General Physics Colloquium 'Fractional quantum Hall physics and topology in lattice systems' Anne E. Nielsen MPI-Quantenoptik, Garching, Germany The discovery of the fractional quantum Hall effect in the early eighties revealed the physical existence of phases of matter that differ fundamentally from previously known phases, and these phases are still under intense investigations today. The property that makes them special is that they are topological. Topology is the study of quantities that do not change when a geometrical object is deformed smoothly. Examples include the twist of a Möbius strip and the hole through a torus. One way that topology can appear in two-dimensional quantum many-body systems is through the existence of anyons. Anyons are localized excitations that look like particles, but nevertheless have properties that normal, isolated particles cannot have. Anyons are interesting from a fundamental point of view and also for, e.g., quantum computation. In recent years, there has been a lot of effort towards clarifying under which conditions the fractional quantum Hall effect can occur. One motivation for this is the hope to find easier and more robust ways to realize the effect experimentally. In this talk, I will first give an introduction to topology and the fractional quantum Hall effect. I will then discuss some recent proposals for engineering fractional quantum Hall physics under new conditions. Wine and cheese will be served at 4 PM.