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The course centers on an in-depth study of the symmetry structure of General Relativity and how this is intimately related to its dynamics and to the challenges posed to its quantization. To achieve this understanding, we will introduce a host of concepts and techniques, broadly (and loosely) known under the name of “Covariant Phase Space Method”. This provides a different perspective on GR’s physics, a perspective in which phase space, rather than spacetime, is front and center. We will apply these ideas and techniques to discuss the so-called Problem of Time, Wald's approach to black hole entropy as a Noether charge, and the relationship between Dirac's Hypersurface Deformation Algebra and GR's symmetries and dynamics. We will also discuss the problem of detecting single gravitons as well as crucial analogies and differences between a quantum electromagnetic and gravitational field. Lecture notes specific for the course will be provided.

We will discuss mathematical aspects of classical and quantum field theory, including topics such as: symplectic manifolds and the phase space, symplectic reduction, geometric quantization, Chern-Simons theory, and others.

Machine learning has become a very valuable toolbox for scientists including physicists. In this course, we will learn the basics of machine learning with an emphasis on applications for many-body physics. At the end of this course, you will be equipped with the necessary and preliminary tools for starting your own machine learning projects.

Quantum phases have become a staple of modern physics, thanks to their appearance in fields as diverse as condensed matter physics, quantum field theory, quantum information processing, and topology. The description of quantum phases of matter requires novel mathematical tools that lie beyond the old symmetry breaking perspective on phases. Techniques from topological field theory, homotopy theory, and (higher) category theory show great potential for advancing our understanding of the characterization and classification of quantum phases. The goal of this workshop is to bring together experts from across mathematics and physics to discuss recent breakthroughs in these mathematical tools and their application to physical problems. 

 

Scientific Organizers

Lukas Mueller
Alex Turzillo
Davide Gaiotto
 

Sponsored in part by the Simons Collaboration on Global Categorical Symmetries 

 

 

Classical probability theory makes the (mostly, tacit) assumption that any two random experiments can be performed jointly.  This assumption seems to fail in quantum theory.  A rapidly growing literature seeks to understand QM by placing it in a much broader mathematical landscape of ``generalized probabilistic theories", or GPTs,  in which incompatible experiments are permitted.   Among other things, this effort has led to  (i) a better appreciation that many "characteristically quantum" phenomena (e.g., entanglement)  are in fact generic to non-classical probabilistic theories, (ii) a suite of reconstructions of (mostly, finite-dimensional) QM from small packages of assumptions of a probabilistic or operational nature, and (iii) a clearer view of the options available for generalizing QM.  This course will offer a survey of this literature,  starting from scratch and concluding with a discussion of recent developments. 

Mathematical prerequisites: finite-dimensional linear algebra, ideally including tensor products and duality, plus some exposure to category theory (though I will briefly review this material as needed).  

Scheduling note: There will be 5 lectures from March 12-26, then a gap of two weeks before the final 2 lectures held April 16 & 18.

Format: In-person only; lectures will be recorded for PIRSA but not live on Zoom.

This course will cover phenomenological studies and experimental searches for new physics beyond the Standard Model, including: naturalness, extra dimension, supersymmetry, grand unification, dark matter candidates (WIMPs and axions) and their detection.

This survey course introduces some advanced topics in quantum field theory and string theory. Topics may include anomalies, conformal field theory, and bosonic string theory and are subject to change depending on the topics covered in the TBD elective course.

This Cosmology course will provide a theoretical overview of the standard cosmological model.
Topics will include: FRW universe, Thermal History, Inflation, Cosmological Perturbation Theory, Structure Formation and Quantum Initial Conditions.

New observational programs and techniques are opening a window to the first galaxies in the universe and bringing surprises along the way. In this workshop, we'll explore how dark matter phenomenology may have impacted the first stars and galaxies, focusing on how improved modeling and simulations can allow us to use new and upcoming high-redshift data to gain insight into dark matter's fundamental nature.

Sponsored in part by: