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Abstracts for Hausdorff School on Log-correlated Fields

Alternatively have a look at the program.

Mini-course: Random matrices and logarithmically correlated fields, Part 2

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Speaker: 
Paul Bourgade
Affiliation: 
NYU
Date: 
Wed, 2018-06-13 09:00 - 10:45
Location: 
MPIM Lecture Hall

For info: the Part 1 will take place in Lipschitz Saal at Uni Bonn (Endenicher Allee 60), Monday 11th June, 14h00-15h45.

Short talk: The Fyodorov-Bouchaud formula and Liouville conformal field theory

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Speaker: 
Guillaume Rèmy
Affiliation: 
ENS Paris
Date: 
Wed, 2018-06-13 11:15 - 11:45
Location: 
MPIM Lecture Hall

Starting from the restriction of a 2d Gaussian free field (GFF) to the unit circle one can define a Gaussian multiplicative chaos (GMC) measure whose density is formally given by the exponential of the GFF. In 2008 Fyodorov and Bouchaud conjectured an exact formula for the density of the total mass of this GMC. In this talk we will explain how to prove rigorously this formula by using the techniques of conformal field theory.

Short talk: First order asymptotic of Liouville four-point correlation function and the conformal bootstrap

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Speaker: 
Guillaume Baverez
Affiliation: 
Cambridge
Date: 
Wed, 2018-06-13 11:45 - 12:15
Location: 
MPIM Lecture Hall

Based on the rigorous path integral formulation of Liouville conformal field theory introduced by David-Kupiainen-Rhodes-Vargas, we compute the first order asymptotic of the four-point correlation function on the sphere as two insertions get close together, which is expected to describe the density of vertices around the root of large random planar maps.

Mini-course: Riemann zeta function and log-correlated fields, Part 2

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Speaker: 
Jon Keating
Affiliation: 
Bristol
Date: 
Wed, 2018-06-13 14:00 - 15:45
Location: 
MPIM Lecture Hall

For info, the Part 1 will take place in Lipschitz Saal, Uni Bonn (Endenicher Allee 60),
Tuesday 12th June, 9h00-10h45.

Freezing transition for the Riemann zeta function on a short interval

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Speaker: 
Louis-Pierre Arguin
Affiliation: 
CUNY Stony Brook
Date: 
Wed, 2018-06-13 16:15 - 17:15
Location: 
MPIM Lecture Hall

In this talk, we will present a proof of the freezing transition for the Riemann zeta function as conjectured by Fyodorov, Hiary & Keating. The connection with log-correlated fields will be emphasized. The problem is related to understanding moments of zeta on a typical short interval. The proof relies on techniques developed to understand the leading order of the maximum of zeta. If time permits, we will discuss the “one-step replica symmetry breaking behaviour” (1-RSB) which can be proved for a simplified model of zeta.

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