Dear all,

Next week RoMaDS https://www.mat.uniroma2.it/~rds/events.php will host a spooky lineup of seminars at the Mathematics Department of Tor Vergata University. Here is the program (for the abstract, see below):

03.11 Giorgio Cipolloni (Tor Vergata) "Logarithmically correlated fields from large random matrices" 14h00 in Aula Dal Passo

05.11 Milton Jara (IMPA, Rio de Janeiro) "NESS for KPZ" 16h00 in Aula D'Antoni

07.11 Maurice Duits (KTH Royal Institute of Technology, Stockholm) "Integrable Structures Behind the Aztec Diamond" 14h00 in Aula D'Antoni

We encourage in-person participation. Should you be unable to come, here is the link to the Teams streaming of all of the seminars: Spooky seminars | Meeting-Join | Microsoft Teams https://teams.microsoft.com/meet/3740857632924?p=3G7X9MF2NwcSKIQczz

Best,

Michele

Abstracts

Giorgio Cipolloni (Tor Vergata) "Logarithmically correlated fields from large random matrices”

We study the Brownian evolution of large non-Hermitian matrices and show that their log-determinant converges to a 2+1 dimensional Gaussian field in the Edwards-Wilkinson regularity class, i.e. logarithmically correlated for the parabolic distance. This gives a dynamical extension of the celebrated result by Rider and Virag (2006) proving that the fluctuations of the eigenvalues of Gaussian non-Hermitian matrices converge to the Gaussian Free Field.

Milton Jara (IMPA, Rio de Janeiro) "NESS for KPZ"

We show that the fluctuations of the density of boundary driven, weakly asymmetric systems are described by energy solutions of the KPZ equation with corresponding boundary conditions. Conditioned on the uniqueness of these energy solutions, we show that the non-equilibrium stationary states (NESS) of these systems are described by the invariant measures of KPZ introduced by Barraquand, Bryc, Corwin, Knizel among others. Joint work with Juan Arroyave (IMPA).

Maurice Duits (KTH Royal Institute of Technology, Stockholm) "Integrable Structures Behind the Aztec Diamond"

The Aztec diamond, under the uniform measure on domino tilings, is one of the classic examples of an exactly solvable model in probability and statistical mechanics. Its rich geometric features—such as limit shapes and arctic boundaries—have long made it a cornerstone of integrable probability. More recently, variants of this model with doubly periodic weights have revealed that much of the underlying structure persists far beyond the uniform case and can be used to uncover new behaviors—such as regions with smooth disorder—that were previously out of reach. At the heart of these models lies a birational map that encodes their integrable character. In this talk, I will describe how this map unifies different regimes of the Aztec diamond—from uniform and periodic settings to models in random environments. I will also discuss how integrable features survive (sometimes unexpectedly) in the presence of disorder, and how they connect to other probabilistic models such as directed polymers. The presentation is aimed at a broad mathematical audience, and no prior background in tilings or integrable systems will be assumed.