Prof. Lukasz Fidkowski is a young pioneer in the research of interacting topological phases. His research focus is on identifying and classifying exotic phases of matter. Traditionally, such phases can be distinguished using a so-called local order parameter: for example, the orientation of a local magnetic moment in a ferromagnetically ordered material, or the pattern of crystal ordering in the ions making up a solid. This approach, termed Ginzburg-Landau theory, has been the cornerstone of solid state physics for many decades, and the quantum field theory structure that underlies it has parallels in high energy physics as well, e.g. in the Higgs and Goldstone phenomena. However, recent experiments have shown that there exist. First observed in the 1980s in the integer and fractional quantum Hall effects in confined electron gases, these are truly new phases, separated by thermodynamic phase transitions from each other, for which there are no distinguishing local order parameters. Rather, these phases are distinguished by a certain elusive non-local order, termed topological order, which is the focus of my current study. This focus is motivated in part by the recent experimental detection of a plethora of new systems exhibiting some version of topological order. New well established examples include a large number of spin-orbit coupled band `topological insulators’ (e.g. BiSb); hints of topological physics have very recently been seen in strongly interacting Kondo systems (SmB6), one dimensional `Majorana’ topological superconductors (InAs), so-called Weyl semi-metals, and various frustrated magnets (e.g. Kagome spin 1/2 anti-ferromagnets). In summary, there are a host of experimental solid state systems which show, or are on the verge of exhibiting, some topological features.

quantum phases of matter beyond this Ginzburg-Landau framework.