Course

This course offers an introduction to general relativity (GR), focusing on the core principles of Einstein's theory of gravity. We will explore key topics such as the equivalence principle, some essential concepts in differential geometry, the Einstein-Hilbert action, and Einstein's field equations. Furthermore, we will examine practical applications of general relativity in understanding black holes, cosmology, and gravitational waves.

This series is a crash course introduction to a handful of advanced topics designed to tackle the general problem of how to engineer Positive Operator-Valued Measures (POVMs) using observable building blocks, the so-called Instrument Manifold Program.  This program emerged from a recent fundamental breakthrough: how to realize the measurement of a spin’s direction, a.k.a. the spin-coherent-state POVM, a spherical set of outcomes analogous to the well known coherent-state POVM of the standard phase plane.

Outline: Oct 27: Introduction: The Planimeter and the "Spherimeter'' Oct 30: The Planimeter and the "Spherimeter'' Nov 03: CANCELLED Nov 06: Indirect Measurement and System-Meter Interaction Nov 10: POVMs and Decoherence Nov 13: POVMs and Decoherence Nov 17: CANCELLED Generalized Observables: Phase-Point and Spin-Direction Nov 20: Classical Measuring Instruments Nov 24: Generalized Observables: Phase-Point and Spin-Direction Nov 27: Generalized Observables: Phase-Point and Spin-Direction Dec 01: Frame Operators and Quasi-Probability Distributions Dec 04: Frame Operators and Quasi-Probability Distributions Dec 08: The Arthurs-Kelly (1965) and D’Ariano (2002) Measurements Dec 11: The Arthurs-Kelly (1965) and D’Ariano (2002) Measurements

Location & Building Access: Alice Room, 3rd Floor, Perimeter Institute, 31 Caroline St N, Waterloo (Exception - November 27 in Space Room, 4th Floor)

Registration: Please sign-up here: https://forms.office.com/r/dEA4EUq0CU

Participants who do not have an access card for Perimeter Institute must sign in at the security desk before each session. For information on parking or accessibility please contact [email protected].

The aim of this course is to explore the main ideas of the statistical physics approach to critical phenomena. We will discuss phase transitions, using the ferromagnetic phase transition and the Ising model as our primary example. The renormalisation group approach will be an important part of this course.

In the last few years, a new perspective on probabilistic reasoning has been extensively developed with the help of tools from category theory. The idea is to shift focus from the measure-theoretic details to structural properties of information flow in the presence of uncertainty - independence, conditioning, nested uncertainty, etc. This shift allows one to reason without the need to specify a concrete model of uncertainty, be it discrete, continuous, Gaussian, possibilistic or one of many other instantiations. In this course I will present a high-level overview of the leading approach to categorical probability that is based on so-called Markov categories. We will focus on the diagrammatic language of Markov categories that can be understood without any knowledge of category theory. Using such diagrams, we can also express basic concepts that have been useful in proving a plethora of categorical versions of classical theorems - strong law of large numbers, de Finetti's theorem, d-separation criterion for Bayesian networks, ergodic decomposition theorem, zero/one laws and others.

Location & Building Access: Alice Room, 3rd Floor, Perimeter Institute, 31 Caroline St N, Waterloo

Participants who do not have an access card for Perimeter Institute must sign in at the security desk before each session. For information on parking or accessibility please contact [email protected].

To request the Zoom link for online participation contact [email protected].

Scroll down to Registration and Enrollment to participate.

Structure:

We will discuss 8 papers which had huge impact in physics. One week Instructor Pedro Vieira will discuss a paper; students should read it beforehand. One week later students discuss recent papers referring to that paper (20 min each student, ~ 3 presentations; at the end of the class Pedro will grade the presentations based on “Physics”, “Presentation”, “Question handling”; and give comments).

By the end of the course, students will have explored a vast set of topics in theoretical physics — spotting potential gaps to be fixed — sharpened their presentation skills through steady practice, and sparked cross-disciplinary conversations through our shared physics language.

Familiarity with Quantum Field Theory and General Relativity is assumed.

The papers:

Sept 12 & 19: On the Quantum Correction for Thermodynamic Equilibrium, Wigner, 1932 Topic: Quantum Mechanics

Sept 22 & 29: Existence theorem for certain systems of nonlinear PDEs, Foures-Bruhat, 1952 Topic: General relativity

Oct 3 & 10: The Renormalization Group and the Epsilon Expansion, Wilson and Kogut, 1973 Topic: Quantum Field Theory

Oct 10 (EXTRA) & 17: More about the Massive Schwinger Model, Coleman, 1976 Topic: 2D Quantum Field Theory

Oct 20 & 27: A sequence of approximated solutions to the S-K model for spin glasses, Parisi, 1980 Topic: Statistical Mechanics

Oct 29 (New Date) & Nov 7: Quantum Field Theory and the Jones Polynomial, Witten, 1988 Topic: Topological Quantum Field Theory

Nov 10 & 17: Exactly Solvable Field Theories of Closed Strings, Brezin, Kazakov, 1989 Topic: 2D Quantum Gravity

Nov 21 & Nov 28: Unpaired Majorana fermions in quantum wires, Kitaev, 2000 Topic: Quantum Matter/Quantum Information

Schedule: This is a Friday / Monday alternating week schedule from 915am-1045am.

Exceptions: There will be an afternoon session at 130pm on Friday October 10 to avoid the Thanksgiving holiday.

Location & Building Access: Alice Room, 3rd Floor, Perimeter Institute, 31 Caroline St N, Waterloo Participants who do not have an access card for Perimeter Institute must sign in at the security desk before each session. For information on parking or accessibility please contact [email protected].

Registration and Enrollment: Please sign-up here: https://forms.office.com/r/nDQ6SDxSR4

Zoom Link https://pitp.zoom.us/j/95238695187?pwd=G6EjbywTpOagSxpbMZtgznxmuwFFBp.1

Quantum field theory intertwines continuous and discrete structures. On the discrete side, combinatorics plays a central role in describing and understanding its expansions and models. This lecture series focuses on the combinatorial aspects of quantum field theory. In the first part, we explore analytic combinatorics techniques, inspired by QFT, for the enumeration of graphs. These methods turn out to be surprisingly powerful in addressing deep questions in algebraic geometry, topology, and statistical models on graphs. In the second part, we turn to discrete structures arising in perturbative expansions of QFT. We study these from a modern combinatorics viewpoint, using tools such as Lorentzian polynomials and generalized permutahedra to better understand the mathematical objects at the heart of quantum field theory.

For updates visit: https://michaelborinsky.com/combqft.html

This course is offered by the University of Waterloo's Department of Combinatorics & Optimization; UW students can enroll through Quest.

Lectures will be held at Perimeter Institute, 31 Caroline St N, Waterloo. Students will need to sign in and out of Perimeter each day. Note: session is cancelled for Sept 25; there is a room change for Oct 2 & Nov 11, and no classes week of October 13.

This is a theoretical physics course that aims to review the basics of theoretical mechanics, special relativity, and classical field theory, with the emphasis on geometrical notions and relativistic formalism, thus setting the stage for the forthcoming courses in Quantum Mechanics, and Quantum Field Theory in particular, as well as in General Relativity and Quantum Gravity. 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

Detector operators, of which the average null energy operator provides the most famous example, arise as direct theoretical models of asymptotic measurements in collider experiments. In QFT, detector operators are expressed in terms of "light-ray operators", whose correlation functions provide an interesting class of non-perturbatively well-defined observables. There has recently been renewed interest in detector operators coming from three distinct directions: In CFTs, there has been progress understanding the space of light-ray operators, their organization into Regge trajectories, and their appearance in Lorentzian operator product expansions. In perturbative QFT and gravity, borrowing techniques from the study of scattering amplitudes, there has been progress understanding multi-point correlation functions of detector operators, in particular, their function space and singularities. Finally, in particle physics, there have recently been direct measurements of correlation functions of detector operators in collider experiments, enabling measurements of their scaling behavior and the structure of multi-point correlators of light-ray operators in QCD. In this mini-course I will give an introduction to the theory of light-ray/ detector operators, their correlators, and their applications in particle phenomenology, and provide an overview of the recent progress in the directions mentioned above. Throughout, I will attempt to highlight the different perspectives and motivations for studying these operators, coming from the CFT, amplitudes and phenomenological communities. I will conclude with a discussion of open problems in both theory and phenomenological applications, as well as highlighting areas where theoretical developments could have an impact on real world applications at colliders. Join live sessions via Zoom link: https://pitp.zoom.us/j/96935592330?pwd=NNtf7839TThLFEWIzdH7fYxNYksyYr.1 View all past talks on PIRSA: https://pirsa.org/c25035

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