NONTECHNICAL SUMMARY This award supports research, education, and outreach activities with a goal to achieve a fundamental understanding of topological matter with emphasis on the existence and properties of unusual particles known as anyons. Topological matter is a new, important class of materials with uniquely robust properties insensitive to undesirable effects, such as material imperfections or interference from the material's environment. This research project focuses on the understanding of how heat is transported within such matter. This is of major importance to quantum information processing platforms, many of which depend on the use of anyons. Introductory physics textbooks teach us that electrons are truly fundamental particles with no constituent parts. The charge of an electron is understood as the smallest possible charge a particle could have. And yet, in topological matter, stable "quasi"-particles that carry a smaller charge than the charge of an electron can form. They are known as anyons. Anyons exhibit highly counterintuitive behavior when they run around each other, which is directly useful for quantum computing. Indeed, using anyons as building blocks of quantum information devices is expected to dramatically suppress error rates and preserve quantum information from undesirable influences. Presently, the properties and often even the existence of anyons are poorly understood and hotly debated. This proposal focuses on devising new ways to theore