Cambridge University Reporter

Mathematical Tripos, Part III, 2006: Notice

In accordance with Regulations 18 and 19 for the Mathematical Tripos (Statutes and Ordinances, p. 330), the Examiners give notice that a candidate may submit an essay on any one of the following topics:

  1. Periodic orbit problems
  2. Contact 3-manifolds
  3. Realizability
  4. Locally presentable and accessible categories
  5. Locale theory
  6. Polynomial invariants of finite groups
  7. Finite-dimensional algebras
  8. Subharmonic functions
  9. Calabi-Yau surfaces
  10. Harmonic forms
  11. Descent calculations on the Jacobian of a hyperelliptic curve
  12. Extremal hypergraph theory
  13. Embedding graphs in surfaces
  14. Zero divisors in group algebras
  15. Judicious partitions
  16. Hereditary properties
  17. Sparse Ramsey theory
  18. Higher ramification theory
  19. Iwasawa theory
  20. Complex multiplication of elliptic curves
  21. Simple groups of Lie type
  22. Surface classification and geography
  23. Set theory without the axiom of foundation
  24. Well-quasi-orders and better-quasi-orders
  25. Sums, products, and distinct distances
  26. 'Singularity' theorems and the cosmic censorship conjectures
  27. Etale cohomology
  28. Intermediate Jacobians and rationality problems
  29. Analysis of a large and complex data set
  30. Convergence of Markov processes
  31. Homogenization of diffusion processes
  32. Entropy and the central limit theorem
  33. Log-concave probability and its applications
  34. Fairness and stability of Internet congestion control
  35. Computing the nonparametric maximum likelihood estimator of a logconcave density
  36. Rates of convergence of maximum likelihood estimators via entropy methods
  37. Optimal bandwidth choice in classification problems
  38. Two-sector stochastic growth models
  39. Contract design
  40. Positive and negative correlation
  41. Transience/recurrence of random walks
  42. Random spanning trees
  43. Malliavin calculus for finance
  44. Quantum communication in the presence of noise
  45. Ruin time moments in the classical risk model
  46. Mechanism design
  47. Greedy algorithms
  48. Regularity and optimal routing
  49. Integrability in Yang-Mills theory
  50. Soliton moduli spaces
  51. The geometry of thermodynamics
  52. G-structures in supergravity
  53. The existence and global dynamics of solutions of the Einstein field equations
  54. QCD on the lattice
  55. Anomalies in the standard model
  56. Anomaly mediated supersymmetry breaking
  57. Seiberg duality
  58. The non-perturbative equivalence of perturbatively inequivalent string theories
  59. Characterization of quantum systems
  60. Optimal control of quantum systems
  61. Topological quantum computation
  62. Instantaneous measurements of nonlocal variables
  63. Entropy inequalities
  64. Symplectic methods for Hamiltonian equations
  65. Intersections of subdivision surfaces
  66. Mean-curvature geometry-sensitive subdivision surfaces
  67. Tuning the natural configuration to approximate a conformal map
  68. Applications of complex differential equations to free boundary problems
  69. Pattern formation on the plane
  70. Dynamics of convection in magnetic fields
  71. The flow of granular media
  72. Flow in a reactive porous medium
  73. Tsunamis
  74. Low-frequency oscillations of rotating stars and giant planets
  75. Nonmodal instability in fluid mechanics
  76. Jet noise
  77. Fluent applied to the driven cavity
  78. Fluent applied to the backward facing step
  79. Displacement of a fluid from a channel
  80. Linear stability of a stratified flow in a inclined channel
  81. Numerical simulations of incompressible two-dimensional turbulence
  82. Mode transitions in a duct
  83. Numerical and laboratory dynamo action
  84. The origin and structure of the sunspot penumbra