Draft list of lecture courses for HT: Advanced Fluid Dynamics Advanced Fluid Dynamics [16 hours] area: CMT, Astro prequels: Kinetic Theory (MT), an undergraduate course on Fluid Dynamics prerequisites: basic familiarity with fluid equations and stress tensors as provided, e.g., by Kinetic Theory (MT). syllabus: Part I. Magnetohydrodynamics (10 lectures) MHD equations: conservation laws in a conducting fluid; Maxwell stress/magnetic forces; induction equation; Lundquist theorem, flux freezing, amplification of magnetic field. MHD in a strong guide field: MHD waves; high-beta and anisotropic limits and orderings; incompressible MHD, Elsasser MHD, Reduced MHD. Static MHD equilibria, force-free solutions, helicity, Taylor relaxation. Energy principle. Instabilities: interchange, Z-pinch. Part II. Complex fluids (6 lectures) Fluid mechanics with general extra stress. Dilute suspension of spheres: Einstein viscosity. Dilute suspension of bead-spring pairs leading to the Oldroyd-B model for polymeric liquids: Elastic waves and normal stress differences (anisotropic pressure). Jeffery's equation for orientable axisymmetric particles. Dilute suspensions of such particles: road map to liquid rystals, swimmers, active matter. sequel: Collisional Plasma Physics (TT), Soft Matter Physics (HT). lecturer: Alex Schekochihin, Paul Dellar department: Maths and Physics course website: link location, times: Department of Physics TBA Advanced Quantum Field Theory Advanced Quantum Field Theory for Particle Physics [24 hours] area: PT prequel/pre-requisite: Quantum Field Theory (MT) syllabus: Quantum Electrodynamics: Introduction, photon propagator, scalar electrodynamics (Feynman rules, radiative corrections), canonical quantization, fermions (fermions propagator, path integral and Feynman rules), spinor electrodynamics, sample calculations (scattering in spinor electrodynamics), beta function in QED. Non-Abelian Quantum Field Theory: SU(N) local gauge theory, path integral, gauge fixing, BRST, spontaneous symmetry breaking, anomalies, introduction to the standard model. sequel: The Standard Model (TT), Beyond the Standard Model (TT), Non-perturbative Methods in Quantum Field Theory (TT) lecturer: Lucian Harland-Lang department: Physics course website: link location, times: Department of Physics TBA Advanced Quantum Theory Advanced Quantum Theory: Path Integrals and Many-Particle Physics [22 hours] areas: CMT, foundational course syllabus: Path integrals in Quantum Mechanics; the propagator. Path Integrals in Quantum Statistical Mechanics; correlation functions; perturbation theory; Feynman diagrams. Path Integrals and Transfer Matrices. Transfer matrix approach to the Ising Model. Second quantisation. Ideal Fermi gas in second quantization. Weakly interacting Bose gas: Bogoliubov theory; superfluidity. Spinwaves in a ferromagnet. Landau theory of phase transitions. lecturer: Fabian Essler department: Physics classes: Problem classes are organized by the major option co-ordinator. There will be 3 classes in MT (usually in weeks 4, 6 and 8). Students can register for these by filling in a doodle poll (a link will be given on the course website). course website: Physics course C6 location, times: Department of Physics TBA Applied Complex Variables Applied Complex Variables [16 hours] area: PT, CMT, Astro prequel: Perturbation Methods (MT) syllabus: Review of core complex analysis, analytic continuation, multifunctions, contour integration, conformal mapping and Fourier transforms. Riemann mapping theorem (in statement only). Schwarz-Christoffel formula. Solution of Laplace's equation by conformal mapping onto a canonical domain: applications including inviscid hydrodynamics; Free streamline flows in the hodograph plane. Unsteady flow with free boundaries in porous media. Application of Cauchy integrals and Plemelj formulae. Solution of mixed boundary value problems motivated by thin aerofoil theory and the theory of cracks in elastic solids. Reimann-Hilbert problems. Cauchy singular integral equations. Complex Fourier transform. Contour integral solutions of ODE's. Wiener-Hopf method. lecturer: Peter Howell department: Maths course website: Maths course C5.6 location, times: Mathematical Institute TBA Astrophysical Gas Dynamics Astrophysical Gas Dynamics [10 hours] area: Astro syllabus: Part I Astrophysical Gas Dynamics. Principles of hydrodynamics. Equilibrium and stability of fluid systems under gravity. Waves. Shocks. Viscous flows. Applications: star formation, blast waves, winds, accretion discs. lecturer: Caroline Terquem department: Physics course website: TBA location, times: Department of Physics TBA Collisionless Plasma Physics Collisionless Plasma Physics [18 hours] area: Astro prequel: Kinetic Theory (MT), an undergraduate course on Electricity and Magnetism. pre-requisites: Kinetic Theory (MT), an undergraduate course on Electricity and Magnetism. syllabus: Part I. Magnetized plasmas: Particle motion. Drift kinetics. Drift waves and slab Ion Temperature Gradient instability. Barnes damping of compressional Alfven waves. Part II. Plasma waves: Cold plasma waves in a magnetized plasma. WKB theory of cold plasma wave propagation in an inhomogeneous plasma, cut-offs and resonances. Hot plasma waves in a magnetized plasma. Cyclotron resonance. sequel: Collisional Plasma Physics (TT) (note however that this course is self-contained and can be taken without continuing to Collisional Plasma Physics). lecturer: Felix Parra-Diaz department: Physics course website: link location, times: Department of Physics TBA Cosmology Cosmology [16 hours] area: PT, Astro prequel/pre-requisite: General Relativity I (MT) or equivalent. syllabus: Einstein field equations and the Friedman equations, universe models, statistics of expanding background, relativistic cosmological perturbations, observations, from the Hubble flow to the CMB. lecturer: Pedro Ferreira, Johannes Noller, Tessa Baker department: Physics course website: link location, times: Department of Physics TBA Galactic and Planetary Dynamics Galactic and Planetary Dynamics ("Celestial Mechanics for the 21st Century") [16 hours] area: Astro prequel: Kinetic Theory (MT) syllabus: Review of Hamiltonian mechanics. Orbit integration. Classification of orbits and integrability. Construction of angle-action variables. Hamiltonian perturbation theory. Simple examples of its application to the evolution of planetary and stellar orbits. Methods for constructing equilibrium galaxy models. Applications. Fundamentals of N-body simulation. Dynamical evolution of isolated galaxies. Interactions with companions. lecturer: John Magorrian department: Physics course website: link location, times: Department of Physics TBA General Relativity II General Relativity II [16 hours] area: PT, Astro prequel/pre-requisite: General Relativity I (MT) or equivalent syllabus: Mathematical background, the Lie derivative and isometries. The Einstein field equations with matter; the energy-momentum tensor for a perfect fluid; equations of motion from the conservation law. Linearised general relativity and the metric of an isolated body. Motion on a weak gravitational field and gravitational waves. The Schwarzschild solution and its extensions; Eddington-Finkelstein coordinates and the Kruskal extension. Penrose diagrams and the area theorem. Stationary, axisymmetric metrics and orthogonal transitivity; the Kerr solution and its properties; interpretation as rotating black hole. lecturer: Xenia de la Ossa department: Maths course website: Maths course C7.6 location, times: Mathematical Institute TBA Geometric Group Theory Geometric Group Theory [16 hours] areas: PT syllabus: Free groups. Group presentations. Dehn's problems. Residually finite groups. Group actions on trees. Amalgams, HNN-extensions, graphs of groups, subgroup theorems for groups acting on trees. Quasi-isometries. Hyperbolic groups. Solution of the word and conjugacy problem for hyperbolic groups. If time allows: Small Cancellation Groups, Stallings Theorem, Boundaries. lecturer: Panos Papazoglou department: Maths course website: Maths course C3.2 location, times: TBA Geophysical Fluid Dynamics Geophysical Fluid Dynamics [16 hours] area: Astro prequel: an introductory course on Fluid Dynamics. syllabus: Rotating frames of reference, vorticity equation, Ertel’s theorem, Rossby number, Ekman number, Taylor-Proudman theorem. Geostrophic and hydrostatic balance, thermal wind relation, pressure coordinates, f and beta-planes. Shallow water and reduced gravity models, conservation laws for energy and potential vorticity, flow over topography, inertia-gravity waves, equations for nearly geostrophic motion, Rossby waves, Kelvin waves. Linearised equations for a stratified, incompressible fluid, internal gravity waves, vertical modes. Planetary Geostrophy. Quasigeostrophic approximation: quasigeostrophic potential vorticity equation and Rossby wave solutions, vertical propagation and trapping. Barotropic and baroclinic instability, necessary conditions for instability of zonal flow, Eady model of baroclinic instability. Wave-mean flow interaction, transformed Eulerian mean, Eliassen-Palm flux, non-acceleration theorem. Ekman layers and upwelling. Sverdrup balance and ocean gyres, western intensification, simple models for the vertical structure of ocean circulation and meridional overturning circulation. Angular momentum and Held-Hou model of Hadley circulations. Applications to atmospheric flow on Mars and gas giant planets. lecturer: Andrew Wells department: Physics course website: TBA. location, times: Department of Physics TBA Introduction to Quantum Information Introduction to Quantum Information [16 hours] area: Astro, CMT, PT prequel/Pre-requisite: The course material should be of interest to physicists, mathematicians, computer scientists, and engineers. Prerequisite notes will be provided giving an account of the necessary material. It would be desirable for you to look through these notes slightly before the start of the course.The following will be assumed as prerequisites for this course: elementary probability, complex numbers, vectors and matrices Dirac bra-ket notation a basic knowledge of quantum mechanics especially in the simple context of finite dimensional state spaces (state vectors, composite systems, unitary matrices, Born rule for quantum measurements) basic ideas of classical theoretical computer science (complexity theory) would be helpful but are not essential. syllabus: Bits, gates, networks, Boolean functions, reversible and probabilisitic computation ``Impossible" logic gates, amplitudes, quantum interference One, two and many qubits Entaglement and entangling gates From interference to quantum algorithms Algorithms, computational complexity and Quantum Fourier Transform Phase estimation and quantum factoring Non-local correlations and cryptography Bell's inequalities Density matrices and CP maps Decoherence and quantum error correction lecturer: Artur Ekert department: Maths course website: https://courses.maths.ox.ac.uk/node/185Maths C7.4 course location, times: Mathematical Institute TBA Lattice Quantum Field Theory Lattice Quantum Field Theory [8 hours] area: PT, CMT pre-requisites: Advanced Quantum Field Theory for Particle Physics (HT) syllabus: An introduction to using computer simulation to obtain the non-perturbative physics of quantum field theories. Euclidean Path Integral and Stat Mech partition functions. Transfer matrix and Hamiltonian. Spin models. Gauge fields on a lattice and continuum limit(s). Strong coupling calculations. Wilson loops and confinement. Markovian Monte Carlo: Metropolis, heat bath. Fermions on a lattice. Some applications. (If there is interest I will run some lectures in TT18, outside the formal course, describing in detail some of the interesting physics calculations that have been carried out using these techniques.) lecturer: Mike Teper department: Physics course website: TBA location, times: Mathematical Institute TBA Networks Networks [16 hours] area: CMT pre-requisites: Maths C5.3 Statistical Mechanics or another undergraduate course in Statistical Mechanics syllabus: 1. Introduction and Basic Concepts (1-2 lectures): nodes, edges, adjacencies, weighted networks, unweighted networks, degree and strength, degree distribution, other types of networks. 2. Small Worlds (2 lectures): clustering coefficients, paths and geodesic paths, Watts-Strogatz networks [focus is on modelling and heuristic calculations]. 3. Toy Models of Network Formation (2 lectures): preferential attachment, generalizations of preferential attachment, network optimization. 4. Additional Summary Statistics and Other Useful Concepts (2 lectures): modularity and assirtativity, degree-degree correlations, centrality measures, communicability, reciprocity and structural balance. 5. Random Graphs (2 lectures): Erdős–Rényi graphs, configuration model, random graphs with clustering, other models of random graphs or hypergraphs; application of generating-function methods [focus is on modelling and heuristic calculations; material in this section forms an important basis for sections 6 and 7]. 6. Community Structure and Mesoscopic Structure (2 lectures): linkage clustering, optimization of modularity and other quality functions, overlapping communities, other methods and generalizations. 7. Dynamics on (and of) Networks (3-4 lectures): general ideas, models of biological and social contagions, percolation, voter and opinion models, temporal networks, other topics. 8. Additional Topics (0-2 lectures): games on networks, exponential random graphs, network inference, other topics of special interest to students [depending on how much room there is and interest of current students]. lecturer: Renaud Lambiotte department: Maths course website: Maths course C5.4 location, times: Mathematical Institute TBA Renormalisation Group Renormalisation Group [16 hours] area: PT/CMT prequels/pre-requisite: Nonequilibrium Staistical Physics (MT) syllabus: Phase transitions in simple systems. Mean eld theory and its limitations (Landau theory). Basic theory of the RG. Scaling and crossover behaviour. Perturbative RG and the epsilon-expansion. Relation to the eld-theoretic RG. Some applications: low-dimensional systems, random magnets, polymer statistics, critical dynamics. lecturer: Paul Fendley department: Physics course website: TBA. location, times: Department of Physics TBA Soft Matter Physics Soft Matter Physics [16 hours] area: CMT, Astro prequels/pre-requisite: Nonequilibrium Staistical Physics (MT) syllabus: Polymers: statics and dynamics. Membranes. Liquid Crystals and topological defects. Colloids: dispersion interactions and transport. Diffusion-reaction processes and pattern formation. Self-assembly sequel: Topics in Soft and Active Matter Physics (TT). lecturer: Julia Yeomans, Ard Louis department: Physics course website: TBA. location, times: Department of Physics TBA String Theory I String Theory I [16 hours] area: PT pre-requisite: Quantum Field Theory (MT) syllabus: String actions, equations of motion and constraints, open and closed strings --- boundary conditions, Virasoro algebra, ghosts and BRS, physical spectrum, elementary consideration of D branes, Veneziano amplitude. sequel: String Theory II (TT), Introduction to Gauge-String Duality (TT) lecturer: Chris Beem department: Maths course website: link location, times: Mathematical Institute TBA Supersymmetry and Supergravity Supersymmetry and Supergravity [16 hours] area: PT pre-requisite: Quantum Field Theory (MT) syllabus: Motivations for supersymmetry, spinor algebras and representations, supersymmetry algebra and representations, extended supersymmetry and BPS states, superfields, SUSY field theories, non-renormalisation theorems, SUSY breaking, the MSSM and its phenomenology, basic properties of supergravity. lecturer: Joseph Conlon department: Physics course website: link location, times: Department of Physics TBA Combined Schedule for Hilary Term - to be added in due course