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The modern view of representing a quantum observable as a semispectral measure as opposed to the traditional approach of using only spectral measures has added a great deal to our understanding of the mathematical structures and conceptual foundations of quantum mechanics. The old questions of 1) how to determine a quantum observable from its classical counter-part (if any), 2) how much statistical information is needed to determine an observable, 3) which observables can be measured together, and 4) are there noiseless measurements, all appear in a new perspective, calling for a study of problems such as: 1) how to obtain a semispectral measure by a quantization map, 2) do the moment operators of a semispectral measure determine the operator measure, 3) are coexistent observables jointly measurable, and 4) does minimal variance occur only in the case of a spectral measure? In my talk I will survey some of the recent developments concerning these questions and problems.

At low energy and small curvature, general relativity has the form of an effective field theory. I will describe the structure of the effective field theory, and show how it can be used to calculate low energy quantum effects.

Geometric flows, especially the Ricci flow, have been used with considerable success in recent years to address the Poincare and Thurston conjectures for 3-manifolds. In this talk, I will briefly introduce these geometric flows, and describe how they appear in a completely different context in the physics of string theory. I will then outline how recently developed techniques in geometric flows could be used to address questions of importance in string theory.

Experiments have ruled out unit-strength scalar-mediated fifth forces on scales ranging from 0.1 mm to 10,000 AU. However, allowing the scalar to have a quartic self-interaction weakens these constraints considerably. This weakening is due to the "chameleon mechanism", which gives the scalar field an effective mass that depends on the local matter density. I will describe the chameleon mechanism and discuss experimental constraints on self-interacting scalar fields. In particular, I will compare the chameleon-mediated self interaction to constraints from the Eot-Wash experiment, at the University of Washington, which comes closest to detecting such a scalar field today. It will be shown that a quartic self interaction of unit strength is just out of reach of the current Eot-Wash experiment, but will be readily visible to their next-generation instrument.