This is a workshop that will take place at Sapienza Università di Roma (Italy), from June 16 to 20, 2025. The focus of the workshop will be on the topics of interest for the research unit in mathematical quantum physics at Sapienza Università di Roma, which include topological matter, quantum transport, adiabatic theory, and phenomena in magnetic materials. The event will bring together established as well as young researchers in theoretical, experimental, and mathematical physics, coming from different parts of the world, to present the latest results in the topics mentioned above and to formulate new challenges for mathematicians and theoreticians stimulated by condensed matter experiments.