In my talk I will provide a general introduction into the topic of almost Mathieu operators which are used to describe electrons in 2D systems. We will discuss the spectral properties of such systems, including the famous Ten Martini Problem.

Operator Algebras and Their Applications in Physics

Twierdzenie Lieba o wklęsłości

Lieb's concavity theorem

Lieb's concavity theorem

Iloczyny tensorowe III

Tensor products III

Iloczyny tensorowe II

Tensor products II

Iloczyny tensorowe

Tensor products

Projections onto *-subalgebras and convexity inequalities II

Projections onto *-subalgebras and convexity inequalities

Kilka przykładów łącznie wypukłych funkcji macierzowych

Examples of jointly convex matrix functions

Operator convexity and monotonicity, p. II

Operator convexity and monotonicity

Introduction to Trace Inequalities and Quantum Entropy

Absence of isolated points in the spectrum of magnetic Laplacians, p. III

Absence of isolated points in the spectrum of magnetic Laplacians, p. II

Absence of isolated points in the spectrum of magnetic Laplacians

The spectrum of almost Mathieu operators for rational alpha II

The spectrum of almost Mathieu operators for rational alpha

Perturbation of the spectrum of almost Mathieu operators, III

Perturbation of the spectrum of almost Mathieu operators, p. II

Perturbation of the spectrum of almost Mathieu operators

Almost Mathieu Operators and Automorphisms of Quantum Torus

Introduction to rotation algebras, p.III

Introduction to rotation algebras, p.II

Introduction to rotation algebras

Introduction to the almost Mathieu operator