Apollonian Circle Packings

该基金资助美国讲师、组织者和学生参加2014年6月23日至27日在斯德哥尔摩米塔格-莱弗勒研究所举办的阿波罗圈包装暑期学校（由欧洲数学女性协会和欧洲数学学会共同主办，作为第六届欧洲数学女性暑期学校）。暑期学校将由Elena Fuchs博士（伯克利）和Hee Oh教授（耶鲁大学）讲授阿波罗圆填充和相关概念，如薄群轨道、几何群论、均匀分布、仿射筛、强近似和扩展器。这个领域处于当今数学的前沿；许多重大突破都发生在过去的5-7年里，自2011年以来，至少有17篇关于这些主题的论文发表。研究生和博士后将受益于在一个统一的演示中学习这些方法，将所有这些想法与阿波罗圈包装的不可抗拒之美联系起来。更多的信息可以在暑期学校的网页上找到：http://www.math.ucsd.edu/~alina/ewm/This暑期学校将对全球年轻的数论学家社区产生广泛的影响，因为它将为这个快节奏的研究领域提供一个入口，并将丰富研究生和博士后参与者的技能。此外，由于其对性别平等的结构性关注，这个暑期学校将在留住已经从事数论的女性以及吸引更多女性研究人员进入该领域方面发挥关键作用。通过在国际舞台上突出两位特色女讲师的研究，暑期学校将提高她们的知名度，特别是对该领域的年轻研究人员。学校还将为参与者提供机会，获得有关数论迷人的新发展的专业知识，以及对该领域当前开放问题的认识。最后，参加者将学习数论与数学其他部分之间的联系，同时扩大他们的数学工具箱，从而补充他们的教育，并帮助他们开始成功的独立研究计划。

This grant funds the participation of US-based lecturers, organizers, and students in the Apollonian Circle Packings Summer School at the Institut Mittag-Leffler, Stockholm, during June 23-27, 2014 (co-hosted by the European Women in Mathematics association and the European Mathematical Society as the 6th European Women in Mathematics Summer School). The summer school will feature lecture series by Dr. Elena Fuchs (Berkeley) and Prof. Hee Oh (Yale University) on Apollonian circle packings and related concepts such as orbits of thin groups, geometric group theory, equidistribution, the affine sieve, strong approximation and expanders. This area is on the cutting edge of current mathematics; many of the major breakthroughs have occurred in the last 5-7 years, and at least 17 papers on these subjects have appeared since 2011. Graduate students and postdocs will benefit from learning about these methods in a unified presentation that ties all of these ideas back into the irresistible beauty of Apollonian circle packings. Further information may be found on the summer school webpage: http://www.math.ucsd.edu/~alina/ewm/This summer school will have potential for broad impact on the worldwide community of young number theorists, as it will provide an entry point to this fast-paced area of research, and will enrich the skills of graduate student and postdoc participants. In addition, due to its structural focus on gender parity, this summer school will serve a key role in retaining women who are already engaged in number theory, as well as in attracting more female researchers to the field. By highlighting the research of the two featured female lecturers on the international stage, the summer school will increase their visibility, particularly for younger researchers in the field. The school will also give participants the chance to gain specialized knowledge on fascinating new developments in number theory as well as an awareness of current open problems in the field. Finally, participants will learn about connections between number theory and other parts of mathematics while enlarging their mathematical toolboxes, thus supplementing their educations and aiding them in starting successful independent research programs.