Mathematical Tripos Part III Lecture Courses in 2019-2020 Department of Pure Mathematics & Mathematical Statistics Department of Applied Mathematics & Theoretical Physics Notes and Disclaimers. • Students may take any combination of lectures that is allowed by the timetable. The examination timetable corresponds to the lecture timetable and it is therefore not possible to take two courses for examination that are lectured in the same timetable slot. There is no requirement that students study only courses offered by one Department. • The code in parentheses after each course name indicates the term of the course (M: Michaelmas; L: Lent; E: Easter), and the number of lectures in the course. Unless indicated otherwise, a 16 lecture course is equivalent to 2 credit units, while a 24 lecture course is equivalent to 3 credit units. Please note that certain courses are non-examinable, and are indicated as such after the title. Some of these courses may be the basis for Part III essays. • At the start of some sections there is a paragraph indicating the desirable previous knowledge for courses in that section. On one hand, such paragraphs are not exhaustive, whilst on the other, not all courses require all the pre-requisite material indicated. However you are strongly recommended to read up on the material with which you are unfamiliar if you intend to take a significant number of courses from a particular section. • The courses described in this document apply only for the academic year 2019-20. Details for subsequent years are often broadly similar, but not necessarily identical. The courses evolve from year to year. • Please note that while an attempt has been made to ensure that the outlines in this booklet are an accurate indication of the content of courses, the outlines do not constitute definitive syllabuses. The lectures and associated course materials as offered in this academic year define the syllabus. Each course lecturer has discretion to vary the material covered. • Some courses have no writeup available at this time, in which case you will see "No description available" in place of a description. Course descriptions will be added to the online version of the Guide to Courses as soon as they are provided by the lecturer. Until then, the descriptions for the previous year (available at http://www.maths.cam.ac.uk/postgrad/mathiii/courseguide.html) may be helpful in giving a rough idea of course content, but beware of the comments in the preceding item on what defines the syllabus. 1 Table of Contents Algebra 3 Algebra(M24) . 3 Lie Algebras and their representations (M24) . 4 D-modules (M16) | Non{Examinable .............................. 4 Profinite Groups (L24) . 5 Modular Representation Theory (L24) . 6 Algebraic Geometry 8 Algebraic Geometry (M24) . 8 Toric geometry (M24) . 8 Complex Manifolds (L24) . 9 Cubic hypersurfaces (L16) | Non{Examinable .......................... 10 Analysis 12 Analysis of Partial Differential Equations (M24) . 12 Introduction to nonlinear analysis (M24) . 13 Introduction to Geometric Measure Theory (L24) . 14 Elliptic Partial Differential Equations (L 24) . 15 Metric Embeddings (L24) . 16 Approximate group actions and Ulam stability (L16) | Non{Examinable . 16 Combinatorics 18 Combinatorics (M16) . 18 Ramsey Theory (M16) . 18 Topics in discrete Fourier analysis (L16) . 19 Extremal Graph Theory (L16) . 20 Algebraic Methods in Combinatorics (L12) | Non{Examinable . 21 Geometry and Topology 22 Algebraic Topology (M24) . 22 Differential Geometry (M24) . 23 Mapping class groups (M16) . 23 Symplectic Topology (L24) . 24 Complex Dynamics (L24) . 25 Geometric Inverse Problems (L24) | Non{Examinable ..................... 26 Geometric Group Theory (L16) | Non{Examinable ....................... 27 Random groups and related topics (L16) | Non{Examinable . 28 2 Logic 29 Category Theory (M24) . 29 Model Theory (L16) . 30 Infinite Games (L24) . 31 Number Theory 32 Modular forms and L-functions (M24) . 32 Elliptic Curves (M24) . 33 Algebraic Number Theory (M24) . 33 Analytic Number Theory (L24) . 34 Probability and Finance 36 Advanced Probability (M24) . 36 Advanced Financial Models (M24) . 37 Percolation and Related Topics (M16) . 37 Mixing times of Markov chains (M16) . 38 Random Walks and Uniform Spanning Trees (L16) . 39 Random planar geometry (L16) . 39 Statistics and Operational Research 41 Modern Statistical Methods (M24) . 41 Causal Inference (M16) . 42 Statistics in Medicine (3 units) . 43 Statistics in Medical Practice (M12) . 43 Analysis of Survival Data (L12) . 44 Additional Information . 45 Astrostatistics (L24) . 45 Stochastic Calculus and Applications (L24) . 46 Topics in Statistical Theory (L16) . 47 Statistical Learning in Practice (L24) . 48 Particle Physics, Quantum Fields and Strings 49 Quantum Field Theory (M24) . 49 Symmetries, Fields and Particles (M24) . 50 Statistical Field Theory (M16) . 51 Advanced Quantum Field Theory (L24) . 52 The Standard Model (L24) . 53 String Theory (L24) . 54 Supersymmetry (L16) . 55 Classical and Quantum Solitons (E16) . 56 Physics Beyond the Standard Model (E8) | Non{Examinable . 56 3 Relativity and Gravitation 58 General Relativity (M24) . 58 Cosmology (M24) . 59 Black Holes (L24) . 60 Field Theory in Cosmology (L24) . 60 Applications of Differential Geometry to Physics . 61 Gauge/Gravity Duality (E16) . 62 Spinor Techniques in General Relativity (L24) | Non{Examinable . 63 Astrophysics 65 Galaxy Formation (M24) . 65 Astrophysical Fluid Dynamics (M24) . 66 Structure and Evolution of Stars (M24) . 67 Extrasolar Planets: Atmospheres and Interiors (L24) . 68 The Life and Death of Galaxies (L24) . 68 Dynamics of Astrophysical Discs (L16) . 69 Binary Stars (L16) . 70 Quantum Computation, Information and Foundations 72 Quantum Computation (M16) . 72 Quantum Information Theory (L24) . 73 Philosophy of Physics 74 Philosophical Aspects of Classical and Quantum Mechanics (M8) | Non{Examinable . 74 Philosophical Aspects of Quantum Field Theory (L8) | Non{Examinable . 76 Applied and Computational Analysis 78 Inverse Problems (M24) . 78 Distribution Theory and Applications (M16) . 79 Topics in Convex Optimisation (M16) . 79 Numerical Solution of Differential Equations (L24) . 80 Hybrid Photonics Computing (L16) . 81 Mathematical Analysis of the Incompressible Navier-Stokes Equations (L24) | Non{Examinable 81 Continuum Mechanics 83 Slow Viscous Flow (M24) . ..