Workshops on the frontiers of Nevanlinna theory

复数分析是微积分在复数上的推广。亚纯函数是在整个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类型的奇点，称为极点。这样的函数在许多理论和实践问题中自然而然地出现。英国在函数理论方面有着深厚的研究传统。其独特的强项是奈万林纳的单变量亚纯函数的值分布理论，以及对动力系统的研究。然而，在过去的几十年里，纳瓦林纳理论和相关领域取得了重大突破，但到目前为止，这些突破似乎对英国影响不大。正在寻求资金来举办一系列小型研讨会，旨在让英国社区参与其中一些重要的研究领域。研讨会的重点将是探索合作，演讲的数量将相应地受到限制。以下是对每个提议的研讨会的简要描述。纳瓦林纳理论的前沿这将是对主要主题的一般性介绍。纳瓦林纳理论和丢番图近似这个工作坊将探索纳瓦林纳理论和一个数论领域之间显著的形式联系。参与者将被邀请从事这一联系的工作，以及那些工作在纯粹的纳瓦林纳理论或丢番图近似。P元空间上的函数论和动力系统对于每个素数p，p元数是一个包含有理数(分数)的数域，但本质上与实数有很大的不同。它们自然而然地出现在数论的许多问题中。人们还可以在p进环境中构造复数的类比，并发展复数分析的大部分，包括nevanlinna理论。最近，人们对动力系统在p元环境下的行为产生了很大的兴趣。经典的Nevanlinna理论在(真的)复数上的动力系统中是一个有用的工具。本研讨会将通过p-adics.w4探讨这种联系。微分差分方程式的函数论在复数域中，有几个关于微分方程式和差分方程式的重要猜想，对于这些猜想，内瓦林纳理论是一个有用的工具。

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.