1st: 2020-03-06: Budapest /// 2nd: 2020-09-22: Vienna - on Zoom /// 3rd: 2021-09-30: Budapest ///
4th: 2022-04-27: Vienna /// 5th: 2023-03-17: Budapest /// 6th: 2023-10-06: Vienna ///
7th: 2024-03-08: Budapest /// 8th: 2024-10-04: Vienna /// 9th: 2025-03-28: Budapest
Venue: ISTA
Outbound trains Budapest Keleti --> Wien Hbf: 07:40 - 10:20 /// 08:40 - 11:20 /// 09:40 - 12:20
Title: The Brownian Web Distance
Abstract: The random walk web distance is a natural directed distance on the trajectory of coalescing simple random walks. It is given by the number of jumps between different random walk paths when one is only allowed to move in one direction. The Brownian web distance is the scale-invariant limit of the random walk web distance and it can be described in terms of the Brownian web. It is integer-valued and has scaling exponents 0:1:2 as compared to 1:2:3 in the KPZ world. The shear limit of the Brownian web distance is still given by the Airy process. A weighted version of the random walk web distance converges to a new explicit distribution that interpolates between the Gaussian and the GUE Tracy-Widom distribution. Based on joint work with Bálint Virág.
Title: Spin Glasses and the Parisi Formula
Abstract: Spin glasses are models of statistical mechanics in which a large number of elementary units interact in a disordered manner. One of the main results of the theory is the Parisi formula, which describes the limit of the free energy of these systems. The goal of my talk will be to present this formula and some open problems that relate to it, as well as partial progress.
Title: The Zigzag Strategy for Random Band Matrices
Abstract: Random band matrices have entries concentrated in a narrow band of width W around the main diagonal, modeling systems with spatially localized interactions. We consider one-dimensional random band matrices with bandwidth W >> N^½, general variance profile, and arbitrary entry distributions. We establish complete isotropic delocalization, quantum unique ergodicity (eigenstate thermalization), and Wigner-Dyson universality in the bulk of the spectrum. The key technical input is a family of local laws capturing the spatial decay of resolvent entries, established using a combination of Ornstein-Uhlenbeck dynamics and Green function comparison (the Zigzag strategy). Based on joint work with László Erdős.
Dinner will be at Pizzeria Riva Favorita, Favoritenstraße 4-6, 1040 Vienna, from 6pm. The restaurant is close to U1 station "Taubstummengasse" which is one stop to "Südtiroler Platz/Hauptbahnhof" for those returning to Budapest at 19:42 or 20:37 (arriving at Budapest-Keleti at 22:19 or 23:19).
Participants who wish to stay overnight in Vienna are kindly asked to make their own arrangements for accommodation.
Please see here for directions.