Course subject: Physics (PHYS)

A brief review of ensembles and quantum gases, Ising model, Landau theory of phase transitions, order parameters, topology, classical solutions.

Special relativity, foundations of general relativity, Riemannian geometry, Einstein's equations, FRW and Schwarzschild geometries and their properties

Probability, entropy, Bayesian inference and information theory. Maximum likelihood methods, common probability distributions, applications to real data including Monte-Carlo methods.

Common algorithms for ode and pde solving, with numerical analysis. Common tasks in linear algebra. Focus on how to write a good code, test it, and obtain a reliable result. Parallel programming.

This course will include the study of Perturbation Theory (Regular and Singular) Speeding Up Convergence: Shanks Transformations and Richardson Extrapolation Taylor Series, Fourier Series and the Gibbs Phenomenon Using Diveregent Series: Generalised Summation Analytic Continuation, Riemann Surfaces and Branch Points Continued Functions and Pade Approximants Steiltjes Functions, the Herglotz Property and the Carleman Bound Feynman Diagrams.

FRW metric, Hubble expansion, dark energy, dark matter, CMB. Thermodynamic history of early universe. Growth of perturbations, CDM model of structure formation and comparison to observations, cosmic microwave background anisotropies, inflation and observational tests.

Superstring spectrum in 10d Minkowski, as well as simple toroidal and orbifold compactifications. T-duality, D-branes, tree amplitudes. Construct some simple unified models of particle physics. Motivate the 10- and 11-dimensional supergravities. Simple supergravity solutions and use these to explore some aspects of AdS/CFT duality.

The following topics will be discussed: The Lorentz Group: Properties and Representations; Manipulating Spinors; Supersymmetry Algebra and Representations; Superfields and Superspace; 4d Supersymmetric Lagrangians; Supersymmetry Breaking; Constructing the MSSM; Collider Phenomenology of Supersymmetric Theories; and Dark Matter.

Review of selected topics in Gravitational Physics

Review of selected topics in Quantum Gravity

Review of selected topics in Quantum Information

Review of selected topics in Condensed Matter Theory

Review of Selected topics in Foundations of Quantum Theory

Review of selected topics in String Theory

Review of Selected topics in Cosmology

Review of formalism of nonrelativistic quantum mechanics including symmetries and invariance. Approximation methods and scattering theory. Elementary quantum theory of radiation. Introduction to one-particle relativistic wave equations.

Review of relativistic quantum mechanics and classical field theory. Quantization of free quantum fields (the particle interpretation of field quanta). Canonical quantization of interacting fields (Feynman rules). Application of the formalism of interactin quantum fields to lowest-order quantum electrodynamic processes. Radiative corrections and renormalization.

Statistical basis of thermodynamics; microcanonical, canonical and grand canonical ensembles; quantum statistical mechanics, theory of the density matrix; fluctuations, noise, irreversible thermodynamics; transport theory; application to gases, liquids, solids.

Solutions to Maxwell's equations; radiation theory; normal modes; multipole expansion; Kirchhoff's diffraction theory; radiating point charge; optical theorem. Special relativity; transformation laws for the electromagnetic field; line broadening; dispersion; Kramers-Kronig relations. Magnetohydrodynamics and plasmas.

Review of essential quantum field theory. Zero and finite temperature Green's functions. Applications.

Laser and nonlinear optics; techniques for controlling laser beams such as mode selection and mode locking; laser spectroscopy.

Offered on demand. Course content depends on topic and instructor.

Offered on demand. Course content depends on topic and instructor.

Phonons, electron states, electron-electron interaction, electron-ion interaction, static properties of solids.

Offered on demand. Course content depends on topics and instructor.

Optoelectronic component fabrication, light propagation in linear and nonlinear media, optical fiber properties, electro-optic and acousto-optic modulation, spontaneous and stimulated emission, semiconductor lasers and detectors, noise effects in fiber systems.

This course provides an overview of the application of physics to medicine. The physical concepts underlying the diagnosis and treatment of disease will be explored. Topics will include general imaging principles such as resolution, intensity and contrast; x-ray imaging and computed tomography; radioisotopes and nuclear medicine, SPECT and PET; magnetic resonance imaging; ultrasound imaging and radiation therapy.

Review of basics of quantum information and computational complexity; Simple quantum algorithms; Quantum Fourier transform and Shor factoring algorithm: Amplitude amplification, Grover search algorithm and its optimality; Completely positive trace-preserving maps and Kraus representation; Non-locality and communication complexity; Physical realizations of quantum computation: requirements and examples; Quantum error-correction, including CSS codes, and elements of fault-tolerant computation; Quantum cryptography; Security proofs of quantum key distribution protocols; Quantum proof systems. Familiarity with theoretical computer science or quantum mechanics will also be an asset, though most students will not be familiar with both.

Offered on demand. Course content depends on topic and instructor.

Offered on demand. Course content depends on topic and instructor.

Multi-wavelength astronomy: radio, infrared, optical and x-ray observations. Radiative Processes: macroscopic description, thermal and non-thermal emission, scattering, line transitions and plasma effects. Gravitational Dynamics: potential and orbits, self-gravitating systems, the Collisionless Boltzmann Equation, gravitational encounters. Fluid Mechanics: simple fluids, soundwaves and shocks, instabilities and transport mechanisms.

Introduction to scalar field theory and its canonical quantization in flat and curved spacetimes. The flat space effects of Casimir and Unruh. Quantum fluctuations of scalar fields and of the metric on curved space-times and application to inflationary cosmology. Hawking radiation.

Friedmann-Robertson-Walker metric and dynamics; big bang thermodynamics; nucleosynthesis; recombination; perturbation theory and structure formation; anisotropies in the Cosmic Microwave Background; statistics of cosmological density and velocity fields; galaxy formation; inflation.