Lecture courses for HT: Advanced Fluid Dynamics Advanced Fluid Dynamics [16 hours] area: CM, 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 beads on springs: Oldroyd-B model for polymeric liquids, elastic waves, anisotropic pressure. Dilute suspension of orientable particles (ellipsoids): road map to liquid crystals, swimmers and active matter. sequel: Collisional Advanced Plasma Physics (TT), Soft Matter Physics (HT). lecturer: Alex Schekochihin, Paul Dellar department: Maths and Physics course website: link location, times: Department of Physics, Mondays 3–5pm [Fisher Room]. Soft Matter Physics Soft Matter Physics [16 hours] area: prequels: 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, Mondays at 12noon [DWB Seminar Room], Fridays at 12noon [DWB Seminar Room]. 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, Mondays at 12noon and Wednesdays at 10am [Dobson Room]. Nonlinear Systems Nonlinear Systems [16 hours] area: CM, Astro prequels/pre-requisites: Nonequilibrium Statistical Physics (MT) syllabus: Part I: Bifurcations. Bifurcation theory: standard codimension one examples (saddle-node, pitchfork, trans-critical, Hopf); normal forms; Conservative and non-conservative systems. Part II: Nonlinear Oscillations. Van der Pol and Duffing's equations. Poincaré-Lindstedt method; Method of multiple scales; Krylov-Bogoliubov method of Averaging; Relaxation and forced oscillations; Synchronization of coupled oscillators. Part III: Maps. Poincaré sections and first-return maps. Stability and periodic orbits; bifurcations of one-dimensional maps. Two-dimensional maps: Hénon map, Chirikov (standard) map. Part IV: Chaos in Maps and Differential Equations. Maps: Logistic map, Bernoulli shift map, symbolic dynamics, Skinny Baker's map, Smale's Horseshoe Map. Differential equations: Lorenz equations, Rossler equations. lecturer: Irene Moroz department: Maths course website: Maths course B5.6 location, times: Mathematical Institute, Mondays at 11am and Tuesday at 4pm [L2]. Advanced Quantum Field Theory Advanced Quantum Field Theory for Particle Physics [24 hours] area: PT prequel: 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: Graham Ross department: Physics course website: link location, times: Mathematical Institute, Wednesdays at 12noon [L3], and Department of Physics,Thursdays at 9am and 3pm [Fisher Room]. Quantum CMP II Quantum Condensed Matter Physics II [24 hours] area: CM Prequel/pre-requisite: Introduction to Quantum Condensed Matter Physics (MT) syllabus: Phase transitions: transfer matrix methods, spontaneous symmetry breaking in the Ising model, Landau theory of phase transitions. Fermi liquid theory. BCS theory of superconductivity. Strong interactions: Mott insulators. Ferromagnetism and antiferromagnetism, Holstein-Primakoff transformation. Quantum Hall effect: integer and fractional QHE; fractional statistics. Disorderd systems: random potential and localization. sequel: Advanced Quantum Condensed Matter Physics (TT), Topics in Quantum Condensed Matter Physics (TT) lecturer: Steve Simon department: Physics course website: link location, times: Department of Physics, Mondays at 9-10am (9-11am in weeks 3 and 4) [Dennis Sciama Lecture Room (weeks 1–2), DWB Seminar Room (weeks 3 & 4) Fisher Room (weeks 5–8)], Wednesdays at 10am [Dennis Sciama Lecture Room (weeks 1–2), Fisher Room (weeks 4–8)], and Thursday at 11am [Dennis Sciama Lecture Room (week 1), Fisher Room (weeks 2, 4–8)]. Nonequilibrium Statistical Physics (continued) Nonequilibrium Statistical Physics (continued)[8 hours] area: PT, CM, Astro, foundational course prequel: Nonequilibrium Statistical Physics (MT) syllabus: Mean-field theory of reaction-diffusion processes. Pattern formation. Kuramoto model, synchronization transition. Stochastic field theory. Dynamical renormalization group. sequel: Topics in Soft & Active Matter Physics (TT) lecturer: Ramin Golestanian department: Physics course website: TBA location, times: Department of Physics, Wednesdays at 3-5pm [Fisher Room (weeks 1–4)]. Waves and Compressible Flow Waves and Compressible Flow [16 hours] area: Astro prequel: Viscous Flow (MT), Kinetic Theory (MT) syllabus: Equations of inviscid compressible flow including flow relative to rotating axes. Models for linear wave propagation including Stokes waves, internal gravity waves, inertial waves in a rotating fluid, and simple solutions. Theories for Linear Waves: Fourier Series, Fourier integrals, method of stationary phase, dispersion and group velocity. Flow past thin wings. Nonlinear Waves: method of characteristics, simple wave flows applied to one-dimensional unsteady gas flow and shallow water theory. Shock Waves: weak solutions, Rankine–Hugoniot relations, oblique shocks, bores and hydraulic jumps. sequel: Geophysical Fluid Dynamics (TT). lecturer: Ian Hewitt department: Maths course website: Maths course B5.4 location, times: Mathematical Institute, Wednesdays and Thursdays at 9am [L3]. 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: Philip Candelas department: Maths course website: TBA location, times: Mathematical Institute, Mondays at 9am [L3] and Wednesdays at 9am [L4]. Networks Networks [16 hours] area: CM pre-requisites: Maths C5.3 or another undergraduate course in Statistical Mechanics syllabus: 1. Introduction and Basic Concepts: nodes, edges, adjacencies, weighted networks, unweighted networks, degree and strength, degree distribution, other types of networks. 2. Small Worlds: clustering coefficients, paths and geodesic paths, Watts-Strogatz networks [focus is on modelling and heuristic calculations]. 3. Toy Models of Network Formation: preferential attachment, generalizations of preferential attachment, network optimization. 4. Additional Summary Statistics and Other Useful Concepts: modularity and assortativity, degree-degree correlations, centrality measures, communicability, reciprocity and structural balance. 5. Random Graphs: Erdos-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: linkage clustering, optimization of modularity and other quality functions, overlapping communities, other methods and generalizations. 7. Dynamics on (and of) Networks: general ideas, models of biological and social contagions, percolation, voter and opinion models, temporal networks, other topics. 8. Additional Topics: 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] sequel: Complex Systems (TT) lecturer: Mason Porter department: Maths course website: Maths course C5.4 location, times: Mathematical Institute, Mondays at 5pm (weeks 1-6) [L3], Tuesdays at 2pm (weeks 1-3, 5, 6) [L2] (week 4) [L3], Wednesdays 4-6pm (week 7 only) [L3]. Thursday at 1pm (weeks 7-8 only) [L3] Collisionless Plasma Physics Collisionless Plasma Physics [16 hours] area: Astro prequel: Kinetic Theory (MT) pre-requisites: Kinetic Theory (MT), an undergraduate course on Electricity and Magnetism. syllabus: Part I. Magnetized plasmas (8 lectures). Particle motion. Drift kinetics. Drift waves and slab Ion Temperature Gradient instability. Barnes damping of compressional Alfven waves. Part II. Plasma waves (8 lectures). 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, Tuesdays at 11am to 1pm [Lindemann Lecture Theatre (weeks 1, 3-5, 7-8), Dobson Room (weeks 2 and 6)]. Galactic and Planetary Dynamics Galactic and Planetary Dynamics ("Celestial Mechanics for the 21st Century") [16 hours] area: 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, Wednesdays and Fridays at 11am [Fisher Room]. Supersymmetry and Supergravity Supersymmetry and Supergravity [24 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, rescaling anomalies, NSVZ beta function, basic properties of supergravity. lecturer: Joseph Conlon department: Physics course website: link location, times: Department of Physics, Tuesdays at 11–1pm [Fisher Room] and Wednesdays at 2pm [Fisher Room (weeks 1–6, 8), T.B.C. (week 7)]. Stellar Astrophysics Stellar Astrophysics [10 hours] area: Astro syllabus: Part I (Part of C1, 10 lectures in HT, of which the first two will be a primer on basic stellar astrophysics): Modern topics in stellar astrophysics. Late stages of stellar evolution; massive stars; supernovae, millisecond pulsars, hypernovae, gamma-ray bursts; compact binaries; the origin of elements, chemical evolution of the Universe. lecturer: Philipp Podsiadlowski department: Physics course website: As part of course C1 in physics location, times: Department of Physics, Tuesdays at 9am, Wednesdays at 12noon (weeks 1–2, 4–8) and Thursdays at 10am (weeks 1–5, 8) [Dennis Sciama Lecture Theatre]. High Energy Astrophysics High Energy Astrophysics [10 hours] area: Astro syllabus: Part I (Part of C1, 10 lectures in HT): Physics of interactions between high energy particles and radiation (synchrotron, inverse-Compton, thermal bremsstrahlung); the Eddington limit; accretion onto compact objects; black holes, active galaxies and relativistic jets. lecturer: Garret Cotter department: Physics course website: As part of course C1 in physics location, times: Department of Physics, Tuesdays at 9am, Wednesdays at 12noon (weeks 1–2, 4–8) and Thursdays at 10am (weeks 1–5, 8) [Dennis Sciama Lecture Theatre]. General Relativity II General Relativity II [16 hours] area: PT/Astro prequel/pre-requisite: General Relativity I (MT) 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, Mondays at 10am (weeks 1-5, 7-8) [L4], Tuesdays at 10am (weeks 1-5, 7-8) [L4], Wednesday at 1pm (week 6 only) [L6] and Thursday at 1pm (week 6 only) [L3]. 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: Johannes Noller department: Physics course website: TBA location, times: Department of Physics, Tuesdays at 2pm and Fridays at 10am [Fisher Room]. Applied Complex Variables Applied Complex Variables [16 hours] area: PT/CM/Astro prequel: Perturbation Methods (MT) syllabus: Review of core complex analysis, especially 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 to inviscid hydrodynamics: flow past an aerofoil and other obstacles by conformal mapping; free streamline flows of 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. Transform methods, 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, Thursdays at 2pm (weeks 1-3, 5-8) [L2] (week 4) [L3], and Fridays at 2pm [L2]. Scientific Computing II Scientific Computing II [12 hours] area: PT/CM/Astro prequel/pre-requisite: Scientific Computing I (MT) syllabus: DIFFERENTIAL EQUATIONS. Algorithms and software for ODE initial-value and boundary-value problems; computational nonlinear dynamics. Finite difference and spectral methods for steady-state and time dependent partial differential equations. Applications. lecturer: Nick Trefethen department: Maths course website: Scientific Computing for DPhil Students location, times: Mathematical Institute, Tuesdays at 9am (weeks 1-6) [L3] and Fridays at 9am (weeks 1-4, 6) [L3] (weeks 5) [L2]. Differentiable Manifolds Differentiable Manifolds [16 hours] area: PT/Astro syllabus: Smooth manifolds and smooth maps. Tangent vectors, the tangent bundle, induced maps. Vector fields and flows, the Lie bracket and Lie derivative. Exterior algebra, differential forms, exterior derivative, Cartan formula in terms of Lie derivative. Orientability. Partitions of unity, integration on oriented manifolds. Stokes' theorem. De Rham cohomology. Applications of de Rham theory including degree. Riemannian metrics. Isometries. Geodesics. lecturer: Dominic Joyce department: Maths course website: Maths course C3.3 location, times: Mathematical Institute, Thursdays at 12noon [L3] and Fridays at 12noon [L3 (weeks 2-4, 6, 8), L5 (week 5), C4 (week 7)]. 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: Andre Henriques department: Maths course website: Maths course C3.2 location, times: Mathematical Institute, Mondays at 11am and Wednesdays at 10am [C2]. Combined Schedule for Hilary Term