In accordance with Regulations 18 and 19 for the Mathematical Tripos (Statutes and Ordinances, p. 322), the Examiners give notice that a candidate may submit an essay on any one of the following topics:
1. Unique ergodicity of horocycle flows
2. Ergodicity of geodesic flows on manifolds of negative curvature
3. Immersions
4. Amoebas
5. Engulfing
6. Green rings and Burnside rings
7. Buildings
8. Left distributive algebras
9. The h-principle in topology and geometry
10. Whitehead torsion
11. Higher dimensional categories
12. Proof theory
13. Realizability
14. Synthetic differential geometry
15. Hurwitz groups
16. Sporadic simple groups
17. Orders of permutation groups
18. The moduli space of curves
19. Bar duality and Koszul duality
20. Lagrangians of hypergraphs
21. Ergodic theory and Ramsey theory
22. Stable differential forms
23. Dirac operators
24. Grothendieck's theorem on Lie groups
25. Convergence of Markov processes
26. Homogenization of diffusion processes
27. Duality in optimal investment/consumption models
28. Analysis of a large and complex data set
29. Random spanning trees
30. Nonparametric regression
31. Differential games
32. Regularity and optimal routing
33. Greedy algorithms
34. Cooling flows in cluster of galaxies
35. SUSY dark matter and colliders
36. Twistor transform
37. Internal wave focusing in a non-uniform stratification
38. Vortex rings colliding with rough boundaries
39. Bacterial fluid dynamics
40. Conformal infinity
41. PH splines
42. Lateral artifacts in surfaces defined by regular grids of points
43. Magnetic fields and turbulence in clusters of galaxies
44. High-resolution methods for hyperbolic conservation laws
45. Why are very close Ba stars eccentric?
46. Numerical solution of highly oscillatory problems
47. Is there a string theory of hadrons?
48. Heteroclinic cycles in symmetric systems
49. Pattern formation on the plane
50. Dynamics of convection in magnetic fields
51. Stretching, bending, folding, and coiling
52. Classical string motion on AdS5 x S5
53. Warped accretion discs
54. Supersymmetric matrix models
55. The role of helicity in large scale dynamos
56. Quantum particles and strings in singular spacetime
57. Mode transitions in a duct
58. Adaptive solution of the Poisson problem
59. Fluent applied to the driven cavity
60. Fluent applied to the backward facing step
61. Linear stability of a stratified flow in an inclined channel
62. Displacement of a fluid from a channel
63. Dynamics of the solar tachocline
64. Three-dimensional discrete quantum gravity as a topological quantum field theory
65. Compressible flow past a cylinder
66. Asymptotics beyond all borders
67. Finite-time singularities
68. Chameleon cosmology
69. Quantum computation with linear optics
70. Global modes in shear flow
71. Flips and higher dimensional birational geometry
72. Arakelov geometry of arithmetic surfaces
73. K3 surfaces
74. Mirror symmetry for P2
75. Inflation and string theory
76. Internet traffic models
77. Yano tensors
78. Ramsey Túran theory
79. L-functions and modular curves
80. Congruences between modular forms
81. Higher regulators of number fields
82. Brane inflation, cosmic strings, and cosmological consequences
83. Pseudo-random graphs
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 2005.
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 2005, and should submit the essay, through his or her Director of Studies, so as to reach the Chairman of Examiners not later than 19 May 2005.