In 2+1 dimensions quantum particles can exist that are neither bosons nor fermions. Such particles, known as "anyons" have been studied theoretically for over forty years. While there has long been good reason to believe that these particles exist, particularly in fractional quantum Hall systems, it has been frustratingly difficult to perform experiments that probe the properties of these particles --- with many failures over the year. However, just in the last few years, with the maturation of a few new technologies, there have now been several very different but increasingly clear experiments that directly measure the exotic exchange statistics of these particles. I will explain the history of some of these experiments, what they have achieved, and what remains to be done.

Abstract: In two dimensional topologically ordered matter, processes depend on gross topology rather than detailed geometry. Thinking in 2+1 dimensions, particle world lines can be interpreted as knots or links, and the amplitude for certain processes becomes a topological invariant of that link. While sounding rather exotic, we believe that such phases of matter not only exist, but have actually been observed in quantum Hall experiments, and could provide a route to building a quantum computer. Possibilities have also been proposed for creating similar physics in systems ranging from superfluid helium to topological superconductors to semiconductor-superconductor junctions to quantum wires to spin systems to graphene to cold atoms. Please contact jung-wook(dot)kim(at)qmul(dot)ac(dot)uk for the zoom link.

In two dimensional topological phases of matter, processes depend on gross topology rather than detailed geometry. Thinking in 2+1 dimensions, particle world lines can be interpreted as knots or links, and the amplitude for certain processes becomes a topological invariant of that link. While sounding rather exotic, we believe that such phases of matter not only exist, but have actually been observed in quantum Hall experiments, and could provide a uniquely practical route to building a quantum computer. Possibilities have also been proposed for creating similar physics in systems ranging from superfluid helium to strontium ruthenate to semiconductor-superconductor junctions to quantum wires to spin systems to graphene to cold atoms.