Course

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. zoom link: https://pitp.zoom.us/j/94143784665?pwd=VFJpajVIMEtvYmRabFYzYnNRSVAvZz09

The course is an introduction to quantum field theory in curved spacetime. Upon building up the general formalism, the latter is applied to several topics in the modern theory of gravity and cosmology where the quantum properties of fundamental fields play an essential role.

Topics to be covered:
1) Radiation of particles by moving mirrors 
2) Hawking radiation of black holes  
3) Production of primordial density perturbations and gravity waves during inflation
4) Statistical properties of the primordial spectra  

Required prior knowledge:
Foundations of quantum mechanics and general relativity

This course is designed to introduce machine learning techniques for studying classical and quantum many-body problems encountered in quantum matter, quantum information, and related fields of physics. Lectures will emphasize relationships between statistical physics and machine learning. Tutorials and homework assignments will focus on developing programming skills for machine learning using Python.

This course will cover phenomenological studies and experimental searches for new physics beyond the Standard Model, including: natruralness, extra dimension, supersymmetry, dark matter (WIMPs and Axions), grand unification, flavour and baryogenesis.

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 will review the notion of information in the most possible general sense. Then we will revisit our definitions of entropy in quantum physics from an informational point of view and how it relates to information theory and thermodynamics. We will discuss entanglement in quantum mechanics from the point of view of information theory, and how to quantify it and distinguish it from classical correlations. We will derive Bell inequalities and discuss their importance, and how quantum information protocols can use entanglement as a resource. We will introduce other notions of quantum correlations besides entanglement and what distinguishes them from classical correlations. We will also analyze measurement theory in quantum mechanics, the notion of generalized measurements and their importance in the processing and transmission of information. We will introduce the notions of quantum circuits and see some of the most famous algorithms in quantum information processing, as well as in quantum cryptography. We will end with a little introduction to the notions of relativistic quantum information and a discussion about quantum ethics.

This mini-course of four lectures is an introduction, review, and critique of two approaches to deriving the Einstein equation from hypotheses about horizon entropy. 

It will be based on two papers: 

• "Thermodynamics of Spacetime: The Einstein Equation of State" arxiv.org/abs/gr-qc/9504004
• "Entanglement Equilibrium and the Einstein Equation" arxiv.org/abs/1505.04753

We may also discuss ideas in "Gravitation and vacuum entanglement entropy" arxiv.org/abs/1204.6349

Zoom Link: https://pitp.zoom.us/j/96212372067?pwd=dWVaUFFFc3c5NTlVTDFHOGhCV2pXdz09 

 

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. (a) Interferometers: Mach-Zehnder interferometer, Elitzur-Vaidman bomb tester, (b) The quantum-Zeno effect. (c) The no cloning theorem. (d) Quantum optics (single mode). Hong-Ou-Mandel dip. Part II Conceptual and interpretational issues. (a) Axioms for quantum theory for pure states. (b) Von-Neumann measurement model. * (c) The measurement (or reality) problem. (d) EPR Einstein’s 1927 remarks, the Einstein-Podolsky-Rosen argument. (e) Bell’s theorem, nonlocality without inequalities. The Tirolson bound. (f) The Kochen-Specker theorem and related work by Spekkens (g) 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. (h) Gleason’s theorem. (i) 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. (a) Reformulating quantum theory: I 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. (b) Generalised probability theories: These are more general frameworks for probabilistic theories which admit classical and quantum as special cases. (c) Reasonable principles for quantum theory: I will review some of the recent work on reconstructing quantum theory from simple principles. (d) Indefinite causal structure and indefinite causal order. Finally I 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.

This course will cover the mathematical structure underlying classical gauge theory. Previous knowledge of differential geometry is not required. Topics covered in the course include: introduction to manifolds, symplectic manifolds, introduction to Lie groups and Lie algebras; deformation quantisation and geometric quantisation; the matematical structure of field theories; scalar field theory; geometric picture of Yang-Mills theory; symplectic reduction. If time permits, we may also look at the description of gauge theory in terms of principal bundles and the topological aspects of gauge theory.

The main objective of this course is to discuss some advanced topics in gravitational physics and its applications to high energy physics. Necessary mathematical tools will be introduced on the way. These mathematical tools will include a review of differential geometry (tensors, forms, Lie derivative), vielbeins and Cartan’s formalism, hypersurfaces, Gauss-Codazzi formalism, and variational principles (Einstein-Hilbert action & Gibbons-Hawking term). Several topics in black hole physics including the Kerr solution, black hole astrophysics, higher-dimensional black holes, black hole thermodynamics, Euclidean action, and Hawking radiation will be covered. Additional advanced topics will include domain walls, brane world scenarios, Kaluza-Klein theory and KK black holes, Gregory-Laflamme instability, and gravitational instantons

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