09:50–10:00

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

10:45–11:10

11:10–11:50 David Khmelnitskii (Cambridge): Tunnel transparency of a disordered system in perpendicular magnetic field

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

12:45–15:20

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 programme

10:00–10:40 Pavel Bleher (Indianapolis): Exact Solution of the Dimer Model on the Triangular Lattice. Monomer-Monomer Correlation Function slides

10:45–11:10

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

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 Günter Stolz (Birmingham, AL): Disordered quantum spin chains slides

16:05–16:30

16:30–17:10 Gian-Michele Graf (Zurich): The bulk-edge correspondence for disordered chiral chains slides

09:50–10:30 Ofer Zeitouni (Rehovot): Experiments and theorems with noise perturbations of non-normal matrices slides

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

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 slides

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 Anna Erschler (Paris): Random walks and Isoperimetry of groups

12:00–12:40 Alex Furman (Chicago, IL): Simplicity of the Lyapunov spectrum via Boundary theory

12:45–14:30

14:30–15:10 Svetlana Jitomirskaya (Irvine, CA): Lyapunov exponents, small denominators, arithmetic spectral transitions, and universal hierarchical structure of quasiperiodic eigenfunctions

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 slides

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

18:30–∞

09:45–10:25 Elena Kosygina (New York, NY): Homogenization of viscous Hamilton-Jacobi equations with non-convex Hamiltonian: examples and open questions slides

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 slides

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

13:00–13:30

We will overview several recent sharp results in this direction, both for general analytic one-frequency quasiperiodic operators in the singular continuous regime, and for specific popular models such as the almost Mathieu operator.

The latter provides in particular the first non-artificial model where Lyapunov–Perron non-regularity can be explicitly studied. For a cocycle over a transformation acting on a space

We will present exact exponential asymptotics of all eigenfunctions and of corresponding cocycles for the almost Mathieu operators for all parameters in the localization regime . This uncovers a universal structure in their behavior. For the frequency resonances, there is a hierarchy governed by the continued fraction expansion of the frequency, explaining predictions in physics literature. For the phase resonances, we will describe a new phenomenon, not even previously described in physics: a reflective hierarchy, where self-similarity holds upon alternating reflections.

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

for any

Kirsty Whatley — Harp

Uri Smilansky — Viola d'Arco

Programme

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