Workshop on function field arithmetic

函数域算术研讨会

• 批准号: EP/I030948/1
• 负责人: Ambrus Pal
• 金额: $ 2.5万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2011
• 资助国家: 英国
• 起止时间: 2011 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FI030948%2F1
• 关键词: Workshop; function; field; arithmetic

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.

这个提议的目的是在2011年6月在帝国理工学院组织一个为期两天的关于函数场算术的研讨会。这将是在英国举行的第一次关于函数场算术的会议，其主要目的之一是向英国数学界普及这一高度发达和享有盛誉的现代数论领域，这一领域仍在迅速发展。函数场的算法以德林菲尔德模和t动机的概念为中心。它们被证明是解决纯数学中几个中心猜想的一个非常强大的工具，即全局和局部朗兰兹猜想，拉马努金-彼得森猜想，雅克-朗兰兹对应，以及卡拉约尔-德列涅猜想。另一方面，虽然他们的研究最初是为了推进上述猜想，但现在它是一门独立的学科，是一门极其丰富的理论，对于经典数论研究的每一个对象都有对应的对象，包括模变分和模形式，L函数和γ函数，伽罗瓦表示和霍奇理论，伯努利数和超越结果，它们经常紧密地反映，但有时，诱人与数字领域的算术背道而驰。此外，函数域的算术技术往往比数域的先进得多，因此该领域仍然是数论主要猜想的重要试验场。该领域还与表示理论、代数和算术几何、群论甚至组合学有着深刻的联系。人们很自然地期望在这一领域仍有许多重大成果有待发现。一些领先的专家已经接受了发言和出席博士生将接触到最新的方法跨越大量的主题选择。研讨会的另一个目的是激发参与者之间的讨论，并进一步研究这一令人兴奋的领域。