In accordance with Regulations 18 and 19 for the Mathematical Tripos (Statutes and Ordinances, p. 328), the Examiners give notice that a candidate may submit an essay on any one of the following topics:
1. Analysis of a large and complex data set
2. Optimal bandwidth choice in classification problems
3. Rates of convergence of maximum likelihood estimators via entropy methods
4. Blocks with a cyclic defect group
5. Symmetric functions and characters of GLn
6. Iwahori-Hecke algebras
7. Zoll surfaces
8. The boundary rigidity problem
9. Synthetic differential geometry
10. Locally presentable and accessible categories
11. Semidefinite programming
12. Combinatorial auctions
13. Higher dimensional categories
14. Reflexive polytopes and Calabi-Yau threefolds
15. Congestion control for the internet and/or wireless networks
16. Gaps between primes
17. Discrepancy of boxes
18. The Littlewood problem
19. Homogenization of diffusion processes
20. Stochastic flows
21. Malliavin calculus
22. The local Langlands correspondence for GL2
23. The space of cuspidal data of a p-adic reductive group
24. Measures of risk
25. Dirac operators
26. K3 surfaces
27. Optimal broadcasting in capacitated networks
28. Gossiping in unstructured networks
29. Cochains
30. Non-Abelian Hodge theory
31. D-modules, representation theory, Hodge theory
32. Hilbert's thirteenth problem
33. Shannon Whittaker reconstruction from irregular sampling
34. Convolution squares
35. Set theory without the axiom of foundation
36. Wellquasiorders and betterquasiorders
37. Influence and sharp thresholds
38. Positive and negative correlation
39. The Nielsen kernel
40. The rate of growth of polynomial images
41. Phase-type distributions in risk theory
42. Universality of the Tracy-Widom distribution
43. Hydrodynamic limits of interacting particle systems
44. p-adic uniformization
45. Higher regulators of number fields
46. Generalized quasi-random graphs
47. Equivalence problem
48. The fluid dynamics of insect flight
49. Pulse propagation in arteries
50. Strong converses in quantum information theory
51. Stretching, bending, folding, and coiling
52. The one way model for quantum computation
53. Rayleigh-Bénard convection
54. Localized pattern formation
55. The experimental evidence for general relativity
56. Skyrmions
57. The Weinberg-Witten theorem
58. The magnetorotational instability in astrophysics
59. Highly oscillatory quadrature
60. Numerical methods for differential equations in Lie groups
61. Applications of lattice QCD
62. Instabilities of rotating stars
63. Numerical and laboratory dynamo action
64. The origin and structure of the sunspot penumbra
65. Fluent applied to the driven cavity
66. Linear stability of a stratified flow in an inclined channel
67. Numerical simulations of incompressible two-dimensional turbulence
68. Calibrations in string theory
69. Does black-hole evaporation imply that physics is non-unitary, and if so, what must the laws of physics look like?
70. Asymptotics beyond all orders
71. Finite-time singularities
72. Compressible flow past a cylinder
73. Non-gaussianity from inflation
74. Phenomenology of extra dimensions
75. Foundations of statistical mechanics
76. Carbon dioxide sequestration
77. Viscous gravity currents and natural lava flows
78. The transport of ice from continent to polar sea
79. Factorizable S-matrices in two dimensions
80. Subdivision schemes with complex eigenvalues
81. Bezier end-conditions for univariate subdivision
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 2007.
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 7 May 2007, and should submit the essay, through his or her Director of Studies, so as to reach the Chairman of Examiners not later than 17 May 2007.