Can the effectiveness of a medical treatment be determined without the expense of a randomized controlled trial? Can the impact of a new policy be disentangled from other factors that happen to vary at the same time? Questions such as these are the purview of the field of causal inference, a general-purpose science of cause and effect, applicable in domains ranging from epidemiology to economics. Researchers in this field seek in particular to find techniques for extracting causal conclusions from statistical data. Meanwhile, one of the most significant results in the foundations of quantum theory—Bell’s theorem—can also be understood as an attempt to disentangle correlation and causation. Recently, it has been recognized that Bell’s result is an early foray into the field of causal inference and that the insights derived from almost 60 years of research on his theorem can supplement and improve upon state-of-the-art causal inference techniques. In the other direction, the conceptual framework developed by causal inference researchers provides a fruitful new perspective on what could possibly count as a satisfactory causal explanation of the quantum correlations observed in Bell experiments. Efforts to elaborate upon these connections have led to an exciting flow of techniques and insights across the disciplinary divide. This course will explore what is happening at the intersection of these two fields. zoom link: https://pitp.zoom.us/j/94143784665?pwd=VFJpajVIMEtvYmRabFYzYnNRSVAvZz09

This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

This course provides a graduate-level introduction to computational fluid dynamics, covering the theoretical concepts and numerical methods that form the foundation of much of modern theoretical astrophysics and cosmology.  Beyond applications in astrophysics and cosmology the concepts introduced here are of relevance in many other fields of physics and engineering.  Assignments will include both analytical problems and hands-on programming problems.  The latter will be python-based and are designed to provide a deeper understanding of the numerical concepts through practical implementation.  A brief introduction to python and jupyter notebooks will be given.