Dear Colleagues, We would like to invite you to the following two SPASS seminars (joint organised by UniPi, SNS, UniFi and UniSi) on Tuesday 3rd March: 14.00-15.00: Logarithmically correlated fields from large random matrices (Aula Tricerri, Dipartimento di Matematica e Informatica, Università di Firenze) by Giorgio Cipolloni (Tor Vergata). 15.00-16.00: Phi^4_d model associated with the harmonic oscillator (Aula Riunioni ex-DMA, Dipartimento di Matematica, Università di Pisa) by Reika Fukuizumi (Waseda University, Japan). Both talks will be also streamed online here: meet.google.com/ydw-gsjr-vza On behalf of the organisers, Elia Bisi ------------------- Abstract (Cipolloni): 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. ------------------- Abstract (Fukuizumi): We present recent developments in the mathematical study of the stochastic Gross–Pitaevskii equation, as a mathematical model for Bose–Einstein condensates subject to thermal fluctuations, such as those occurring near the critical temperature of condensation. In this regime, interactions between the condensate and the surrounding thermal cloud of non-condensed atoms must be incorporated in a way consistent with the fluctuation–dissipation principle, ensuring relaxation toward the correct physical equilibrium. The damping and noise terms are precisely balanced so that the dynamics formally admits a Gibbs measure associated with the Gross–Pitaevskii Hamiltonian as an invariant measure. This talk, which will be on the existence of the local / global solution, construction of the Gibbs measure, and long time behaviors, is a summary of several collaborative works with A. de Bouard, A. Debussche, A. Deya, T. Iwabuchi, L. Thomann. ————————— Elia Bisi Assistant Professor (RTT) University of Florence Department of Mathematics & Computer Science Personal homepage Florence Probability group