WORKSHOP: Research Symposium: Logic and Mathematics 09

研讨会：研究研讨会：逻辑与数学 09

• 批准号: EP/G057192/1
• 负责人: Nigel John Cutland
• 金额: $ 1.09万
• 依托单位: University of York
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2009
• 资助国家: 英国
• 起止时间: 2009 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FG057192%2F1
• 关键词: WORKSHOP; Research; Symposium; Logic; Mathematics

Logic and Mathematics 09 will be a five day workshop/research symposium to be held at the University of York in August 2009 devoted to the interaction between ideas and techniques from mathematical logic and other areas of mathematics. On the logic side this includes: - nonstandard analysis (the modern theory of infinitesimal and infinite numbers) and its extensions. This theory gives access to ideal structures that otherwise exist only on an intuitive basis- model theory: the study of relationships between the language of mathematics and its logic and the actual world of mathematical objects and structures. Current research focusses in particular on definability theory - the study of objects that can be precisely defined using logical language- constructive mathematics and its logical foundations- reverse mathematics (or proof mining) - the investigation of exactly what logical principles and assumptions are needed for particular mathematical resultsAreas of mathematics that are involved in such interactions include classical mathematical analysis, differential equations, number theory, probability theory, stochastic analysis, algebraic geometry, mathematical physics and mathematical finance.The Symposium will bring together researchers whose work involves interactions between mathematical logic and other areas of mathematics, in order to share ideas and the results of recent work, as well as to explore new avenues of research. An underlying theme is the recognition of the essential unity of mathematics in spite of the fact that the mushrooming of research activity has led to compartmentalization of the subject area. Thus the participants will represent a wide variety of topics within the general theme Logic and Mathematics.The current proposal to the EPSRC is for the support (travel and subsistence) of five participants from overseas (Di Nasso, Jin, Keisler, Loeb, Ross) who have already indicated their willingness to participate, and for subsistence for five further as yet unspecified participants from among those who have indicated that they will participate. It is anticipated that there will be 14 - 18 invited participants, all invited to give a presentation of their current work. Invited participants other than those covered by this proposal will be supported from other sources. Other non-invited participants will have the opportunity to present their work for discussion but there will be a refereeing process.

逻辑与数学09将是一个为期五天的研讨会/研究研讨会将于2009年8月在约克大学举行，致力于从数学逻辑和其他数学领域的思想和技术之间的相互作用。在逻辑方面，这包括：-非标准分析（无穷小和无穷数的现代理论）及其扩展。这一理论提供了一个理想的结构，否则只存在于一个直观的基础上-模型理论：研究数学语言及其逻辑与数学对象和结构的实际世界之间的关系。目前的研究主要集中在可定义性理论上--研究可以用逻辑语言精确定义的对象--建构数学及其逻辑基础--逆向数学（或证明挖掘）-调查特定数学结果究竟需要什么逻辑原则和假设。涉及这种相互作用的数学领域包括经典数学分析，微分方程，数论、概率论、随机分析、代数几何、数学物理和数学金融。研讨会将汇集工作涉及数学逻辑与其他数学领域相互作用的研究人员，以分享最近工作的想法和成果，并探索新的研究途径。一个基本的主题是认识到数学的本质统一，尽管研究活动的蓬勃发展导致了学科领域的划分。因此，参加者将代表逻辑和数学总主题范围内的各种主题。（旅费和生活津贴）（迪纳索，金，凯斯勒，勒布，罗斯）谁已经表示愿意参加，并为表示将参加的另外五名尚未确定的参加者提供生活费。预计将有14 - 18名受邀与会者，所有与会者都将应邀介绍其目前的工作。除本提案所涵盖的与会者外，其他与会者将得到其他来源的支助。其他未被邀请的参与者将有机会介绍他们的工作以供讨论，但将有一个裁判过程。