Connections between curves, automorphic forms, and L-functions

曲线、自守形式和 L 函数之间的联系

• 批准号: 1400905
• 负责人: John Jones
• 金额: $ 4.5万
• 依托单位: Arizona State University
• 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: 2014-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1400905&HistoricalAwards=false
• 关键词: Connections; between; curves; automorphic; forms

This funding is for the conference "Curves and Automorphic Forms" to be held at Arizona State University from March 10th to 14th, 2014. There will be approximately 10 speakers and an anticipated 75 participants. The theme will be extensions of the modularity theorem for elliptic curves over the rationals. Talks will describe work on computations of elliptic curves over number fields and of hyperelliptic curves over the rationals, on the conjecturally corresponding modular forms (e.g., Hilbert, Siegel, Bianchi), and on associated L-functions. The format will be a hybrid of a traditional conference and a workshop with lectures in the morning and afternoons devoted to collaborative work. We hope that bringing together experts on these various objects will encourage collaborations in new directions.By its very nature, the conference seeks to connect different areas of mathematical research, and thus should be useful in exposing researchers of all levels to ideas which have increasing importance. The grant includes funding for graduate students, postdocs, young researchers, and mathematicians from underrepresented groups. We hope that the conference will draw not only mathematicians who work directly in these areas, but also others from neighboring areas of mathematics. Part of the workshop activities will be to incorporate results from computations into the L-function and Modular Form Database, http://www.LMFDB.org, which provides data and information on mathematical objects for both researchers and a general mathematical audience. The conference website can be found at http://hobbes.la.asu.edu/lmfdb-14.

这笔资金是为将于2014年3月10日至14日在亚利桑那州立大学举行的“曲线和自同构形”会议提供资金。将有大约10名发言者，预计将有75名与会者。主题将是椭圆曲线的模性定理在有理数上的推广。讲座将描述数域上的椭圆曲线和有理数域上的超椭圆曲线的计算工作，猜想对应的模形式(例如，Hilbert，Siegel，Bianci)，以及相关的L函数。这种形式将是传统会议和研讨会的混合体，上午和下午都有专门讨论协作工作的讲座。我们希望聚集这些不同对象的专家将鼓励新方向的合作。由于其本身的性质，会议寻求将数学研究的不同领域联系起来，因此应该有助于让所有级别的研究人员接触到越来越重要的思想。这笔赠款包括资助研究生、博士后、年轻研究人员和来自代表性不足群体的数学家。我们希望这次会议不仅能吸引直接在这些领域工作的数学家，还能吸引来自邻近数学领域的其他人。讲习班活动的一部分是将计算结果纳入L函数和模块化形式数据库http://www.LMFDB.org，，该数据库为研究人员和普通数学读者提供有关数学对象的数据和信息。会议网址为：http://hobbes.la.asu.edu/lmfdb-14.。