CBMS Conference: L-Functions and Multiplicative Number Theory

这一国家科学基金奖为将于2019年5月20-24日在密西西比大学密西西比大学举行的CBMS会议：L-函数和乘法数论提供支持。这次会议将由斯坦福大学的Kannan Soundarajan教授进行一系列十场演讲，他以在这一领域的多产和有影响力的研究以及作为讲师和讲解员的技能而闻名。Soundarajan教授的讲座将以说明性专著结束，这将是当前和未来研究人员的宝贵资源。会议还将增加六场讲座，以补充和加强主要系列讲座。大约30名参与者将得到支持，其中许多人将是研究生。组织者打算将初学者和更成熟的研究人员聚集在一起，以促进在这一当前研究主题上的进步和合作。组织者将积极招募女性参与者以及来自数学科学中代表性不足的其他群体的参与者。根据NSF-CBMS的目标，主办机构有兴趣升级和改进其研究工作，并努力建立一个强大的数论研究小组。数论是数学中一个古老而又非常活跃的分支，而L函数理论在数论的现代发展中起到了核心作用。研究L函数的工具涉及分析、代数、代数几何、自同构形式与表示论、概率与随机矩阵，甚至数学物理等多个领域。大会的大主题将是泽塔和L的价值分配-函数。该系列讲座将涉及几个重要问题，包括L函数的最大规模，L值矩的渐近性，零点的分布，以及L函数在特殊点的非零性。此外，还将展示矩研究中使用的技术如何在理解乘法数论中的其他问题时具有密切的对应性。该系列讲座和随附的专著将为这一高度集中的研究领域提供一个广阔的视角，以帮助各级研究人员了解该领域的主要想法和可能的未来方向。有关会议的信息可以在https://math.olemiss.edu/cbms2019/.This上找到，该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This National Science Foundation award provides support for the CBMS Conference: L-functions and Multiplicative Number Theory, to be held at the University of Mississippi in Oxford, MS on May 20-24, 2019. The conference will feature a series of ten lectures by Professor Kannan Soundararajan from Stanford University who is well known for his prolific and influential research in this area, and also for his skill as a lecturer and expositor. Professor Soundararajan's lectures will culminate in an expository monograph that will be a valuable resource for current and future researchers. The conference will also feature six additional lectures intended to complement and enhance the main lecture series. Approximately thirty participants will be supported, many of whom will be graduate students. The organizers intend to bring together both beginning and more established researchers to stimulate advances and collaboration on this current research topic. The organizers will actively recruit female participants as well as participants from other groups that are underrepresented in the mathematical sciences. In accordance with the NSF-CBMS goals, the host institution is interested upgrading and improving its research efforts, and trying to build a strong research group in number theory. Number theory is an old and very active branch of mathematics, and the theory of L-functions has played a central role in its modern development. The tools used to study L-functions draw from many fields including analysis, algebra, algebraic geometry, automorphic forms and representation theory, probability and random matrices, and even mathematical physics. The broad theme for the conference will be the value distribution of zeta and L-functions. The lecture series will touch upon several important questions including the maximal size of L-functions, asymptotics for moments of L-values, the distribution of zeros, and non-vanishing of L-functions at special points. Moreover, it will be shown how the techniques used in the study of moments have close counterparts in the understanding of other problems in multiplicative number theory. The lecture series and accompanying monograph will give a broad perspective of this sharply focused research area in a way that will help researchers of all levels understand the major ideas and possible future directions for the field. Information regarding the conference can be found at https://math.olemiss.edu/cbms2019/.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.