Number Theory: From Arithmetic Statistics to Zeta Elements II

这笔旅行补助金将帮助美国初级数学家（学生，博士后研究员和其他资源有限的年轻研究人员）到蒙特利尔的数学研究中心（CRM）参加2015年冬季的三个研讨会，主题如下：* 调节器，马勒措施和L函数的特殊值（2015年2月16日至20日）;* 经典自守形式理论中的p-adic方法（2015年3月9日至14日）;和 * 库德洛方案（2015年4月6日至10日）。这些主题在数论中具有很大的当前兴趣，这些会议将为年轻的美国研究人员提供与该领域领先研究人员互动的机会。讲座和演讲将提供给学生和最近的博士学位获得者谁是相对较新的主题。 在过去的二十年里，在数论领域取得了许多令人振奋的新进展，包括：* Birch猜想和Swinnerton-Dyer猜想的重大进展;* Shimura-Taniyama-Weil猜想、Serre猜想、Fontaine-Mazur猜想的二维Galois表示和Sato-Tate猜想的证明;* 调和分析和加法组合学的革命性思想融合技术，以及算术级数中素数的突破;* 对代数对象的新解释以及椭圆曲线和更高亏格曲线上点的秩的结果;* 在确定素数之间的差距界限方面取得了巨大进展。从算术统计到Zeta元素”的目的是扩大这些壮观的结果对广大社区的影响，并发展他们之间的联系;这一系列会议将扩大年轻参与者的参与，并鼓励他们与来自世界各地的人建立联系。 二月的会议“调节器，马勒措施，和L函数的特殊值”关注与这些主题相关的有趣的身份（http：//www.crm.umontreal.ca/2015/Mahler15/index_e.php）。3月会议“经典自守形式理论中的p-Adic方法”是关于p-adic方法和伽罗瓦表示理论，自守形式族，p-adic Hodge理论和Langlands程序（http：//www.crm.umontreal.ca/2015/Automorph15/index_e.php）。 最后，四月会议“库德拉计划”处理的最新发展，从相关的思想的傅立叶系数的中心导数的不连贯的西格尔爱森斯坦系列的算术交叉的特殊周期的酉和正交志村品种（http：//www.crm.umontreal.ca/2015/Kudla15/index_e.php）。

This travel grant will help bring junior US mathematicians (students, postdoctoral fellows, and other young researchers with limited access to resources) to the Centre de Recherches Mathematiques (CRM) in Montreal to participate in three workshops in winter 2015 on the following topics:* regulators, Mahler measures, and special values of L-functions (February 16-20, 2015);* p-adic methods in the theory of classical automorphic forms (March 9-14, 2015); and* the Kudla programme (April 6-10, 2015).These subjects are of great current interest in number theory, and these meetings will present opportunities for young US researchers to interact with leading researchers in the field. Talks and presentations will be made accessible to students and recent doctoral degree recipients who are relatively new to the subjects. Their participation will further existing relationships between researchers in the US and Canada.The past two decades have seen a wealth of new and exciting developments related to number theory, including:* striking progress on the Birch and Swinnerton-Dyer conjecture;* proofs of the Shimura-Taniyama-Weil conjecture, Serre's conjectures, the Fontaine-Mazur conjecture for two-dimensional Galois representations, and the Sato-Tate conjectures;* revolutionary ideas blending techniques in harmonic analysis and additive combinatorics, and a breakthrough on primes in arithmetic progressions;* new interpretations of algebraic objects and consequences for ranks of elliptic curves and points on higher genus curves;* great progress in establishing bounds on gaps between primes.The CRM thematic year "Number Theory: From Arithmetic Statistics to Zeta Elements" is intended to broaden the impact of these spectacular results to a wide community and to develop the connections between them; this series of conferences will broaden participation by young participants and encourage them to build connections with people from all over the world. The February conference "Regulators, Mahler Measures, and Special Values of L-Functions" concerns the intriguing identities relating these topics (http://www.crm.umontreal.ca/2015/Mahler15/index_e.php). The March conference "p-Adic Methods in the Theory of Classical Automorphic Forms" is on p-adic methods and the theory of Galois representations, families of automorphic forms, p-adic Hodge theory, and the Langlands program (http://www.crm.umontreal.ca/2015/Automorph15/index_e.php). Finally, the April conference "The Kudla Programme" treats the latest developments stemming from the ideas relating the Fourier coefficients of central derivatives of incoherent Siegel Eisenstein series to arithmetic intersections of special cycles on unitary and orthogonal Shimura varieties (http://www.crm.umontreal.ca/2015/Kudla15/index_e.php).