Course

This course introduces Scientific Machine Learning, beginning with an overview of traditional and modern machine learning methods illustrated with examples from physics. It then transitions to physics-informed approaches, where physical laws, symmetries, and mechanistic models are embedded into learning frameworks. Tutorials and assignments will emphasize developing programming skills in Python.

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.

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, inflation and scalar field dynamics, along with selected aspects of cosmological perturbation theory time permitting.

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.

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.

Location & Building Access: Alice Room, 3rd Floor, Perimeter Institute, 31 Caroline St N, Waterloo *Note On Thursday January 29 lecture will take place in the Time Room, 2nd Floor.

Zoom Link: https://pitp.zoom.us/j/99324374767?pwd=mUq9s15pbrgalwk5ILqLPOcvNcdXxV.1

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 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.

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).

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.

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 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.