These are a few of the seminars I have given over the past few years.

**Acceleration, Then and Now**There is good evidence that the universe underwent an epoch of accelerated expansion sometime in its very early history, and that it is entering a similar phase now. The ‘Then’ part of this talk describes how the predictions of theories suggested by quantum gravity (specifically string theory) for the early epoch have fared when compared with recently announced observations from the Planck satellite. Although it is too early for these predictions to be regarded as being comprehensive, I argue that a survey of those that were made shows they broadly agree with what was seen.The talk’s second part (‘Now’) provides an update on an approach to solving the “cosmological constant problem”, which is a theoretical obstruction that makes it difficult to understand the origins of the present epoch of acceleration. (In a nutshell: observations agree well with what would be expected if the universe were now beginning to be dominated by the energy density of the vacuum, but the vacuum energy density required by observations is extremely tiny compared with all known calculations of its expected size.) In the approach described – Supersymmetric Large Extra Dimensions, or SLED – observations can be reconciled with a large vacuum energy because the energy curves the extra dimensions and not the ones we measure in cosmology. The update shows that various quantum effects did not ruin this picture, and the main remaining worry to to verify that the theory’s predictions do not alter the way other things gravitate in an observationally unacceptable way.**Good Things from the Back-reaction of Higher Codimension Branes**Randall-Sundrum models are examples of co-dimension one braneworlds for which back-reaction plays an important role, with the warping produced by the branes changing the nature of the low-energy effective theory in an important way. Yet back-reaction for higher-codimension branes remains much less well-explored. In particular, the fields sourced by higher co-dimension objects generically diverge at the positions of the sources, complicating the calculation of the properties of the bulk from those of the sources. This talk describes a solution to this matching problem for codimension-two branes, and uses the result to show how back-reacting codimension-two systems can have surprising properties – such as by providing de Sitter solutions to higher-dimensional supergravity (despite the existence of various no-go theorems), naturally exponentially large dimensions (as could be useful for the hierarchy problem), and volume-suppressed on-brane curvatures compared with the typical scale of on-brane physics (as could be useful for the cosmological constant problem).**Extra Dimensions, the Cosmological Constant Problem and the LHC**Two uncertainties define the prevailing attitude toward the LHC: uncertainty about what new physics it may find (if any); and disappointment with the prospects of finding just a “vanilla” standard-model Higgs. These are wrapped in dissatisfaction with the “technical naturalness” arguments which (when applied to the hierarchy problem) help suggest what we should be looking for. The dissatisfaction arises because of a wide-spread despair about finding a technically natural solution to the cosmological constant problem, despite much effort spent seeking it. In this talk I describe a mechanism within supersymmetric extra-dimensional theories that allows the low-energy effective cosmological constant naturally to be of order the Kaluza-Klein scale. If this is the solution to the cosmological constant problem, then it requires extra dimensions that are both very supersymmetric and large enough to be relevant to the LHC. For the LHC it implies in particular two hard predictions, and two (so-far successful) general expectations. The predictions are (1) many missing energy channels, with a gravity scale at or just above 10 TeV; and (2) the existence of string excitations of standard-model particles, likely *below* 10 TeV. The (so far – successful) general expectations are that no MSSM particles exist to be discovered, despite the low-energy supersymmetry; and (2) the Higgs is likely to be vanilla.**AdS/QHE: Towards a Holographic Description of Quantum Hall Experiments**Many experimental features of Quantum Hall systems seem to be well-described by the phenomenological assumption that the dynamics of the charge carriers enjoys a large duality symmetry group: a level-two subgroup of SL(2,Z) acting on the Hall and Ohmic conductivities. What has been missing is an understanding of how this symmetry might emerge from the underlying properties of the electrons, or from any other kind of strongly interacting system. After describing the experimental evidence for the symmetry, this talk describes a first step towards a theoretical understanding by showing how the required symmetry emerges naturally from an AdS/CFT description of 2+1 dimensional charge carriers. This suggests that AdS/CFT techniques may provide a natural language for describing Quantum Hall systems.**Colourful Things the LHC Might See Early**It is widely believed that existing electroweak data requires a Standard Model (SM) Higgs to be light, while electroweak and flavour physics constraints require other scalars charged under the SM gauge couplings to be heavy. New Higgs-like scalars that are also colour octets – well-motivated in the sense that they arise in models having approximate custodial symmetry and minimal flavour violation – provide counter-examples to both of these statements since the scalars can be all simultaneously light (~ 100 GeV} or heavy (~ 1 TeV}, without running afoul of direct searches and electroweak precision measurements.**Are Inflationary Predictions Sensitive to Very High Energy Physics?**It has been proposed that the successful inflationary description of density perturbations on cosmological scales is sensitive to the details of physics at extremely high (trans-Planckian) energies. I will critically analyse this idea by examining how inflationary predictions depend on higher-energy scales within a simple model where the higher-energy physics is well understood. The result is the best of all possible worlds: inflationary predictions are robust against the vast majority of high-energy effects, but *can* be sensitive to some effects in certain circumstances, in a way which does not violate ordinary notions of decoupling. This implies both that the comparison of inflationary predictions with CMB data is meaningful, and that it is also worth searching for small deviations from the standard results in the hopes of learning about very high energies.**String/Brane Cosmology**String theory is our best candidate for a theory of the physics at very short distances, but is very much a theory in search of an observable application. Conversely, scalar field theories can successfully describe the phenomenology of inflation or dark energy, but have proven difficult to embed into a realistic theory of short distances. However, the branes arising in string theory can have strong implications for the naturalness problems which obstruct this embedding. This is interesting in itself, since short distance physics (like string theory) normally decouples from long-distance phenomena (like cosmology). But can cosmology and string theory help answer each other’s problems? This talk describes recent progress in bringing these ideas together.