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F-theory compactifications on Calabi-Yau fourfolds provide one way to obtain N=1 supersymmetric grand unified models of particle physics from string theory. With this motivation in mind, I will consider F-theory on a particularly simple class of local Calabi-Yau fourfolds, for which a low-energy analysis based upon topological gauge theory is valid. For these models, I will explain how the geometry of the fourfold determines the spectrum of massless charged matter and the effective superpotential in four dimensions. If time permits, I will also discuss the relation between certain surface operators in gauge theory and brane recombination in F-theory.

How sure are you that spacetime is continuous? One of the more radical approaches to quantum gravity, causal set theory, models spacetime as a discrete structure: a causal set. Allowing the possibility that spacetime is discrete then how should we do physics on it? Carrying over the usual continuum descriptions in terms of differential equations seems like a difficult option. This talk begins with a brief introduction to causal sets then describes an approach to modelling the propagation of scalar particles on a causal set. We obtain the continuum causal retarded propagator by summing quantum mechanical amplitudes assigned to paths in the causal set - a kind of \'discrete path integral\' that agrees with the continuum result. The propagator so obtained should serve as a building block towards a model for quantum field theory on a causal set.

Hawking\'s black hole information paradox is one of the great thought experiments in physics. It points to a breakdown of some central principle of physics, though which one breaks down is still in dispute. It has led to the discovery of ideas that seem to be key to unifying quantum mechanics and gravity, namely the holographic principle and gauge/gravity duality. I review this subject, and discuss ongoing work and future directions.

The consequences of a modified gravity (MOG) are explored. I demonstrate how the solutions of the field equations obtained from the action principle of the MOG lead to a theory without any free, adjustable parameters or ad-hoc empirical formulae. The theory successfully explains solar system observations, the dispersion velocities of globular clusters, the rotation curves of galaxies, the mass profiles of X-ray clusters, the dispersion velocities of satellite galaxies, the Bullet Cluster and cosmological observations without exotic dark matter. The peculiar features of the recent data obtained for the merging cluster Abell 520 are discussed. MOG predicts agreement with data from the scale of the solar system to cosmological scales without dark matter. With no undetermined free parameters, the theory can be used to make firm predictions that may be verifiable in the foreseeable future.