Reporter 27/11/02: Mathematical Tripos, Part III, 2003: Notice by the Examiners

Mathematical Tripos, Part III, 2003: Notice by the Examiners

In accordance with Regulations 18 and 19 for the Mathematical Tripos (Statutes and Ordinances, p. 335), the Examiners give notice that a candidate may submit an essay on any one of the following topics:

Algebraic monoids
Quantum groups
Well-quasi-orders and better-quasi-orders
Lagrangians of hypergraphs
Ergodic Theory and Ramsey Theory
Ramsey Túran Theory
Pseudo-random graphs
Locally presentable and accessible categories
Uniform locales
Applications of modular forms
Arithmetic progressions of length 3
Algebraic homotopy and weak categories
Operads and n-categories
Enveloping algebras of finite dimensional nilpotent lie algebras
Sentences preserved under algebraic operations
Existentially complete models of algebraic theories
The Riemann Hilbert problem
Simple groups of lie type
Orders of permutation groups
The topology of algebraic varieties
Derived categories of coherent sheaves on algebraic varieties
Dirac operators
Complex multiplication
p-adic uniformization
Polarization and the symmetry of analytic functions
Nevanlinna Theory and solutions of algebraic differential equations
The travelling salesman problem and harmonic analysis
Prime Fano 3 folds
Curvature, the Grothendieck-Katz conjecture, and q-analogues
Global structure in the homotopy groups of spheres
The Lüroth problem and singularities of theta divisions
Formal deformations and their algebraizations
The Hofer-Zehnder capacity
Exotic spheres with positive curvature
Congruent numbers
Holomorphic discs and three-manifolds
Imperfect and/or perfect simulation
Random fractals
The stability of Internet congestion control
Least favourable families
Matching priors
Markov chains with a large finite state-space
Entanglement in Quantum Information Theory
Estimation of ruin probabilities
Analysis of a large and complex data set
Global modes in slowly spatial developing flows
Mass transfer in eccentric binary stars
Gravitational radiation from accreting neutron stars
The biophysics of DNA condensation and packing
Collective behaviour of motor proteins: instabilities and patterns
Mechanics of cell adhesion and motility
Stokes flow in corners
Recent global results in classical general relativity
Quark stars
Flux quantization in M-theory
Intersection of subdivision surfaces
Subdivision: an annotated structured bibliography
Numerical methods for differential equations in lie groups
The thrust of a swimming fish and its vortex wake
Spin networks, from Penrose to the Barrett-Crane model
Electroweak baryogenesis
Dynamics of convection in magnetic fields
Faraday waves
Networks of coupled cells or oscillators
A nonlinear dynamical systems approach to forecasting volcanic eruptions
The dynamics of Black Hole accretion flows
Accretion flows onto magnetized stars
Dirac equation in a background field
Convection with temperature dependent viscosity
Internal wave focusing in a non-uniform stratification
Cold room storage and turbulent jets
Ashtekar variables and self-duality
The Sunyaev-Zeldovich effect
Planet-disc interactions
Information encoding in small neural systems
Chaotic advection in the atmosphere
Baroclinic instability and baroclinic turbulence
Numerical solutions of two-dimensional driven cavity flow
An almost Burgers' equation
Completion of oil wells
Numerical simulations of incompressible two-dimensional turbulence
Compressible flow past a cylinder
Separation on a free surface
Very-high-energy electron proton scattering
Balance and Lighthill radiation in atmosphere-ocean dynamics
Jet noise
Sunspots
The holographic nature of gravity
The connection between critical phenomena and relativistic quantum field theories
Rigidity theory for circle homeomorphisms
The spatial spread of an infectious disease
Quasipatterns

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 2003.

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 2 May 2003, and should submit the essay, through his or her Director of Studies, so as to reach the Chairman of Examiners not later than 15 May 2003.

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