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In accordance with Regulations 18 and 19 for the Mathematical Tripos (*Statutes and Ordinances*, p. 327), the Examiners give notice that a candidate may submit an essay on any one of the following topics:

Calibrated Manifolds

Hodge Theorem for Manifolds with Boundary

Vanishing Cycles

Mapping Class Groups

Curvature and Betti Numbers

Closed Geodesics on Riemannian Manifolds

The Hofner-Zehnder Capacity

Iwahori-Hecke Algebras

Symmetric Functions

Representations of Finite General Linear Groups

Reflection Groups and Coxeter Groups

Allegories

Synthetic Differential Geometry

Recognising the Three-dimensional Sphere
*p*-adic Uniformization

Higher Regulators of Number Fields

Symmetries and Reductions of KdV and KP Equations

The Toda Chain

Cohomology of Discrete Groups

The h-Principle in Topology and Geometry

Set Theory without the Axiom of Foundation

Well-quasi-orders and Better-quasi-orders

Cochains

Finite Simple Groups

Higher Ramification Theory

Shannon Whittaker Reconstruction from Irregular Sampling

Groebner Bases and Convex polytopes

Automorphisms of Free Groups

Arithmetic Progression in Sumsets

Canonical Ramsey Theory

K-Theory and Representation Theory

The High Dimensional Poincaré Conjecture

Sumsets and Product Sets

Embedding Graphs in Surfaces

Analysis of a Large and Complex Data Set

Capacities of Quantum Channels

Duality Methods in Investment/Consumption Models

Bagging

Large Deviations in Mathematical Models of Re-insurance

Bin Packing

P vs. NP

Search and Rendezvous

Positive and Negative Correlation

Transience/Recurrence of Random Walks

Causality in Discrete Models of Quantum Spacetime

Fluxes of Anti-symmetric Tensor Fields in String Theory

String Theorists' Search for the Standard Model

The Motion of Granular Material

The Application of Statistics to Volcanology

Three-dimensional Einstein-Weyl Gravity

The Numerical Analysis of Hamiltonian Problems

The Functional Schrödinger Representation of QFT

Structure in Saturn's Rings

Holonomic Quantum Evolutions

Cooling Flows in Clusters of Galaxies

Finite Temperature Gauge Field Theory

Intersection of Subdivision Surfaces

Is there an Interpolating Dual Subdivision Curve Scheme?

Greedy Algorithms for the *n*-term Approximation

Parametrizing Common Envelope Evolution

Fine Structure in Sunspots

Noncommutative Geometry from String Theory

Convection with Temperature-dependent Viscosity

Double Diffusive Convection due to Horizontal Gradients

Internal Wave Focusing in a Non-uniform Stratification

Vortex Rings Colliding with Rough Boundaries

Spatially Extended Pattern Formation

Networks of Coupled Oscillators

Turbulent Magnetic Fields

Distributional Sources in General Relativity

Dark Energy

Waves in Vertical Flow

Instabilities of a Sheared Elastic Liquid

Oceanic Rossby Waves

Stratospheric Variability and the Implications for the Troposphere

CMB Polarization

Cosmological Perturbations from Multifield Inflation

Melt Transport in the Mantle

Drips to Drops - Bridging the Gap

Finite-time Singularities

Compressible Flow past a Cylinder

Separation on a Free Surface

Bacterial Fluid Dynamics

Candidates are reminded that they may request leave to submit an essay on a topic other than those given above provided that the request is made, through their Director of Studies, so as to reach the Secretary of the Faculty Board, Mathematics Faculty Office, Centre for Mathematical Sciences, Wilberforce Road, not later than 1 February 2004.

A candidate who proposes to submit an essay should inform the Chairman of Examiners, through his or her Director of Studies, on a form which will be provided, by 3 May 2004, and should submit the essay, through his or her Director of Studies, so as to reach the Chairman of Examiners not later than 13 May 2004.

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Cambridge University Reporter, 19 November 2003

Copyright © 2011 The Chancellor, Masters and Scholars
of the University of Cambridge.