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.

We
employ the effective field theory approach for multi-field inflation which is a
generalization of Weinberg's work. In this method the first correction terms in
addition to standard terms in the Lagrangian have been considered. These terms
contain up to the fourth derivative of the fields including the scalar field
and the metric. The results show the possible shapes of the interaction terms
resulting eventually in non-Gaussianity in a general formalism. In addition
generally the speed of sound is different but almost unity. Since in this
method the adiabatic mode is not discriminated initially so we define the
adiabatic as well as entropy modes for a specific two-field model. It has been
shown that the non-Gaussianity of the adiabatic mode and the entropy mode are
correlated in shape and amplitude. It is shown that even for speed close to
unity large non-Gaussianities are possible in multi-field case. The amount of
the non-Gaussianity depends on the curvature of the classical path in the
phase-space in the Hubble unit such that it is large for the large curvature.
In addition it is emphasized that the time derivative of adiabatic and entropy
perturbations do not transform due to the shift symmetry as well as the
original perturbations. Though two specific combinations of them are invariant
under such a symmetry and these combinations should be employed to construct an
effective field theory of multi-field inflation.

We consider the production of strongly interacting, heavy SUSY pairs at the LHC. When the centre of mass energy is close to the production threshold of the pair, the corresponding cross sections receive large higher-loop QCD corrections. These corrections are classified as the so-called soft logarithms and Coulomb singularities and they lead to a break down of the usual perturbation expansion. In this talk I review the origin of these large corrections and explain how they can be resummed by using Effective Field theories. Finally, I will present some resummed results for the pair production cross sections of heavy squarks and gluinos. Based on: arXiv:1202.2260 and 1211.3408.