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In accordance with Regulations 18 and 19 for the Mathematical Tripos (*Statutes and Ordinances*, p. 323), the Examiners give notice that a candidate may submit an essay on any one of the following topics:

Representations of SL(2,R)

Symplectic 4-manifolds

Cohomology Operations

The Borel-Weil-Bott Theorem and Generalizations

The Narasimhan-Seshadri Theorem and Generalizations

The 3-manifold Geometrisation Conjecture of W. P. Thurston

Shannon Whittaker Reconstruction from Irregular Sampling

Bloch Functions

The Travelling Salesman Problem and Harmonic Analysis

Some Attempted Proofs of the Michael Conjecture

Proof Theory

Realizability

Allegories

Synthetic Differential Geometry

Set Theory without the Axiom of Foundation

Well-quasi-orders and Better-quasi-orders

Left-Distributive Algebras

Higher-Dimensional Algebras

Rational Double Points

Surface Classification and Geography

The Topology of Algebraic Varieties

The Mori Cone of the Moduli Space of Curves

Lehmer's Problem and Mahler's Measure

Cohomological Approach to Class Field Theory

Higher Ramification Theory

Intersecting Set Systems

Pseudo-random Graphs

Canonical Ramsey Theory

Lagrangians of Hypergraphs

Arithmetic Progressions in Sumsets

Sporadic Simple Groups

Simple Groups of Lie Type

Quivers and Finite-Dimensional Algebras

Symmetric Functions and Characters in *GL _{n}*

Iwahori-Hecke Algebras

Zsigmondy's Theorem and its Algebraic Applications

Imperfect and/or Perfect Stimulation

Random Fractals

Conformal Invariance and Universality

Homogenization

Convergence of Markov Processes

Analysis of a Large and Complex Data Set

Game Contingent Plans

Advanced Methods of Classical and Quantum Coding

Mathematical Aspects of Quantum Computing: Beyond Shor's Algorithm

Perpetuities

Matching Priors

Least Favourable Families

Rotating Rayleigh Benard Convection

Faraday Waves

Global Bifurcations of Codimension Two and Three

Mean Flow Effects in Modulational Instabilities

Localized Solutions in Pattern Forming Instabilities

Baroclinic Instability and Baroclinic Turbulence

Instabilities of a Sheared Elastic Liquid

Dust Resuspension by Raindrops

Human Plumes

Internal Wave Focusing in a Non-uniform Stratification

Cold Room Storage and Turbulent Jets

Elastic Jumps in Flexible Fluid-filled Tubes

Balance and Lighthill Radiation in Atmosphere-Ocean Dynamics

Fast Flows in Curved pipes: a Conundrum?

Instability Analysis for Swirling Jets: Vortex Breakdown?

Separation on a Free Surface

Drips to Drops - Bridging the Gap

The Fluid Dynamics of the Earth's Outer Core

CP Violation and B-Mesons

Chiral Symmetry and Lattice Fermions

The Real Space Renormalization Group and its Application in Two Dimensions

Quantification and Qualification of Mixed-state Entanglement 'Interaction Free' Measurements

A Recycling Universe from Colliding Branes

The Role of Metrics of Special and Exceptional Holonomy in M-Theory

Neutrino Oscillations

Brane World Cosmology

Mass Transfer in Eccentric Binary Stars

Warped Accretion Discs

Solar Activity and Climactic Change

Turbulent Magnetic Fields

Rotational Dynamics of the Sun

The Experimental Evidence for General Relativity

The Ionization History of the Universe

The End of Inflation: Reheating or Preheating the Universe

Quantum Cosmology

De Sitter Space Revisited

The N=1 Ramond Algebra

The Large N limit of SU(N) Gauge Theory

Spin Foam Models and Quantum Gravity

The Age of the Universe

Can an Even-arity Antiphase Interpolating Refinement Exist?

Level-set Methods

Applications of Integrable Systems to Geometry

Defect Formation in Phase Transitions

Algebraic *K*-Theory

Algebraic Cycles

Exotic Spheres with Positive Curvature

The Hofer-Zehnder Capacity

Cyclic Dynamics of Natural-Enemy Populations

The Power-Law Behaviour of Populations

Macro v Micro Parasites: a Comparison between Methods and Models

The Role of Volatiles in Volcanic Eruptions

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 2002.

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 2002, and should submit the essay, through his or her Director of Studies, so as to reach the Chairman of Examiners not later than 16 May 2002.

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Cambridge University Reporter, 28 November 2001

Copyright © 2001 The Chancellor, Masters and Scholars of the University of Cambridge.