Workshop on function field arithmetic

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The purpose of this proposal is to organise a two day workshop on the arithmetic of function fields at Imperial College in June 2011. This will be the first meeting on the arithmetic of function fields held in the UK and one of its main aims is to popularise this highly developed and prestigious area of modern number theory, which is still rapidly evolving, to the UK mathematical community. The arithmetic of function fields centres around the concepts of Drinfeld modules and t-motives. They proved to be an immensely powerful tool in resolving several central conjectures in Pure Mathematics, namely the global and local Langlands conjectures, the Ramanujan-Petersson conjecture, the Jaquet-Langlands correspondence, and the Carayol-Deligne conjecture. On the other hand although their study were originally undertaken in order to make advance on the above-mentioned conjectures, now it is a discipline on its own, an extremely rich theory which have a counterpart for every object which is studied by classical number theory, including modular varieties and modular forms, L- and Gamma-functions, Galois representations and Hodge theory, Bernoulli numbers and transcendence results and which often closely mirrors, but sometimes tantalising diverges from the arithmetic of number fields. Moreover very often the state of art in the arithmetic of function fields is far more advanced than in the case of number fields, hence the area still serves its role as an important testing ground for the major conjectures of number theory. The area also has deep connections to representation theory, algebraic and arithmetic geometry, group theory and even combinatorics. It is very natural to expect that many major results in this area are still to be discovered. Some of the leading experts have already accepted to speak and attending Ph. D. students will be exposed to the latest methods spanning a large selection of topics. The other aim of the workshop is to stimulate discussion among its participants and further research in this exciting area.