Professor Sir Martin Taylor

Warden

Professor Sir Martin Taylor, FRS, Professor of Pure Mathematics and Past Vice-President and Physical Secretary of the Royal Society, took up office as Warden of Merton College on 2 October 2010. Professor Taylor was a Professor of pure mathematics at Manchester since he moved from Trinity College, Cambridge in 1986. Most recently his research has led him to study various aspects of arithmetic geometry: in particular, he and his collaborators have demonstrated how geometric properties of zeros of integral polynomials in many variables can be determined by the behaviour associated L-functions. Professor Taylor read Mathematics at Pembroke College, Oxford before gaining a PhD at King's College London.

In 1982 he was awarded the London Mathematical Society's Whitehead Prize and the Adams Prize (shared) in 1983. He became President of the London Mathematical Society in 1998, and in the same year was given an EPSRC Senior Fellowship. In 2003 he received a Royal Society Wolfson Merit Award and became Chairman of the International Review of Mathematics (Steering group).

Publications

  1. Galois module structure of classgroups and units, Mathematika (22) 1975, 156-160 
  2. Local constants, Algebraic Number Fields, ed. A. Fröhlich, Academic Press, 1974, prepared in collaboration with C.J. Bushnell from lectures by J. Tate 
  3. Locally free classgroups of groups of prime power order, J. Alg. 50, 1976, 463-487 
  4. Adams operations, local root numbers and Galois module structure of rings of integers, Proc. L.M.S. (3), 39, 147-175 
  5. Galois module structure of relative abelian extensions, J. reine angew. Math., 303, 1978, 97-101 
  6. On the self-duality of a ring of integers as a Galois module, Invent. Math., 46 (1978), 173-177 
  7. A logarithmic approach to class groups of integral group rings, J. Alg. (66) 1980, 321-353 
  8. The locally free classgroup of the symmetric group, Illinois J. Math., (23) 4, 1976, 687-701 
  9. (with A. Fröhlich), The arithmetic theory of local Galois Gauss, sums for tame characters, Phil. Trans. Roy. Soc. 298, 1980, 141-181 
  10. On Fröhlich’s conjecture for rings of integers of tame extensions, Invent. Math., 63 (1981), 41-79 
  11. Galois module structure of rings of integers in Kummer extensions, Bull. L.M.S. (12), 1980, 96-98
  12. Monomial representations and rings of integers, J. reine angew. Math. 324, 1981, 1127-1135 
  13. Galois module structure of rings of integers, Journées arithmétiques, ed. J.V. Armitage, L.M.S Lecture Notes, 1982 
  14. Fröhlich’s conjecture and logarithmic methods, Integral Representations and Applications, ed. K. Roggenkamp, Springer Lecture Notes 882, (1980) 
  15. Galois module type congruences for values of L-functions, Jour. L.M.S. 24, (1981), 441-448 
  16. Structure galoisienne des anneaux d’entiers, Sém. Théorie des nombres, Paris 1970-80, Birkhauser, 312-316 
  17. Local Gauss Sums, Sém. Théorie des nombres de Bordeaux 1978/9, 801-809 
  18. On the structure of certain completed character rings, J. Alg. (76), 1982, 226-233 
  19. A logarithmic description of determinants in group rings, Algebraic K. theory, Springer Lecture Notes 967, (1980), ed. R. Keith Dennis 
  20. (with Ph. Cassou-Noguès) Local root numbers and Hermitian Galois module structure of rings of integers, Math Annalen 263, 251-261 (1983) 
  21. (with Ph. Cassou-Noguès) Constante de l’équation fonctionelle de la fonction L d’Artin d’une representation symplectique et modérée. Annales de l’Inst. de Fourier, 33 (2), 1983, 1-17 
  22. (with Ph. Cassou-Noguès) Opérations d’Adams et groupe de classes d’algèbre de groupe, J. Algebra, 95(1), 1985, 125-152 
  23. Group laws and rings with normal bases, J. reine angew. Math. 337, 1982, 121-141 
  24. Relative Galois module structure of rings of integers and elliptic functions. Cam. Phil. Soc., 94, pp. 389-397, 1983 
  25. Structure galoisienne des anneaux d’entiers des extensions abéliennes d’un corps quadratique imaginaire. Sém. Théorie des nombres de l’Université de Bordeaux, Exposé 13, (1982) 
  26. Galois module structure of rings of integers, Annales de l’Inst. Fourier, 30 (3), 1980, 11-48 
  27. On a conjecture of C.T.C. Wall for determinants in group rings, Topology, Vol. 22, No.3, pp. 351-355, 1983 
  28. (with Ph. Cassou-Noguès) L’invariant de Clifford équivariant d’un caractère othogonal, Journ. of Algebra, 99, 1986, 167-180 
  29. On the equidistribution of Frobenius in cyclic extensions of a number field, Jour. L.M.S. (2), 29, (1984), 211-223 
  30. Relative Galois module structure of rings of integers and elliptic functions II, Ann. of Math., 121, 1985, 519-535 
  31. (with Ph. Cassou-Noguès) Opérations d’Adams sur certains groupes de Grothendieck, Sém. Th. Nombres de Bordeaux, exposé no. 5, 1982 
  32. Relative Galois module structure of rings of integers and elliptic functions III, Proc. L.M.S. (3), 51 (1985), 415-431 
  33. Formal groups and the Galois module structure of local rings of integers, Jour. reine angew. Math., 358, 97-103 
  34. Relative Galois module structure of rings and integers, Proc. Oberwolfach Conference on “Rings and Orders”, ed. K. Roggenkamp, Springer Lecture Notes, No. 1142 
  35. (with Ph. Cassou-Noguès) Les constantes locales et globales de l’équation fonctionelle de la fonction L d’Artin d’une représentation symplectique, Séminaire Théorie des nombres, Paris, Birkhäuser, (1984), 37-50 
  36. (with Ph. Cassou-Noguès) Relèvement galoisien d’invariant de Clifford équivariant. Sèm. Th. Nombres de Bordeaux 1985 
  37. Hopf structure and the Kummer theory of formal groups, J. reine angew. Math., 375/6, 1987, 1-11 
  38. (with Ph. Cassou-Noguès) Fonctions elliptiques et génération d’anneaux d’entiers, SMF Astérisque 147/8, 1987, 49-70 
  39. Mordell-Weil groups and the Galois module structure of rings of integers, Illinois Journal of Mathematics, Vol. 32, 137, 1988, 428-452 
  40. (with Ph. Cassou-Noguès) A note on elliptic curves and the monogeneity of rings of integers, Jour. L.M.S. (2) 37, (1988), 63-72 
  41. Rings of integers and trace forms for tame extensions of odd degree, Math. Zeitschrift, 202, 313-341, (1989) 
  42. (with Ph. Cassou-Noguès) Unités modulaires et monogenéité d’anneaux d’entiers, Séminaire de Théorie des Nombres de Paris 1986/87, ed. G Goldstein, Birkhaüser, PM 75, 1989 
  43. (with A Srivastav) Elliptic Curves with Complex Multiplication and Galois Module Structure, Inventiones Mathematicae, 99, 165-184, (1990) 
  44. Structure galoisienne des anneaux d’entiers et groupes de Mordell-Weil, Séminaire de Théorie des Nombres de Bordeaux, 1987-88, Exposé No.1 
  45. Root numbers and the local Langlands conjecture, in Representation Theory and Number Theory in Connection with the local Langlands conjecture, ed. J. Ritter, Contemporary Mathematics, Vol. 86, 1989 
  46. (with Ph. Cassou-Noguès) Un élément de Stickelberger quadratique, Journal of Number Theory, Vol. 37, No. 3, 1991, 307-342 
  47. (with Ph. Cassou-Noguès) The trace form and Swan modules, Bull. London Math. Soc. 22 (1990), 422-428 
  48. Résolvandes et espaces homogènes principaux de schémas en groupe, Séminaire de théorie des nombres, Bordeaux 2 (1990), 255-271 
  49. (with B. Erez) Hermitian modules in Galois extensions of number fields and Adams operations, Annals of Mathematics, 135 (1992), 271-296 
  50. The Galois module structure of certain arithmetic principal homogeneous spaces, Journal of Algebra, vol. 153 (1992), 203-214 
  51. L-functions and Galois modules: Explicit Galois Modules, pp. 124-134 in L-functions and Arithmetic, LMS Lecture Notes 153, Cambridge University Press, 1991 
  52. (with A. Agboola) Class Invariants and Mordell Groups, J. reine angew. Math. 447 (1994), 23-61 
  53. On the Galois module structure of wild, abelian extensions, Jour. LMS (2) 42, 1995, 23-61 
  54. (with Ph. Cassou-Noguès) Structure galoisienne et courbes eilliptiques, in "Autour des unités", Université de Caen, 1992 
  55. (with Ph. Cassou-Noguès) Espaces homogènes principaux, unités elliptiques et fonctions L, Ann. Inst. Fourier, Grenoble, 33, 3(1994), 631¬661
  56. The trace form for tame abelian extensions of number fields, Proc. Cam. Phil. Soc. 1996, 119, 209-230 
  57. (with T. Chinburg, B. Erez and G. Pappas) Tame actions of group schemes: integrals and slices, Duke Math. Journal, Vol 82, No. 2, 1996, 269-308
  58. (with T. Chinburg, B. Erez and G. Pappas) Riemann-Roch theorems for arithmetic schemes with a group action, Jour. reine angew. Math., 489 (1997), 151-187
  59. (with T. Chinburg, B. Erez and G. Pappas) ε-constants and the Galois structure of de Rham cohomology, Annals of Mathematics, 146 (1997), 411- 473
  60. (with T. Chinburg, B. Erez and G. Pappas) ε-constants for varieties over finite fields, Amer. J. Math., 119 (1997), 503-522
  61. (with T. Chinburg, B. Erez and G. Pappas) ε-constants for arithmetic schemes, Math. Annalen, 311 (1998), 377-395
  62. (with T. Chinburg, B. Erez and G. Pappas) Localisations of Grothendieck groups and Galois structure, Contemporary Mathematics, 224 (1999), 47- 63
  63. (with T. Chinburg and G. Pappas) ε-constants and the Galois structure of de Rham cohomology II. Jour. reine angew. Math 519 (2000), 201-230
  64. (with Ph. Cassou-Noguès) Opérations d’Adams et théorèmes de points fixes en K-théorie des algèbres de groupes, J. Algebra 216 (1999), 334-365
  65. (with Ph. Cassou-Noguès) Galois module structure for wild extensions, in Algebraic Number Theory and Diophantine Analysis, ed. F. Halter-Koch and R.F. Tichy, Walter de Gruyter, 2000 Berlin, 69-91
  66. (with T. Chinberg and G. Pappas) ε-constants and Arakelov Euler characteristics, Math. Research Letters 7 (2000), 433-446
  67. (with Ph. Cassou-Noguès and B. Erez) Invariants of a quadratic form attached to a tame covering of schemes, Jour. de la Th. Nombres de Bordeaux 12 (2000), 597-660
  68. (with T. Chinburg and G. Pappas) Discriminants and Arakelov Euler characteristics, Number Theory for the Millennium, I (Urbana, IL, 2000), 229-255, AK Peters, Natick, MA, 2002
  69. (with T. Chinburg and G. Pappas) ε-constants and equivariant Arakelov Euler characteristics, Ann. Sci. École Norm. Sup. (4) 35 (2002), no. 3, 307- 352
  70. (with Ph. Cassou-Noguès amd B. Erez) Hasse-Witt invariants of symmetric complexes: an example from geometry, C.R. Acad. Sci. Paris, Ser. I 334 (2002), 839-842
  71. (with T. Chinburg and G. Pappas) Duality and hermitian Galois module structure, Proc. L.M.S. (3) 87 (2003), No. 1, 54-108
  72. (with Ph. Cassou-Noguès and B.Erez) Fröhlich twisted bundles, St Petersburg Mathematical Society Journal , vol 11, 2005, p105-122
  73. (with Ph. Cassou-Noguès and B.Erez) Fröhlich twisted bundles, AMS Russian Translations,, Series 2, Volume 219 (2006), 165 pages.
  74. (with Ph. Cassou-Nogués and B. Erez) Twists of Symmetric Bundles, Proc. L.M.S. (3) 95 (2007), 248 – 272
  75. (with T. Chinburg and G. Pappas) Pfaffians, the G-signature theorem and Galois Hodge discriminants. Compositio Mathematica. 143 (2007) 5, 1213 – 1254 
  76. (with T. Chinburg and G. Pappas) Cubic Structures Equivarient Euler characteristics and lattices of Modular Forms, Ann. Of Math (2) 170 (2); 561-608, 2009
  77. (with T. Chinburg and G. Pappas) K1 of a pedic group ring1: the determinantal image, Journal of Algebra, 326 (2011), 74-112.   
  78. (with T. Chinburg and G. Pappas) Cubic Structures Equivariant Euler characteristics and lattices of Modular Forms, Ann. Of Math (2) 170 (2); 561-608, 2009
  79. (with T. Chinburg and G. Pappas) K1 of a p-adic group ring1: the determinantal image, Journal of Algebra, 326 (2011), 74-112.   
  80. (with Ph. Cassou- Noguès), Equivariant Euler Characteristics and Sheaf Resolvents, Annales de l’Institut Fourier. Tome 62 (2012), fascicule 6, 2315-2345.
  81. (with T. Chinburg and G. Pappas) The Group Logarithm Past and Present, Noncommutative Iwasawa Main Conjectures over Totally Real Fields, Editors J. Coates, P. Schneider, R. Sujatha, O. Venjakob. Springer Proceedings in Mathematics and Statistics, 51-78, (2013).

Arxiv

  1. (with T. Chinburg, L. Moret-Bailly and G. Pappas) Finite morphisms to projective space and capacity theory. Arxiv 1201.0678.
  2. (with T. Chinburg and G. Pappas) Higher adeles and non-abelian Riemann-Roch Arxiv 1204.4520. 
  3. (with Ph. Cassou-Noguès, T. Chinburg, B. Morin) Orthogonal representations of affine group schemes and twists of symmetric bundles, Arxiv 1111.1590.
  4. (with Ph. Cassou-Noguès, T. Chinburg and B. Morin) The Classifying Topos of a Group Scheme and Invariants of Symmetric Bundles, Arxiv 1301.4928.
  5. (with Ph Cassou-Noguès, T. Chinburg, B. Erez) Derived Category Invariants and L-Series. Arxiv 1301.7663
  6. (with T. Chinburg and G. Pappas) K_1 of a p-adic Group Ring II: the Determinantal Kernel SK_1. Arxiv 1303.5337

Books

  1. Classgroups of group rings, L.M.S. Lecture Notes series, no. 91, Cambridge University Press, 1984.
  2. (with Ph. Cassou-Noguès) Rings of integers and elliptic functions, Progress in Mathematics series no.66, Birkhäuser.
  3. (with A. Fröhlich) Algebraic Number Theory, Cambridge Studies in Advanced Mathematics 27, Cambridge University Press, 1991.
  4. (with J. Coates) L-functions in Arithmetic, Proceedings of the L.M.S. Symposium, LMS Lecture Notes 153, C.U.P.
  5. (with K. Roggenkamp), Group rings and classgroups. DMV Seminar 18, Birkhäuser Verlag.

Biographical memoirs

  1. Albrecht Fröhlich FRS, Bulletin of the L.M.S. 38 (2006) 329-350).
  2. (with B.J.Birch) Albrecht Frõhlich FRS, Biographical Memoirs of the Royal Society, 51 (2005) 149-168).