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The manifold of pure quantum states can be regarded as a complex projective space endowed with the unitary-invariant Fubini-Study metric. The physical characteristics of a given quantum system can then be represented by a variety of geometrical structures that can be identified in this manifold. This talk will review a number of examples of such structures as they arise in the state spaces of spin-1/2, spin-1, spin-3/2, and spin-2 systems, and various types of entangled systems, all of which have fascinating and beautiful geometries associated with them. The geometric approach offers interesting insights into the nature of quantum systems, and is also useful in the consideration of foundational issues such as those related to the measurement problem.

It has been known for a long time that instanton effects control the large order behavior of the perturbation series in quantum mechanics and gauge theories. I present a study of this connection in the context of matrix models in 1/N-expansion and topological strings. I will show how to compute the one-instanton corrections for a generic matrix model. Due to a recent matrix model inspired formalism for the topological string amplitudes on local Calabi-Yau manifolds, this can be used to compute nonperturbative effects in topological string theory and make predictions about the asymptotics of the string perturbation series. I discuss various cases where our predictions can be tested, yielding spectacular agreement with the asymptotics extracted by standard numerical methods.

It is known that finite fields with d elements exist only when d is a prime or a prime power. When the dimension d of a finite dimensional Hilbert space is a prime power, we can associate to each basis state of the Hilbert space an element of a finite or Galois field, and construct a finite group of unitary transformations, the generalised Pauli group or discrete Heisenberg-Weyl group. Its elements can be expressed, in terms of the elements of a Galois field. This group presents numerous applications in Quantum Information Science e.g. tomography, dense coding, teleportation, error correction and so on. The aim of our talk is to give a general survey of these properties and to present recently obtained results in connection with three problems: -the so-called ''Mean King's problem'' in prime power dimension, -discrete Wigner distributions, -and quantum tomography . Finally we shall discuss a limitation of the possible dimensions in which the so-called epistemic interpretation can be consistently formulated, in relation with the existence of finite affine planes, Euler's conjecture and the 36 officers problem.

The role of outflows in global star formation processes has become hotly debated even as fundamental questions about the nature of these outflows continues to receive attention. In this talk I discuss both problems and new approaches to their resolution. Astrophysical outflows have always been a subject at the forefront of the numerical technologies and in the first act of the talk I introduce AstroBEAR, a new Adaptive Mesh Refinement MHD tool developed at Rochester for the study of star formation outflow issues. The question of \'feedback\', the mechanisms by which protostellar outflows can drive turbulence in either clouds or clusters, is then addressed via AstroBEAR simulations. In these studies we seek to understand the detailed mechanisms by which outflows can return energy to their environment and, perhaps, drive turbulent motions. Finally we turn to the MHD processes involved with the outflows themselves and focus on a new tool, High Energy Density Laboratory experiments. I will present results from a campaign of experiments carried out at Imperial Collage in London which directly address issues of magnetically dominated radiative outflows and jets.

Many experts are convinced that large scale, practical implementations of quantum information systems hold great promise for society, much as the laser and the transistor have already revolutionized the world. This stems from a long history of research that included an intense, raging battle of epic proportions between scientific giants. In tracing these steps, you will learn why Albert Einstein and Niels Bohr argued over the nature of entangled states where pairs of sub-atomic particles are strangely correlated from 1935 until their very deaths. You will also find out how, decades later, John Bell discovered his famous inequalities that made it possible for experimentalists, including Alain Aspect and others, to settle the great debate and help propel a new era of fundamental understanding with concepts and methods that seek to harness unique properties of atoms to process and transmit information.

One of the cool, frustrating things about quantum theory is how the once-innocuous concept of "measurement" gets really complicated. I'd like to understand how we find out about the universe around us, and how to reconcile (a) everyday experience, (b) experiments on quantum systems, and (c) our theory of quantum measurements. In this talk, I'll try to braid three [apparently] separate research projects into the beginnings of an answer. I'll begin from the premise that you make a measurement to find something out, then attack some specific questions: "How do we find out about quantum systems?", "What can we find out about quantum systems?", and finally "What do we actually know, afterward?" I'll give precise statements of these questions, then present [partial] answers.

f(R) theories are an alternative approach at the phenomenon of cosmic acceleration, in which the Einstein-Hilbert action for gravity is modified by adding a function of the Ricci scalar, f(R). While at the background level viable f(R) models must closely mimic LCDM, the difference in their prediction for the growth of large scale structures can be sufficiently large to leave detectable signatures in future surveys. In this talk, after reviewing the conditions for the background viability of f(R) theories, I will focus on scalar perturbations. I will present in some details the dynamics of linear perturbations, showing what are the characteristic imprints of f(R) models in the growth of structures and consider possible observational tests