Luis F. Urrutia: Departamento de Física de Altas Energías Instituto de Ciencias Nucleares Universidad Nacional Autonóma de México A.P. 70-543, 04510 México CDMX, México

The discovery of topological phases of matter has open up a revival in the study of magnetoelectric media both from a microscopic and a macroscopic perspective. We concentrate on this second topic by discussing a non-dynamical version of axion electrodynamics as the basic effective macroscopic theory describing the electromagnetic response of these materials. The essential physical ingredient is the magnetoelectric effect described by an additional electromagnetic parameter of the medium: the magnetoelectric polarizability θ(t, x) which distinguishes among the different phases like normal insulators, topological insulators and Weyl semimetals, for example. This parameter is coupled to the so called U(1) Pontryagin density yielding a modified set of Maxwell equations in a medium which can be deal with similar tools as in standard electrodynamics. After reviewing the new features introduced we briefly discuss some specific applications pointing to expose additional manifestations of the magnetoelectric effect. We deal mainly with the static regime but we also present some extensions to the time-dependent situation by considering two interesting cases: (i) the Casimir effect in a topological insulator between metallic plates and (ii) the discovery of reversed Cherenkov radiation in naturally existing magnetoelectric media, which was previously thought to occur only in left-handed metamaterials. Along the talk we emphasize the close interrelation that arises between this particular topic in condensed matter physics and some relevant endeavors in particle physics, which might provide additional sources for the symbiosis between ideas in these fields, that has proved very fruitful along the years.