Collections

We will study how General Relativity (GR) is similar to and especially how it differs from other gauge theories. This will explain why, from a structural perspective, it is much harder to quantize GR than other theories without relying on any specific approach to quantization. To achieve this goal, we will introduce the so-called “Covariant Phase Space Method” and use to study in detail the symmetry structure of GR and how it is intimately related to its dynamics. Along the way we will touch on (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.

How do relativistic effects influence quantum information processing? This fundamental question has developed over the past decade into the new active field of Relativistic Quantum Information. It brings together concepts and ideas from special relativity, quantum optics, general relativity, quantum communication, and quantum computation. Its aims are to understand the relationship between relativistic physics and quantum information, to harness them for new techniques in quantum information processing and to better comprehend the foundations of relativistic quantum physics.

This course introduces key concepts in modern quantum matter, including spontaneous symmetry breaking, topological phases, and quantum criticality, illustrated through simple and instructive examples.

Advanced quantum field theory in lower dimension. The course will cover topics of advanced quantum field theory in lower dimension (d=2 or d=3) The topics may include string theory and/or integrability.

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.

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 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 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.

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.

This course teaches basic numerical methods that are widely used across many fields of physics. The course is based on the Python programming language. Topics include an introduction to Python, linear algebra, Monte Carlo methods, root finding, integration, differential equations, and are based on applications by researchers at Perimeter. The course will also teach principles of software engineering ensuring reproducible results.