Talks

While the properties of gravity, and its consistency with General Relativity (GR), are well tested on solar system scales, within our system and the decay of binary pulsar orbits, they are, by comparison, poorly tested on cosmic scales. This is of particular interest as we try to understand the origins of cosmic acceleration, and whether they are a signature of deviations from GR. Using the latest measurements of the universe's expansion history, twinned with the evolution of large scale structure, we discuss the current constraints on gravity's behavior on the largest scales observable today.

Standard inflationary theory predicts that primordial fluctuations in the universe were nearly Gaussian random. Therefore, searches for, and limits on, primordial nongaussianity are some of the most fundamental tests of inflation and the early universe in general. I first briefly review the history of its measurements from the cosmic microwave background anisotropies and large-scale structure in the universe. I then present results from recent work where effects of primordial nongaussianity on the distribution of largest virialized objects was studied numerically and analytically. We found that the bias of dark matter halos takes strong scale dependence in nongaussian cosmological models. Therefore, measurements of scale dependence of the bias, using various tracers of large-scale structure, can - and do - constrain primordial nongaussianity more than an order of magnitude better than previously thought.

The graph isomorphism (GI) problem plays a central role in the theory of computational complexity and has importance in physics and chemistry as well. While no general efficient algorithm for solving GI is known, it is unlikely to be NP-complete; in this regard it is similar to the factoring problem, for which Shor has developed an efficient quantum algorithm. In this talk I will discuss our investigations of quantum particles walking on graphs and their implications for possible algorithms for GI. We find that single-particle quantum random walks fail to distinguish some nonequivalent graphs that can be distinguished by random walks with two interacting particles. The implications of these observations for classical and quantum algorithms for GI will be discussed.