipschitz-Saal, Endenicher Allee 60

Organizers: GaĆ«tan Borot (Bonn), Anton Bovier (Bonn), Margherita Disertori (Bonn), Patrik Ferrari (Bonn)

### Details

The properties of log-correlated fields, and in particular their extreme values, are very interesting and actively studied due to their multiscale nature - the two-dimensional Gaussian free field is perhaps one of their simplest realisation. They form a universality class which is as common in mathematics as 2d conformal field theory is in statistical physics. In the past ten years, an increasing number of results show that several objects exhibit properties similar to log-correlated fields

(1) branching Brownian motion

(2) the logarithm of the absolute value of the characteristic polynomial of a random matrix

(3) the absolute value of the Riemann zeta on the critical line.

The study of these problems is often interrelated, involving ideas imported from random matrix theory, analytic number theory, and stochastic processes, and benefits from physical arguments based, e.g., on the replica trick and the study of random energy landscapes. The conjectures of Fyodorov, Hiary and Keating, in particular, carries information from (2) to (3), extending the older connection between random matrices and L-functions, and the last years have witnessed significant mathematical progress on the random matrix theory side (Fyodorov, Keating, and many others), as well as in proving properties of the extreme of Zeta (Bourgade, Arguin, Najnudel, and many others).

### Speakers:

- Lisa Hartung (New York)
- Paul Bougarde (New York)
- Jon Keating (Bristol)

In case you are interested in participating, please fill out the application form. The deadline for applications is 30th March 2018. All applications, submitted after that will be considered on an individual basis.