Giuseppe De Nittis is Assistant Professor of the Facultad de Matemáticas at the Pontificia Universidad Católica de Chile in Santiago. He got his PhD in 2010 at SISSA (Trieste, Italy) working on the geometric interpretation of the Quantum Hall Effect and its relation with the Kubo formula. In the last years he worked constantly at the boundary between topology, algebra and analysis to face problems coming from the condensed matter area, with a special focus on the theory of topological insulators. More information can be found on his web page (gdenittis.wordpress.com). Max Lein is Assistant Professor at the Advanced Institute of Materials Research, which is associated to Tohoku University in Sendai Japan. He completed his PhD in 2011 at the Technische Universität München under the supervision of Prof. H. Spohn. He has worked for over 10 years on the rigorous analysis of problems from condensed matter physics, in particular topological effects, using tools from analysis and algebra. More recently, he broadened his field of interest to periodic light conductors. In his analyses, he has applied and developed pseudodifferential and semiclassical methods, and combined algebraic and analytic techniques (e. g. to analyze essential spectra of magnetic pseudodifferential operators). More information can be found on his homepage (maxlein.com).