Connections between curves, automorphic forms, and L-functions

这笔资金用于将于2014年3月10日至14日在亚利桑那州州立大学举行的“曲线和自守形式”会议。 将有大约10名发言者和预计75名与会者。 主题是有理数上椭圆曲线的模性定理的推广。 讲座将描述在数域上的椭圆曲线和有理数上的超椭圆曲线的计算工作，在几何上对应的模形式（例如，Hilbert，Siegel，比安奇），以及相关的L-函数。 形式将是一个传统的会议和研讨会的混合体，上午和下午的讲座专门用于协作工作。 我们希望，汇集专家对这些不同的对象将鼓励在新的方向合作。就其本身的性质，会议旨在连接不同领域的数学研究，因此应该是有益的，暴露在各级研究人员的想法，有越来越重要。该补助金包括为研究生，博士后，年轻研究人员和来自代表性不足群体的数学家提供资金。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将是将计算结果纳入L函数和模块形式数据库http://www.LMFDB.org，该数据库为研究人员和一般数学受众提供关于数学对象的数据和信息。 会议的网址是http://hobbes.la.asu.edu/lmfdb-14。

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.