Considering clean and regular systems brings significant convenience to theoretical studies and numerical simulations of topological phases of matter. However, the interplay of topological orders with ubiquitous disorder and defects is essential for understanding the stability of topological phases and other exotic disorder and defect-induced phenomenon. In this talk, I will discuss this topic in fractional quantum Hall systems. In the first part , I will discuss the 1/3 filling disordered fractional quantum Hall liquid in the continuum lowest Landau level, where the topological phase is destroyed by strong disorder and a ground-state transition to a trivial insulator occurs. I will show that quantum entanglement is a new and powerful diagnostic of this phase transition. In the second part , I will consider defects that can effectively change the space topology of lattice fractional quantum Hall systems. In this case, topological orders cannot only survive, but also endow defects with non-Abelian properties.  Zhao Liu and R. N. Bhatt, Phys. Rev. Lett. 117, 206801 (2016), Editor's Suggestion.  Zhao Liu, Gunnar Möller, Emil J. Bergholtz, arXiv: 1702.05115.
Simple systems with only 3 or 4 interacting particles can behave in a bizarre, counter-intuitive manner. Examples to be discussed in this Colloquium include ultra-long-range Rydberg molecules with enormous electric dipole moments, as well as states of a few neutral particles that resonantly form a cluster. Moreover, insights from a few-body viewpoint can help to understand some of the rich many-body systems being actively explored, from the unitary Bose gas to the fermionic or bosonic flavors of the fractional quantum Hall effect.
RNA nanotechnology has the great potential to allow us to produce well-defined nanostructures and devices inside cells and thus open up a wide range of design opportunities in synthetic biology. To achieve this goal we need to understand the design principles of geometry, folding kinetics and topology that will allow us to genetically encode well-defined RNA nanostructures that self-assemble during the transcription process. We have recently introduced the single-stranded RNA origami method and validated the architecture by transcribing RNA tiles that assemble into lattices of different geometries. I will introduce new software tools that allow interactive design of RNA origami structures using a library of functional modules and new sequence design approaches that allow large structures to be designed. Also I will show our latest progress in developing larger three-dimensional RNA origami structures and functional RNA nanodevices with applications in biosensing and diagnostics.