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L-functions and arithmetic

Participation in INI programmes is by invitation only. Anyone wishing to apply to participate in the associated workshop(s) should use the relevant workshop application form.

1st January 1993 to 30th June 1993
Bryan Birch
Don Blasius
John Coates
Roger Heath-Brown

Organisers: B. Birch (Oxford), D. Blasius (UCLA), S. Bloch (Chicago), J. Coates (Cambridge), J.-M. Fontaine (Orsay), R. Heath-Brown (Oxford), K. Kato (Tokyo)

Programme Theme

Over the last thirty years, number theorists have come to realise that the mysterious connexions between arithmetic problems and the properties of zeta and L-functions, initially discovered in the first half of the nineteenth century, are far more extensive than had been imagined earlier. A vast web of overlapping conjectures has now been formulated, stretching from the Riemann hypothesis and Fermat's last theorem to the Tamagawa numbers of motives. The programme will bring together mathematicians from arithmetical algebraic geometry, automorphic forms, and classical analytic number theory, to work on several of these conjectures.


There will be a regular seminar programme throughout the period, held at 16.15 on Tuesdays and 11.15 on Thursdays. In addition the following periods of concentration have been planned:

  • 15-27 February. Instructional course on Langlands. This will be a course strictly for non-experts. It will consist of 40 lectures spread over 10 days, broken up into 8 courses. The lectures will be given by J.Coates, M.Harrison, J-P.Labesse, P.Schneider, A.Scholl, M.Taylor and R.Taylor.
  • 5-10 April. Workshop on Motives attached to Automorphic Forms, organised by R.Taylor and D.Blasius.
  • 12-17 April. Workshop on L-functions and Classical Problems, organised by B.Birch and R. Heath-Brown.
  • 28 May. London Mathematical Society `Spitalfields Day' on L-functions and Arithmetic.
  • 21-26 June. Workshop on p-adic representations, Iwasawa theory, and the Tamagawa numbers of motives organised by S.Bloch, J.Coates, J-M.Fontaine.

All are welcome to attend any of these activities.


The following have accepted invitations to participate in the programme for the periods indicated:

A. Agboola (MSRI), 1 Feb-1 Mar; M. Kurihara (Tokyo), 1 May-30 Jun; P. Berthelot (Rennes), 1 Jun-30 Jun; J-P. Labesse (Paris), 14 Feb-28 Feb; B. Birch (Oxford), 1 Jan-30 Jun; G. Laumon (Orsay), 1 Apr-15 Apr; D. Blasius (UCLA), 1 Apr-30 Jun; B. Mazur (Harvard), 1 May-30 Jun; S. Bloch (Chicago), 1 Apr-30 Jun; W. Messing (Minnesota), 1 May-30 Jun; E. Bombieri (IAS, Princeton), 1 Jun-30 Jun; J. Neukirch (Regensburg), 1 Apr-15 Apr; N. Boston (Illinois), 1 Jan-30 Jun; B. Perrin-Riou (Paris), 1 Jun-30 Jun; C. Bushnell (KCL, London), 1 Apr-30 Apr; M. Ram Murty (McGill), 15 Mar-15 Apr; J. Coates (Cambridge), 1 Jan-30 Jun; D. Ramakrishnan (Caltech), 21 Mar-15 Apr; L. Clozel (Orsay), 1 Apr-30 Apr; M. Rapoport (Wuppertal), 15 Mar-20 Apr; P. Colmez(ENS, Paris), 1 May-31 May; K. Ribet (Berkeley), 12 May-30 Jun; C. Deninger (M), 15 Feb-14 Mar; K. Rubin (Ohio), 30 May-26 Jun; U. de Shalit (Jerusalem), 1 Jun-30 Jun; J-M. Fontaine (Orsay), 1 May-30 Jun; C. Schmidt (Karlsruhe), 15 Mar-18 Apr; A. Granville (Georgia), 1 Jan-30 Jun; P. Schneider (Cologne), 15 Feb-15 Apr; R. Greenberg (Seattle), 1 May-30 Jun; A. Scholl (Durham), 1 Feb-30 Apr; G. Harder (Bonn), 20 Mar-10 Apr; J. Tate (Austin), 1 Jun-30 Jun; M. Harris (Brandeis), 1 Apr-30 Apr; M. Taylor (UMIST), 15 Feb-28 Feb; R. Heath-Brown (Oxford), 1 Apr-15 Jun, 20 Mar-30 Apr; G. Henniart (Orsay), 1 Apr-30 Apr; R. Taylor (Cambridge), 1 Jan-30 Jun; H. Hida (UCLA), 1 Apr-15 May; R. Vaughan (IC, London), 1 Feb-30 Apr; Y. Ihara (Kyoto); 1 Jun-30 Jun; A. Wiles (Princeton), 15 May-30 Jun; L. Illusie (Orsay), 1 Jun-30 Jun; K. Wingberg (Heidelberg), 1 Feb-8 Apr; U. Jannsen (Cologne), 15 Feb-14 Apr; T. Wooley (Ann Arbor), 1 Mar-30 Apr; K. Kato (Tokyo), 15 Mar-15 Jun; N. Yui (Queen's), 1 Jan-31 Mar; V. Kolyvagin (Moscow), 1 May-30 Jun; S. Zhang (Beijing), 1 Jan-31 Mar; S. Kudla (Maryland), 1 Apr-30 Apr.

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