Cambridge University Reporter


Mathematical Tripos, Part III, 2005: Notice

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.