Whether it is a bottle of soda, the tires of a car or the human body: Objects in everyday life can be described by only a few parameters, like temperature, pressure or volume. But how is this possible, if each of these systems are complex assemblies of atoms and molecules giving rise to a vast number of  coordinates, on the order of 10^23?

Ergodic theory is the mathematical attempt to provide an answer to this fundamental question. In this talk we will tackle the problem based on a prominent example - the Einstein model for a solid. It will be shown that this problem is reduced to studying rotations on a circle, for which we will prove a version of the ergodic theorem.

In this talk, we shall consider the near-invisibility cloaking in acoustic scattering by non-singular transformation media. A general lossy layer is included into our construction. We are especially interested in the cloaking of active/radiating objects. Our results on the one hand show how to cloak active contents more efficiently, and on the other hand indicate how to choose the lossy layer optimally.

We give a proof of the Hölder continuity of weak solutions for the doubly nonlinear parabolic equation in the degenerate case. The analysis discriminates between large scales, for which a Harnack inequality is used, and small scales, that require intrinsic scaling methods. The focus of the talk will be on the precise construction of the sequence of nested and shrinking cylinders where the oscillation of the solution is to be evaluated, and its relation to the structure of the pde. This is a joint work with Tuomo Kuusi and Juhana Siljander (Aalto University, Finland) that will soon appear in Indiana Univ. Math. J.