Elliptic Curves, Torsors, and L-functions

该奖项主要资助初级研究人员(博士后和研究生)参加由研讨会《椭圆曲线、扭矩和L-函数》组成的会议，以及B.H.格罗斯在杰出系列讲座`弗吉尼亚数学讲座‘中关于椭圆曲线的排名的讲座。研讨会和讲座将于3月24日至29日在弗吉尼亚大学举行。格罗斯的讲座将包括对Birch-Swinnerton-Dyer猜想的概述，以及关于有理数域上所有椭圆曲线的平均秩和超椭圆曲线的算术的最新结果。研讨会上的讲座将通过扩展到算术几何和代数群的算术理论的相关领域来补充格罗斯的讲座。这次会议部分是由弗吉尼亚大学数学系的数学科学研究所赞助的。网站is http://www.people.virginia.edu/~lww8k/workshop/workshop.html.The排名是Q上椭圆曲线的最重要但最不为人所知的不变量。M.Bhargava，B.H.葛罗斯，B.Poonen和其他人最近关于平均排名的工作通过引入‘算术统计’的观点标志着该领域的一项突破；即，研究这种算术不变量的分布。算术统计的一般方法适用于许多邻近的算术几何领域。计划在弗吉尼亚大学举办的研讨会的目的正是为了迎合从事相关领域工作的人对这些方法的浓厚兴趣，将这一主题的专家与来自邻近算术几何领域的资深和初级研究人员聚集在一起。

The award provides funding to support participation of primarily junior researchers (postdocs and graduate students) in the meeting consisting of the workshop ``Elliptic Curves, Torsors and L-functions" and the lectures by B.H. Gross on the ranks of elliptic curves in the Distinguished Lecture Series ``Virginia Mathematics Lectures." The workshop and the lectures will take place March 24-29 at the University of Virginia. The lectures by Gross will include a survey of the Birch--Swinnerton-Dyer conjecture as well as very recent results on the average rank for all elliptic curves over the field of rational numbers and the arithmetic of hyperelliptic curves. The lectures in the workshop will complement Gross's lectures by expanding into related areas of arithmetic geometry and the arithmetic theory of algebraic groups. The meeting is sponsored in part by the Institute of Mathematical Sciences at the UVA Mathematics Department. The website is http://www.people.virginia.edu/~lww8k/workshop/workshop.html.The rank is the most important but least understood invariant of elliptic curves over Q. The recent work of M. Bhargava, B.H. Gross, B. Poonen and others on `average' ranks marked a breakthrough in the field by introducing the viewpoint of `arithmetic statistics'; that is, studying the distribution of such arithmetic invariants. The general methods of arithmetic statistics are applicable to many adjacent areas of arithmetic geometry. The objective of the planned workshop at UVA is precisely to cater to the intense interest in these methods from those working on related areas, by bringing together experts on this topic with both senior and junior researchers from adjacent areas of arithmetic geometry.