09:50–10:00

10:00–10:40 Leonid Pastur (Kharkov): Large block asymptotics of entanglement entropy of free fermions

10:45–11:10

11:10–11:50 David Khmelnitskii (Cambridge): TBA

12:00–12:40 Uzy Smilansky (Rehovot): Anderson Localization in the time domain

12:45–14:30

14:30–15:10 Senya Shlosman (Marseille): A (four-parameter) continuum of extremal states of the Ising model in 3D halfspace

15:20–16:00 Konstantin Khanin (Toronto): On global solutions to the random heat equation

16:05–16:30

16:30–17:10 Dmitry Dolgopyat (Maryland): Limit theorems for circle rotations

17:30–18:30

18:30–19:30 Ensemble Le Basile: Arithmetic, Geometry, Music, Astronomy: Hearing the Medieval Quadrivium

10:45–11:10

11:10–11:50 Mariya Shcherbina (Kharkov): Local eigenvalue statistics of 1d random band matrices

12:00–12:40 Leonid Bunimovich (Atlanta, GA): Finite time dynamics

12:45–14:30

14:30–15:10 Barry Simon (Pasadena, CA): Szegő–Widom asymptotics for Chebyshev polynomials on subsets of

15:20–16:00 Frederic Klopp (Paris): Resonances for large random samples

16:05–16:30

16:30–17:10 Günter Stolz (Birmingham, AL): Disordered quantum spin chains

17:20–18:00 Gian-Michele Graf (Zurich): The bulk-edge correspondence for disordered chiral chains

10:35–11:15 Yuri Kifer (Jerusalem): Limit theorems for non-conventional arrays

11:20–11:40

11:40–12:20 Martin Zerner (Tübingen): Recurrence and transience of some contractive Markov chains with super-heavy tailed innovations in random environment

12:25–13:05 Alain-Sol Sznitman (Zurich): On porous interfaces and disconnection

13:10–14:30

10:45–11:10

11:10–11:50 Alex Furman (Chicago, IL): Simplicity of the Lyapunov spectrum via Boundary theory

12:00–12:40 Yves Guivarc'h (Rennes): Spectral gap properties and asymptotic of extreme values for multivariate affine stochastic recursions

12:45–14:30

14:30–15:10 Svetlana Jitomirskaya (Irvine, CA): TBA

15:20–16:00 Stanislav Molchanov (Charlotte, NC): On the spectrum of the Schrödinger operator associated with the Dyson-Vladimirov Laplacian: cases of the fast-decreasing potentials and the Anderson model

16:05–16:30

16:30–17:10 Shin'ichi Kotani (Osaka): KdV equation with ergodic initial data

17:20–18:00 Abel Klein (Irvine, CA): Manifestations of localization in the random XXZ spin chain

18:30–∞

10:30–11:10 Christophe Sabot (Lyon): Reinforced random walks, random Schrödinger operators and hitting times of Brownian motions

11:15–11:35

11:35–12:15 Xiaoqin Guo (Madison, WI): Quantitative homogenization and Harnack inequality for a degenerate nondivergence form random difference operator

12:20–13:00 Erwin Bolthausen (Zurich): On the Thouless – Anderson – Palmer equations for the perceptron

13:00–13:30

We are interested in solutions having complicated oscillation such as of almost periodicity or more generally ergodicity. Algebro-geometric quasi-periodic solutions had been known in the early stage of the research. This case is exactly corresponding to the Schrödinger operators with finite gaps and the reflectionless property on the spectrum. In 1994 Egorova had succeeded to obtain limit periodic solutions. Recently in 2016 Damanik-Goldstein got a certain analytic quasi-periodic solutions, but they had to assume smallness of the initial data. The purpose of the present talk is to develop an algebraic method discovered by Sato and his school. In this trial the representation of the tau-functions by the Weyl-Titchmarsh functions is crucial. So far what we could show is the possibility of the construction of the solutions with ergodic initial data satisfying

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