Talks

Time-reversal invariant band insulators can be separated into two categories: `ordinary' insulators and `topological' insulators. Topological band insulators have low-energy edge modes that cannot be gapped without violating time-reversal symmetry, while ordinary insulators do not. A natural question is whether more exotic time-reversal invariant insulators (insulators not connected adiabatically to band insulators) can also exhibit time-reversal protected edge modes. In 2 dimensions, one example of this is the fractional spin Hall insulator (essentially a spin-up and spin-down copy of a fractional quantum Hall insulator, with opposite effective magnetic fields for each spin). I will discuss another family of strongly interacting insulators, which exist in both 2 and 3 dimensions, that can have time-reversal protected edge modes. This gives a new set of examples of `fractional' topological insulators.

Cosmology and quantum gravity have not always had the smoothest of interactions. As a case in point I'll summarize the calculation behind the prediction of tensor modes in inflationary universes and discuss the difficulties found in recasting this calculation in terms of Ashtekar-Barbero-Immirzi variables. Contrary to the belief that ``inflation is shielded from quantum gravity'', novelties are found, leading to the interesting prediction of a chiral signature in the gravitational wave background, proportional to the imaginary part of the Immirzi parameter. This would leave a distinctive imprint in the polarization of the cosmic microwave background. On a more theoretical level, our remarks shed light on matters permeating quantum gravity, such as the inner product, the ground state (which we prove is NOT the Kodama state) and ordering issues.