Mathematical Tripos Part III Lecture Courses in 2020-2021 Department of Pure Mathematics & Mathematical Statistics Department of Applied Mathematics & Theoretical Physics Notes and Disclaimers. • Students may attend any combination of lectures but should note that it is 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 the 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 2020-21. 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 6 Finite dimensional Lie and associative algebras (M24) . 6 Commutative Algebra (24 lectures, MT20) . 7 Representation Theory of Symmetric Groups (L24) . 8 Profinite Groups and Group Cohomology (L24) . 8 Lie algebras, Vertex algebras, Shtuka (L24) | Non{Examinable ................ 9 Sofic Groups (L16) | Non{Examinable .............................. 10 Algebraic Geometry 12 Algebraic Geometry (M24) . 12 Algebraic surfaces (L24) . 12 Geometric aspects of p-adic Hodge theory (M16) . 13 Analysis 15 An Introduction to Non Linear Analysis (M24) . 15 Fractal Geometry and Additive Combinatorics(L16) . 16 Metric Embeddings (L24) . 17 Combinatorics 19 Topics in Combinatorics (M16) . 19 Ramsey Theory (M16) . 20 Additive Combinatorics (L24) . 20 Higher-order uniformity and applications (E12) | Non{Examinable . 21 Geometry and Topology 23 Algebraic Topology (M24) . 23 Differential Geometry (M24) . 23 Mapping class groups (L16) . 24 Complex Dynamics (M16) . 25 Symplectic topology (L16) . 26 Homotopy Theory (L24) . 26 Logic 28 Category Theory (M24) . 28 Model Theory (M24) . 29 Infinite Games (L24) . 30 2 Number Theory 31 Local Fields (M24) . 31 Algebraic Number Theory (L24) . 31 Elliptic Curves (M24) . 32 Modular Forms (L24) . 33 Multiplicative functions (M16) . 34 Diophantine Analysis (L24) . 34 Probability and Finance 36 Advanced Probability (M24) . 36 Mixing times of Markov chains (M16) . 37 Percolation and Related Topics (M16) . 37 Random planar geometry (L16) . 38 Stochastic Calculus and Applications (L24) . 39 Information Theory (L16) . 39 Statistics and Operational Research 41 Causal Inference (M16) . 41 Robust Statistics (L16) . 42 Topics in Statistical Theory (M16) . 43 Statistics in Medicine (3 units) . 44 Statistics in Medical Practice (M12) . 44 Analysis of Survival Data (L12) . 44 Additional Information . 45 Functional Data Analysis (L16) . 46 Astrostatistics (L24) . 46 Statistical Learning in Practice (L24) . 47 Statistics in Medicine (3 units) . 48 Statistics in Medical Practice (M12) . 48 Analysis of Survival Data (L12) . 49 Additional Information . 49 Particle Physics, Quantum Fields and Strings 51 Symmetries, Fields and Particles (M24) . 51 Symmetries, Fields and Particles (M24) . 52 Statistical Field Theory (M16) . 52 Non-Equilibrium Statistical Field Theory (M8) | Non{Examinable . 53 Advanced Quantum Field Theory (L24) . 54 The Standard Model (L24) . 55 String Theory (L24) . 56 Supersymmetry (L16) . 57 Classical and Quantum Solitons (E16) . 58 Physics Beyond the Standard Model (E8) . 59 3 Relativity and Cosmology 60 Cosmology (M24) . 60 General Relativity (M24) . 61 Black Holes (L24) . 62 Field Theory in Cosmology (L24) . 63 Applications of Differential Geometry to Physics(L16) . 64 Applications of Analysis in Physics (L16) | Non{Examinable . 64 Gauge/Gravity Duality (E16) . 65 Astrophysics 66 Structure and Evolution of Stars (M24) . 66 Galaxy Formation (M24) . 67 Planetary System Dynamics (M24) . 67 Extrasolar Planets: Atmospheres and Interiors (M24) . 69 The Life and Death of Galaxies (L24) . 70 Astrophysical Fluid Dynamics (L24) . 71 Dynamics of Astrophysical Discs (L16) . 72 Binary Stars (L16) . 73 Astrophysical black holes (L16) . 74 Astrostatistics (L24) . 75 Quantum Computation, Information and Foundations 76 Quantum Computation (M16) . 76 Quantum Information Theory (L24) . 77 Philosophy of Physics 78 Philosophical Aspects of Quantum Fields (M8) . ..