Scientific Series

I will review recent developments in our theoretical understanding of the abundance and clustering of dark matter haloes. In the first part of this talk, I will discuss a toy model based on the statistics of peaks  of Gaussian random field (Bardeen et al 1986) and show how the clustering properties of such a point set can be easily derived from a generalised local bias expansion. In the second part, I will explain how  this peak formalism relates to the excursion set approach and present parameter-free predictions for the  mass function and bias of dark matter halos.

A fundamental open problem in condensed matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. In this talk I describe recent work showing that there are 6 new electronic topological insulators that have no non-interacting counterpart. Combined with the previously known band-insulators, these produce a total of 8 topologically distinct phases. Two of the new topological insulators have a simple physical description as Mott insulators in which the electron spins form spin analogs of the familiar topological band-insulator. The remaining are obtained as combinations of these two `topological paramagnets' and the topological band insulator. These 8 phases form a complete list of all possible interacting topological insulators, and are classified by a $\mathbb{Z}_2^3$ group-structure. As a necessary part of the talk I will also review progress in the theory of bosonic Symmetry Protected Topological phases in 3d.