Conference: Group Theory and Number Theory: Interactions

该基金用于资助参与者参加“群论与数论：相互作用”会议，该会议将于2023年10月16日至20日在普林斯顿大学举行。这次会议汇集了群论和数论领域的专家，将提供新的交流机会，并促进这两个数学分支的研究人员之间的重要研究合作。群论的动机是研究在科学、艺术和技术的许多领域中发现的物体的对称性，从分子结构到粒子的自旋，从密码系统的模式到和弦的结构。数论的动机是研究整数、素数、整数值函数和这些对象的推广，并在与群论相同的领域有应用。在群论的许多关键问题中，人们看到了与数论的自然关系，反之亦然。这两个领域最近的进展和公开的猜想已经清楚地表明，能够将两者的技术结合起来是非常有益的。这次会议将激发重要问题的进展，同时也拓宽了这两个领域的研究人员可用的工具和思想，并培养了研究群论和数论相互作用的新一代研究人员。特别鼓励女性学生、早期职业研究人员和数学家以及其他未被充分代表的群体参与。在群论（更具体地说，是表示论）和数论之间有明确关系的最著名的例子之一是朗兰兹纲领。主讲人将代表群论和数论两个领域中一些最有影响力的名字和趋势，讨论与Langlands程序相关的新结果，以及代数群，置换群，表征理论和单词增长的概率方法，特征理论中的局部-全局猜想，以及连接群论/表征理论和数论两个领域的其他主题。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知识价值和更广泛的影响审查标准进行评估，认为值得支持。

This grant is to support travel of participants to attend the conference "Group Theory and Number Theory: Interactions", which will take place October 16-20, 2023 at Princeton University. Bringing together experts in the areas group theory and number theory, this conference will provide new networking opportunities and stimulate important research collaborations between researchers in these two branches of mathematics. Group theory is motivated by the study of symmetries of objects found in many areas of science, art, and technology, from molecular structures, to the spin of particles, to the patterns in cryptosystems, to the structure of musical chords. Number theory is motivated by the study of the integers, prime numbers, integer-valued functions, and generalizations of these objects, and has applications to the same areas as group theory. In many of the key problems in group theory, one sees natural relationships to number theory, and vice versa. Recent advances and open conjectures in the two areas have made it clear that there is a strong benefit to being able to combine the techniques from both. This conference will inspire progress on important questions, while also broadening the tools and ideas available to researchers in both areas, and fostering a new generation of researchers studying interactions of group theory and number theory. Students, early-career researchers, and mathematicians who identify as women and other underrepresented groups will be especially encouraged to participate. One of the most well-known examples with a clear relationship between group theory (and, more specifically, representation theory) and number theory is the Langlands program. The main speakers, representing some of the most influential names and trends currently in the two areas of group theory and number theory, will give talks discussing new results related to the Langlands program, as well as new results on algebraic groups, permutation groups, probabilistic approaches to representation theory and word growth, local-global conjectures in character theory, and other topics that bridge the two areas of group theory/representation theory and number theory. The conference website is: https://sites.google.com/view/tiep60conference/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.