Workshop Proposal: Elliptic Curves over Q(\sqrt{5})

研讨会提案：Q(sqrt{5}) 上的椭圆曲线

• 批准号: 1207199
• 负责人: Ramin Takloo-Bighash
• 金额: $ 3万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-04-01 至 2013-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1207199&HistoricalAwards=false
• 关键词: Workshop; Proposal; Elliptic; Curves; over

A workshop on elliptic curves over a real quadratic extension of the rational numbers will take place April 27-29, 2012 at the University of Illinois at Chicago. The organizers of this workshop are William Stein (University of Washington at Seattle) and Ramin Takloo-Bighash (University of Illinois at Chicago). The invited speakers are Jennifer Balakrishnan (Harvard), Jonathan Bober (University of Washington at Seattle), John Cremona (Warwick), Lassina Dembele (Warwick), Noam Elkies (Harvard), Edray Goins (Purdue), Matthew Greenberg (Calgary), Richard Pinch, Kenneth Ribet (UC Berkeley), William Stein (UW Seattle), Nike Vatsal (UBC), and John Voight (University of Vermont). This is part of the annual Oliver Atkin Memorial Lecture and Workshop at UIC. The theme of the workshop is the theoretical and computational aspects of elliptic curves over totally real fields, Hilbert modular forms, and the arithmetic of elliptic curves in general. The website of the workshop is http://www.math.uic.edu/~rtakloo/atkin2012.html Elliptic curves are of fundamental interest in number theory. The theory of these objects over the field of rational numbers is starting to look like a coherent theory, but as soon as one steps away from rational numbers our understanding of these objects becomes extremely patchy. This workshop focuses on the theory of elliptic curves on a very simple field different from the field of rational numbers. We hope that bringing together experts working in the area would create an environment in which to exchange ideas and to start new projects which will hopefully lead to a better understanding of these fundamental objects.

有理数实二次扩张上的椭圆曲线研讨会将于2012年4月27日至29日在芝加哥伊利诺伊大学举行。本次研讨会的组织者是威廉·斯坦(华盛顿大学西雅图分校)和Ramin Takloo-Bighash(伊利诺伊大学芝加哥分校)。特邀演讲者有：Jennifer Balakrishnan(哈佛大学)、Jonathan Bober(西雅图华盛顿大学)、John Cremona(Warwick)、Lassina Dembele(Warwick)、Noam Elkies(哈佛大学)、Edray Goins(普渡大学)、Matthew Greenberg(卡尔加里大学)、Richard Pinch、Kenneth Ribet(加州大学伯克利分校)、William Stein(西雅图大学)、Nike Vatsal(UBC)和John Voight(佛蒙特州大学)。这是UIC一年一度的奥利弗·阿特金纪念讲座和研讨会的一部分。研讨会的主题是全实域上椭圆曲线的理论和计算方面，希尔伯特模形式，以及椭圆曲线的一般算法。工作坊的网站是http://www.math.uic.edu/~rtakloo/atkin2012.html，椭圆曲线是数论中的基本兴趣。有理数领域中关于这些物体的理论开始看起来像是一个连贯的理论，但一旦人们离开有理数，我们对这些物体的理解就变得极其杂乱无章。本课程的重点是椭圆曲线在一个非常简单的域上的理论，不同于有理数的域。我们希望，将在该领域工作的专家聚集在一起，将创造一种交流思想和启动新项目的环境，希望这将有助于更好地了解这些基本目标。