In this talk we will review some recent results on random Schrödinger operators, which are used to model electronic transport in disordered quantum systems and to study the phenomenon of Anderson localization. After a short introduction to the…
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Conservative iterative solvers in computational fluid dynamics – Philipp Birken (Lund University)
The governing equations in computational fluid dynamics such as the Navier-Stokes- or Euler equations are conservation laws. Finite volume methods are designed to respect this and the theorem of Lax-Wendroff underscores the importance of it. It…
Almost sure asymptotic behaviour of Birkhoff sums for infinite measure-preserving dynamical systems – Tanja Schindler (Scuola Normale Superiore)
We are interested in the limit behaviour of Birkhoff sums over an infinite sigma-finite measure space. If the observable is integrable then — by a classical theorem by Aaronson — there exists no sequence of real numbers such that the Birkhoff sum…
Explicit integral Galois module structure of weakly ramified extensions of local fields – Henri Johnston (Univiesity of Exeter)
Let $L/K$ be a finite Galois extension of complete local fields with finite residue fields and let $G={\rm Gal}(L/K)$. Let $G_{1}$ and $G_{2}$ be the first and second ramification groups. Thus $L/K$ is tamely ramified when $G_{1}$ is trivial and we…
From the liquid drop model for nuclei to the ionization conjecture for atoms – Rupert Frank (Mathematics Institute, University of Munich)
The liquid drop model is an isoperimetric problem with a competing non-local term. It was originally introduced in the nuclear physics literature in 1930 and has received a lot of attention recently as an interesting problem in the calculus of…
Eigenvalue asymptotics and eigenvector localization for non-Hermitian noisy Toeplitz matrices – Martin Vogel (Université de Strasbourg)
A most notable characteristic of non-Hermitian matrices is that their spectra can be intrinsically sensitive to tiny perturbation. Although this spectral instability causes the numerical analysis of their spectra to be extremely unreliable, it has…
Localization of the continuous Anderson hamiltonian in 1-d and its transition towards delocalization – Laure Dumaz (École Normale supérieure)
We consider the continuous Schrödinger operator – d^2/d^x^2 + B’(x) on the interval [0,L] where the potential B’ is a white noise. We study the entire spectrum of this operator in the large L limit. We prove the joint convergence of the eigenvalues…
Geometric means of quasi-Toeplitz matrices – Jie Meng (University of Pisa)
We study means of geometric type of quasi-Toeplitz matrices, that are semi-infinite matricesA = (a_{i,j}) i,j=1,2,… of the form A = T(a) + E, where E represents a compact operator, and T(a) is a semi-infinite Toeplitz matrix associated with the…
Looking at Euler flows through a contact mirror: Universality and Turing completeness – Eva Miranda and Daniel Peralta-Salas (Universitat Politècnica de Catalunya and Instituto de Ciencias Matemáticas, Spain)
The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao launched a programme to address the global existence problem for the Euler and Navier Stokes equations based on the…