Talks

We discuss the possibility that spacetime geometry may be an emergent phenomenon. This idea has been motivated by the Analogue Gravity programme. An \'effective gravitational field\' dominates the kinematics of small perturbations in an Analogue Model. In these models there is no obvious connection between the \'gravitational\' field tensor and the Einstein equations, as the emergent spacetime geometry arises as a consequence of linearising around some classical field. After a brief introduction on this topic, we present our recent contributions to the field.

This course is aimed at advanced undergraduate and beginning graduate students, and is inspired by a book by the same title, written by Padmanabhan. Each session consists of solving one or two pre-determined problems, which is done by a randomly picked student. While the problems introduce various subjects in Astrophysics and Cosmology, they do not serve as replacement for standard courses in these subjects, and are rather aimed at educating students with hands-on analytic/numerical skills to attack new problems.

This course is aimed at advanced undergraduate and beginning graduate students, and is inspired by a book by the same title, written by Padmanabhan. Each session consists of solving one or two pre-determined problems, which is done by a randomly picked student. While the problems introduce various subjects in Astrophysics and Cosmology, they do not serve as replacement for standard courses in these subjects, and are rather aimed at educating students with hands-on analytic/numerical skills to attack new problems.

Our present Core Theory of matter (aka “standard model”) was born in the 1970s, a Golden Age for fundamental physics. To date it has passed every experimental test, extending – by many orders of magnitude – to higher energies, shorter distances, and greater precision than were available in the 1970s. Yet we are not satisfied, because the Core Theory postulates four separate interactions and several different kinds of matter, and its equations are lopsided. In this lecture, Prof. Wilczek will describe powerful and extremely beautiful ideas for restoring unity and symmetry to the fundamental laws. These ideas are firmly rooted in empirical reality, but at present the evidence for them is circumstantial. The Large Hadron Collider (LHC) will provide critical tests. If Nature has been teaching, not teasing, discoveries at the LHC will inaugurate a new Golden Age, bringing our fundamental understanding of the physical world to a new level. Standard model, fundamental physics, experiment, LHC, unification, particle physics, supersymmetry, vacuum fluctuation

We analyze how quantum complexity poses bounds to the simulation of quantum systems. While methods as Density Functional Theory (DFT) and the Density Matrix Renormalization Group (DMRG) work very well in practice, essentially nothing on the formal requirements is known. In this talk, we consider these methods from a quantum complexity perspective: First, we discuss DFT which encapsulates the difficulty of solving the Schroedinger equation in a universal functional and show that this functional cannot be efficiently computed unless several complexity classes collapse. Second, we consider DMRG, a method to deal with quantum spin chains, and show that even under reasonable assumptions -- a polynomial gap and matrix product ground states -- finding the ground state is still a computationally hard problem. Beyond pinpointing the limitations of the methods, this helps us to understand under which assumptions we might be able to prove their convergence.

We review how renormalization, born in quantum field theory has evolved into a rather universal tool to analyze the change of physical laws under scaling. Recent developments in non commutative geometry with hopefully potential applications to the quantization of gravity will be discussed.

The unparalleled empirical success of quantum theory strongly suggests that it accurately captures fundamental aspects of the workings of the physical world. The clear articulation of these aspects is of inestimable value --- not only for the deeper understanding of quantum theory in itself, but for its further development, particularly for the development of a theory of quantum gravity. Recently, there has been growing interest in elucidating these aspects by expressing, in a less abstract mathematical language, what we think quantum theory might be telling us about how nature works, and trying to derive, or reconstruct, quantum theory from these postulates. In this talk, I describe a simple reconstruction of the finite- dimensional quantum formalism. The derivation takes places with a classical probabilistic framework equipped with the information (or Fisher-Rao) metric, and rests upon a small number of elementary ideas (such as complementarity and global gauge invariance). The complex structure of quantum formalism arises very naturally. The derivation provides a number of non-trivial insights into the quantum formalism, such as the extensive nature of the role of information geometry in determining the quantum formalism, the importance of global gauge invariance, and the importance (or lack thereof) of assumptions concerning separated systems.