Impact of Computation on Number Theory, July 30 - August 3, 2014

计算对数论的影响，2014 年 7 月 30 日至 8 月 3 日

• 批准号: 1414219
• 负责人: Wen-Ching Li
• 金额: $ 3.54万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-07-15 至 2016-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1414219&HistoricalAwards=false
• 关键词: Impact; Computation; Number; Theory; July

A conference on the impact of computation on number theory will take place July 30 to August 3, 2014, at the National Center for Theoretical Sciences (NCTS), in Hsinchu, Taiwan. The purpose of this conference is to gather international experts to share experiences in how computation has impacted their research in number theory (broadly understood), to present cutting-edge results, and to discuss the future role of computation in number theory. Support from this award will partially defray the expenses of the invited speakers and invited participants from the US.Calculation has always played a significant role in number theory. Beginning in the middle of the last century and continuing today, machine computation has played an increasingly prominent role. Many important statements in number theory, like the conjecture of Birch and Swinnerton-Dyer and the formula of Gross and Zagier, were formulated based on extensive data collected from computation. In situations where we lack a deeper understanding, such as in Grothendieck's theory of dessins d'enfants, the only way to gain understanding is to compute examples first. It is hoped that this conference will shed light on how important conjectures in number theory were discovered, how to comb through numerical data to detect phenomena, how to take advantage of modern technology to assist future research, and to learn the types of problems better suited for numerical explorations. One of the goals for the conference is to broaden participation by inspiring young participants and to encourage them to build connections with people from all over the world. A three-week course in arithmetic geometry and number theory will serve as a good prelude and preparation for the conference for graduate students.Conference web site: http://math.cts.nthu.edu.tw/Mathematics/2014ICNT.htm

关于计算对数论影响的会议将于 2014 年 7 月 30 日至 8 月 3 日在台湾新竹国家理论科学中心 (NCTS) 举行。 本次会议的目的是聚集国际专家，分享计算如何影响他们在数论（广义）研究中的经验，展示前沿成果，并讨论计算在数论中的未来作用。该奖项的支持将部分支付来自美国的受邀演讲者和受邀参与者的费用。计算在数论中一直发挥着重要作用。从上世纪中叶开始一直持续到今天，机器计算发挥着越来越突出的作用。 数论中的许多重要陈述，例如 Birch 和 Swinnerton-Dyer 猜想以及 Gross 和 Zagier 公式，都是基于从计算中收集的大量数据得出的。 在我们缺乏更深入理解的情况下，例如在格洛腾迪克的儿童设计理论中，获得理解的唯一方法是首先计算示例。 希望通过这次会议能够阐明数论中的重要猜想是如何被发现的，如何梳理数值数据来发现现象，如何利用现代技术来辅助未来的研究，并了解更适合的问题类型用于数值探索。会议的目标之一是通过激励年轻参与者来扩大参与范围，并鼓励他们与来自世界各地的人们建立联系。 为期三周的算术几何与数论课程将为研究生们的会议做一个良好的前奏和准备。会议网址：http://math.cts.nthu.edu.tw/Mathematics/2014ICNT.htm