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Workshops on the frontiers of Nevanlinna theory

Nevanlinna 理论前沿研讨会

基本信息

批准号：
EP/I013334/1
负责人：
Rodney Halburd
金额：
$ 3.09万
依托单位：
University College London
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2010
资助国家：
英国
起止时间：
2010 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FI013334%2F1
关键词：
Workshops frontiers Nevanlinna theory

项目摘要

Complex analysis is the extension of calculus to the complex numbers. Meromorphic functions are functions that are differentiable throughout the complex plane except possibly at isolated points where the functions may have the simplest kind of singularities, called poles. Such functions arise naturally in many theoretical and practical problems. Britain has a strong tradition of research in function theory. Among its particular strengths are Nevanlinna's value distribution theory for meromorphic functions of a single variable, as well as the study of dynamical systems. However, during the last couple of decades there have been major breakthroughs in Nevanlinna theory and related areas which appear to have had little impact in Britain to date. Funds are sought to run a series of small workshops that are aimed at engaging the UK community with some of these important lines of research. The emphasis of the workshops will be on exploring collaborations and the number of talks will be restricted accordingly.Below are brief descriptions of each proposed workshop.W1. Frontiers of Nevanlinna theoryThis will be a general introduction to the main themes.W2. Nevanlinna theory and Diophantine approximationThis workshop will explore the remarkable formal connection between Nevanlinna theory and an area of number theory. Participants will be invited who work on this connection as well as those working in pure Nevanlinna theory or Diophantine approximation.W3. Function theory and dynamical systems over p-adic spacesFor each prime number p, the p-adic numbers are a field of numbers that contain the rational numbers (fractions) but are quite different in nature to the real numbers. They arise naturally in many problems in number theory. One can also construct analogues of the complex numbers in the p-adic setting and develop large parts of complex analysis, including Nevanlinna theory. Recently there has been a lot of interest in the behaviour of dynamical systems in the p-adic setting. Classical Nevanlinna theory has been a useful tool in dynamical systems over the (genuine) complex numbers. This workshop will explore this connection over the p-adics.W4. Function theory of differential and difference equationsThere are several important conjectures concerning differential and difference equations in the complex domain for which Nevanlinna theory would be a useful tool.

复分析是微积分在复数上的推广。亚纯函数是在复平面上可微的函数，除了可能在孤立点处，函数可能具有最简单的奇点，称为极点。在许多理论和实际问题中，自然会出现这种功能。英国在函数论研究方面有着悠久的传统。其特别的优势是Nevanlinna的值分布理论的亚纯函数的一个单一的变量，以及研究的动力系统。然而，在过去的几十年里，内万林纳理论和相关领域取得了重大突破，迄今为止在英国几乎没有影响。寻求资金来运行一系列的小型研讨会，旨在使英国社区参与其中一些重要的研究领域。工作坊的重点将放在探讨合作上，讲座的数量也会相应地有所限制。以下是每个拟议工作坊的简要描述。Nevanlinna理论的前沿这将是对主要主题的一般介绍。Nevanlinna理论和丢番图近似这个研讨会将探讨Nevanlinna理论和数论领域之间显着的正式联系。与会者将被邀请谁的工作在这个连接以及那些工作在纯Nevanlinna理论或丢番图近似。p-adic空间上的函数论和动力系统对于每个素数p，p-adic数是包含有理数（分数）但在性质上与真实的数完全不同的数域。它们在数论中的许多问题中自然出现。人们也可以在p-adic设置中构造复数的类似物，并开发复分析的大部分，包括Nevanlinna理论。最近有很多的兴趣在动力系统的行为在p-adic设置。经典Nevanlinna理论是研究（真）复数上动力系统的一个有用工具。本研讨会将探讨p-adics. W 4上的这种联系。微分和差分方程的函数理论有几个重要的理论，涉及微分和差分方程在复杂的区域，Nevanlinna理论将是一个有用的工具。