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This course will be an introduction to world-sheet and space-time aspects of topological strings. Topics that will be discussed include: the world-sheet formulation of both the A and B model topological strings, axiomatics of topological string theories, categories of branes, string field theory, the relation to the physical string; and dualities.

We will study topics in theoretical physics through the lens of differential geometry and algebraic topology. The topics will be chosen among the following: differential forms on manifolds, homology, homotopy, de Rham cohomology, gauge theory and principal fiber bundles, nonperturbative effects and topology, characteristic classes, basics of solitons (ex: why is the instanton number a number?), index theorems, introduction to anomalies.

The course will give introduction into the structure of the Standard Model of particle physics and its field content. The emphasis will be made on the underlying principles, such as gauge invariance, cancellation of quantum anomalies, and Brout-Englert-Higgs mechanism. Effective low-energy description of strong interactions will be also discussed. It will be assumed that students are familiar with the basics of quantum field theory.

We will study advanced topics in gravitational physics and their applications to high energy physics. After reviewing topics in differential geometry, including differential forms, Cartan's formalism, and the Gauss-Codazzi equations for the geometry of embedded hypersurfaces, we will address the Einstein-Hilbert variational principle and the Hawking-York term, which plays an important role in the gravitational path integral. We will then study the Kerr solution for rotating black holes, and address topics in black hole thermodynamics using the Euclidean action, as well as Hawking radiation. Time allowing we will touch on some more advanced topics such as domain walls, brane world scenarios, Kaluza-Klein (KK) theory & KK black holes, Gregory-Laflamme instability, and Gravitational instantons.

This course will explain why textbook quantum “theory” is merely a mathematical recipe rather than a proper physical theory. It will then cover the most serious obstacles to fixing this problem and to providing a clear metaphysics underpinning the mathematics of quantum theory. We will focus on key no-go theorems (e.g., Bell’s theorem, contextuality theorems, and Extended Wigner’s friend arguments), as well as on key frameworks (e.g., generalized probabilistic theories and ontological models).

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.

Mostly ignore the Introduction content of the Oct 27 lecture (up to 14:14). The content and direction of the course evolved such that different portions of the “Old Schedule” (at 0:27) were covered. The schedule on this page has been corrected and now accurately reflects the content of the lectures.

The “Supplements” on Oct 30 and Nov 06 are actually just Lectures.

Outline:
Oct 27: The Planimeter and the Weyl-Heisenberg Group of Kinematic Transformations
Oct 30: The Planimeter and the Weyl-Heisenberg Group of Canonical Transformations
Nov 03: No Class
Nov 06: Measuring Instruments, Indirect Quantum Measurement, and Positive Gaussian Kraus Operators
Nov 10: Gaussian Channels, Gaussian Random Unitaries, and Sequential Measurements
Nov 13: Wiener Increments and the Ito Rules
Nov 17: No Class
Nov 20: General Gaussian Kraus Operators, Lindblad Operators, and Diffusive Measurement
Nov 24: The Markov Property and The Central Limit Theorem
Nov 27: Instrumental Groups, von Neumann Measurement, and Diffusive Heterodyne
Dec 01: No Class
Dec 04: The Stratonovich Product, The Maurer-Cartan Stochastic Differential, and Indirect Homodyne
Dec 08: The Kraus-Operator Density and The Fokker-Planck-Kolmogorov Equation of a Diffusive Measurement
Dec 11: Simultaneous Diffusive Measurements of Non-Commuting Observables and the Instrument Manifold Program

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.

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