Course

The main goal of this course is to show in which ways General Relativity (GR) is similar, and especially in which ways it is different, from other gauge theories. The largest component of the course is dedicated to studying the specific symmetry structure of GR and how it intimately relates to its dynamics. To do so, 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. Along the way we will take a few detours: we will explore (parts of) the historical debate on whether gravity should be quantized at all, discuss how to think of time evolution when there is no absolute time, and go through Wald’s proposal of black hole entropy as a Noether charge. The intended outcome of the course is to provide a new perspective on GR which, hopefully, will inform you on why it is much harder to quantize than other theories – especially from a non-perturbative perspective. In this sense the course always keeps an eye on Quantum Gravity, even though there will be very little “quantum” in it. It is also a course that does not hinge on any specific approach to the quantization of gravity. Also, it is worth noting that the covariant phase space techniques are broadly used in the current literature on the black hole information paradox, soft symmetries, and holography, and is therefore a useful tool to learn if you are interested in any of these topics. Instructor: Aldo Riello Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

This course will cover quantum phases of matter, with a focus on long-range entangled states, topological states, and quantum criticality. Instructor: Chong Wang/Subhayan Sahu Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

We will cover the basics of the gauge/gravity duality, including some of the following aspects: holographic fluids, applications to condensed matter systems, entanglement entropy, and recent advances in understanding the black hole information paradox. Instructor: David Kubiznak/Gang Xu Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

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. Instructor: Robert Spekkens/Bindiya Arora Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

This course in Cosmology provides a theoretical overview of the standard cosmological model. Key topics include the FRW metric and the homogeneous universe, the thermal history of the universe (with an emphasis on the hot Big Bang and equilibrium thermodynamics), inflation and scalar field dynamics, along with selected aspects of cosmological perturbation theory (time permitting). Instructor: Neal Dalal/Ghazal Geshnizjani Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

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. Instructor: Mohamed Hibat Allah Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

The course will cover the basics of conformal field theories and also some applications, including exact computations of the critical exponents in 2d statistical models. Instructor: Jaume Gomis/Mykola Semenyakin Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

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. Instructor: Kevin Costello/Mykola Semenyakin Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

This course will introduce some advanced topics in general relativity related to describing gravity in the strong field and dynamical regime. Topics covered include properties of spinning black holes, black hole thermodynamics and energy extraction, how to define horizons in a dynamical setting, formulations of the Einstein equations as constraint and evolution equations, and gravitational waves and how they are sourced. Instructor: William East/Ghazal Geshnizjani Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

We look to understand the possibilities and limits of quantum information processing, and how an information theory perspective can inform theoretical physics. Topics covered include: entanglement, tools for measuring nearness of quantum states, characterizing the most general possible quantum operations, entropy and measuring information, the stabilizer formalism, quantum error-correcting codes, the theory of computation, quantum algorithms, classical and quantum complexity. Instructor: Alex May/Bindiya Arora Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

This course will introduce you to some of the geometrical structures underlying theoretical physics. Previous knowledge of differential geometry is not required. Topics covered in the course include: Introduction to manifolds, differential forms, symplectic manifolds, symplectic version of Noether’s theorem, integration on manifolds, fiber bundles, principal bundles and applications to gauge theory. Instructor: Mykola Semenyakin/Maite Dupuis Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

This course will cover the basics of Quantum Foundations under three main headings. Part I – Novel effects in Quantum Theory. A number of interesting quantum effects will be considered. Interferometers: Mach-Zehnder interferometer, Elitzur-Vaidman bomb tester, The quantum-Zeno effect. The no cloning theorem. Quantum optics (single mode). Hong-Ou-Mandel dip. Part II - Conceptual and interpretational issues. Axioms for quantum theory for pure states: Von-Neumann measurement model. * The measurement (or reality) problem. EPR Einstein’s 1927 remarks, the Einstein-Podolsky-Rosen argument. Bell’s theorem, nonlocality without inequalities. The Tirolson bound. The Kochen-Specker theorem and related work by Spekkens On the reality of the wavefunction: Epistemic versus ontic interpretations of the wavefunction and the Pusey-Barrett-Rudolph theorem proving the reality of the wave function. Gleason’s theorem. Interpretations. The landscape of interpretations of quantum theory (the Harrigen Spekkens classification). The de Broglie-Bohm interpretation, the many worlds interpretation, wave- function collapse models, the Copenhagen interpretation, and QBism. Part III - Structural issues. Reformulating quantum theory: we will look at some reformulations of quantum theory and consider the light they throw on the structure of quantum theory. These may include time symmetric quantum theory and weak measurements (Aharonov et al), quantum Bayesian networks, and the operator tensor formalism. Generalised probability theories: These are more general frameworks for probabilistic theories which admit classical and quantum as special cases. Reasonable principles for quantum theory: we will review some of the recent work on reconstructing quantum theory from simple principles. Indefinite causal structure and indefinite causal order. Finally we will conclude by looking at (i) the close link between quantum foundations and quantum information and (ii) possible future directions in quantum gravity motivated by ideas from quantum foundations. Instructor: Lucien Hardy/Bindiya Arora Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses