Talks

We explore the hypothesis that a dynamical dark energy is related to a time-variation of the fundamental mass scale. A dilatation anomaly induced by quantum fluctuations could explain the small value of the present dark energy. Reformulated as a scalar field theory this would predict a quintessence potential which asymptotically relaxes to zero rather than to a nonvanishing constant. An observable consequence of such a scenario results in "early dark energy " contributing a few percent to the energy density of the Universe even at high redshift. Quintessence would be related to a new "fundamental" macroscopic force and induce a small time variation of fundamental constants.

In nearly every quantum algorithm which exponentially outperforms the best classical algorithm the quantum Fourier transform plays a central role. Recently, however, cracks in the quantum Fourier transform paradigm have begun to emerge. In this talk I will discuss one such development which arises in a new efficient quantum algorithm for the Heisenberg hidden subgroup problem. In particular I will show how considerations of symmetry for this hidden subgroup problem lead naturally to a different transform than the quantum Fourier transform, the Clebsch-Gordan transform over the Heisenberg group. Clebsch-Gordan transforms over finite groups thus appear to be an important new tool for those attempting to find new quantum algorithms. [Part of this work was done in collaboration with Andrew Childs (Caltech) and Wim van Dam (UCSB)]

Modern motivations for extra spacetime dimensions will be presented, in particular the surprising AdS/CFT connection to particle compositeness. It will be shown how highly curved, "warped", extra-dimensional geometries can naturally address several puzzles of fundamental physics, including the weakness of gravity, particle mass hierarchies, dark matter, and supersymmetry breaking. The possibility of direct discovery of warped dimensions at particle colliders such as the CERN Large Hadron Collider will be discussed. Some current questions in warped cosmology will also be introduced.