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

2) Hawking radiation of black

3) Production of primordial

4) Statistical properties of

Required prior knowledge:

Foundations of quantum mechanics and general relativity

### Courses

### Winter 2023 Courses

Usual Meeting Time: Fridays from 10-11am and 2-4pm

Usual Meeting Time: Tuesdays and Thursdays from 10am-Noon

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.

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

Usual Meeting Time: Tues/Thurs - 10am-Noon

In this mini course, I shall introduce the basic concepts in 2D topological orders by studying simple models of topological orders and then introduce topological quantum computing based on Fibonacci anyons. Here is the (not perfectly ordered) syllabus.

- Overview of topological phases of matter
- Z2 toric code model: the simplest model of 2D topological orders
- Quick generalization to the quantum double model
- Anyons, topological entanglement entropy, S and T matrices
- Fusion and braiding of anyons: quantum dimensions, pentagon and hexagon identities
- Fibonacci anyons
- Topological quantum computing

### Spring 2023 Courses

Usual Meeting Time: Monday and Wednesday mornings from 10am-11:30am

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

### Fall 2022 Courses

Usual Meeting Time: Tuesdays from 10am-Noon and 230pm-430pm.

This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

### Winter 2022 Courses

Usual Meeting Time: Mondays and Thursdays from 4:00 pm - 5:20 pm

### Fall 2020 Courses

Usual Meeting Time: Tuesdays and Thursdays from 3:30 - 5:00 pm

This course provides a graduate-level introduction to computational fluid dynamics, covering the theoretical concepts and numerical methods that form the foundation of much of modern theoretical astrophysics and cosmology. Beyond applications in astrophysics and cosmology the concepts introduced here are of relevance in many other fields of physics and engineering. Assignments will include both analytical problems and hands-on programming problems. The latter will be python-based and are designed to provide a deeper understanding of the numerical concepts through practical implementation. A brief introduction to python and jupyter notebooks will be given.

### Spring 2020 Courses

This course has two main goals: (1) to introduce some key models from condensed matter physics; and (2) to introduce some numerical approaches to studying these (and other) models. As a precursor to these objectives, we will carefully understand many-body states and operators from the perspective of condensed matter theory. (However, I will cover only spin models. We will not discuss or use second quantization.)

Once this background is established, we will study the method of exact diagonalization and write simple python programs to find ground states, correlation functions, energy gaps, and other properties of the transverse-field Ising model. We will also discuss the computational limitations of exact diagonalization. Finally, I will introduce the concept of matrix product states, and we will see that these can be used to study ground state properties for much larger systems than can be studied with exact diagonalization.

Each 90-minute session will include substantial programming exercises in addition to lecture. Prior programming experience is not expected or required, but I would like everyone to have python (version 3) installed on their computer prior to the first class, including Jupyter notebooks; see “Resources” below.

The goal of this course is to introduce the path integral formulation of quantum mechanics and a few of its applications. We will begin by motivating the path integral formulation and explaining its connections to other formulations of quantum mechanics and its relation to classical mechanics. We will then explore some applications of path integrals. Each 90-minute session will include roughly equal amounts of lecture time and activities. The activities are designed to enhance your learning experience and allow you to assess your own level of understanding.

The aim of this course is to understand the thermodynamics of quantum systems and in the process to learn some fundamental tools in Quantum Information. We will focus on the topics of foundations of quantum statistical mechanics, resource theories, entanglement, fluctuation theorems, and quantum machines.

The aim of this course is to explore some of the many ways in which symmetries play a role in physics. We’ll start with an overview of the concept of symmetries and their description in the language of group theory. We will then discuss continuous symmetries and infinitesimal symmetries, their fundamental role in Noether’s theorem, and their formalisation in terms of Lie groups and Lie algebras. In the last part of the course we will focus on symmetries in quantum theory and introduce representations of (Lie) groups and Lie algebras.

### Winter 2020 Courses

### Fall 2019 Courses

Usual Meeting Time: 10:00-12:00

### Spring 2019 Courses

### Fall 2018 Courses

Usual Meeting Time: Every Wednesday from 10:30am to 12:00pm