In accordance with Regulations 18
and 19 for the Mathematical Tripos (*Statutes and Ordinances*, p. 361), the Examiners give notice that a candidate may submit an essay on any one of the
following topics:

1. |
Cliques of primes in Noetherian rings |

2. |
Braid groups |

3. |
Groups of piecewise linear jomeomorphisms of the real line |

4. |
The main conjecture of Iwasawa theory for cyclotomic fields |

5. |
The enigmatic Tate-Shafarevich group |

6. |
Abelian varieties over finite fields |

7. |
Wellquasiorders and betterquasiorders |

8. |
D-modules, Representation Theory, Hodge Theory |

9. |
Cochains |

10. |
Geometry of the flag variety, combinatorics of the Weyl group |

11. |
Blocks with a cyclic defect group |

12. |
Groups characters and symmetric functions |

13. |
Modular representation theory of finite groups of lie type in the defining characteristic |

14. |
Two-descent on the Jacobians of hyperelliptic curves |

15. |
Parametric families of solutions |

16. |
Birational geometry in positive characteristic |

17. |
Stable differential forms |

18. |
Harmonic forms |

19. |
The Weinstein conjecture |

20. |
Arnold’s cord conjecture |

21. |
Representations of knot groups in SU(2) |

22. |
Contact structures and symplectic filling |

23. |
Heegaard Floer homology and knots |

24. |
Extremal hypergraph theory |

25. |
Colouring triangle-free graphs |

26. |
The cone conjecture for Calabi-Yau surfaces |

27. |
The theory of K3 surfaces |

28. |
Analysis of a large and complex data set |

29. |
Random motions in spacetime |

30. |
Scaling limit of the long-range contact process |

31. |
Sorting networks and the exclusion process |

32. |
Entanglement manipulation under finite resources |

33. |
Random Fouriers series with applications to statistics |

34. |
Brownian motion and complex analysis |

35. |
Markov modelling in biology |

36. |
Shape-constrained density estimation |

37. |
Functional data analysis |

38. |
High-dimensional variable selection |

39. |
Problems in optimal investment |

40. |
Put–call symmetry |

41. |
Utility maximization with correlation |

42. |
Duality between risk models and queues |

43. |
Regret minimization |

44. |
Stability of queueing systems |

45. |
Mixing efficiency in stratified fluids |

46. |
Natural ventilation |

47. |
Meanderings rivers |

48. |
The fluid dynamics of stable long-term
CO |

49. |
Fluid flow and crystal growth |

50. |
Global modes in shear flow |

51. |
Can an internal wave attractor form on a stair case? |

52. |
How many puffs does it take to make a jet? |

53. |
Jets and turbulence in atmosphere and ocean |

54. |
Stretching, bending, folding, and coiling |

55. |
Wave scattering from rough surfaces |

56. |
Sampling methods in inverse scattering |

57. |
Elasto-capillarity |

58. |
The magnetic buoyancy instability and solar magnetic fields |

59. |
Dynamo action due to the magneto-rotational instability |

60. |
Computation of hamiltonian problems |

61. |
Landau-Kolmogorov inequalities |

62. |
Statistical mechanics without ignorance |

63. |
Localization in relativistic quantum theories |

64. |
Decoherence and the Everett interpretation of quantum theory |

65. |
Quantum computation on Fermionic chains |

66. |
How fast can information come out of a black hole? |

67. |
Jet algorithms |

68. |
Observational tests of primordial (non-)Gaussianity |

69. |
Integrability in large-N gauge theory |

70. |
Affine geometry in mirror symmetry |

71. |
Spontaneous symmetry breaking and effective field theory |

72. |
Cosmic superstrings |

73. |
From topological strings to matrix models |

74. |
The AdS/CFT correspondence |

75. |
The first law of black hole mechanics |

76. |
Critical phenomena in gravitational collapse |

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 2010.

A candidate who proposes to submit an essay should inform the Chairman of Examiners, through her or his Director of Studies, on a form which will be provided, by 30 April 2010. Candidates should submit their essay, through her or his Director of Studies, so as to reach the Chairman of Examiners not later than 30 April 2010.