Conference: Group Theory and Number Theory: Interactions

会议：群论和数论：相互作用

• 批准号: 2321445
• 负责人: Mandi Schaeffer Fry
• 金额: $ 4.97万
• 依托单位: University of Denver
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-06-01 至 2024-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2321445&HistoricalAwards=false
• 关键词: Conference; Group; Theory; Number; Interactions

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.

这笔赠款是支持与会者的旅费参加会议“群论和数论：相互作用”，这将发生在2023年10月16日至20日在普林斯顿大学。这次会议将群论和数论领域的专家聚集在一起，将提供新的网络机会，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，到密码系统中的模式，再到音乐和弦的结构。数论的动机是研究整数，素数，整数值函数，以及这些对象的推广，并应用于与群论相同的领域。在群论中的许多关键问题中，人们可以看到数论的自然关系，反之亦然。这两个领域的最新进展和公开成果清楚地表明，能够将两者的技术联合收割机结合起来具有很大的好处。本次会议将激发重要问题的进展，同时也扩大了这两个领域的研究人员可用的工具和想法，并培养新一代研究人员研究群论和数论的相互作用。学生，早期职业研究人员和数学家谁确定为妇女和其他代表性不足的群体将特别鼓励参加。在群论（更具体地说，表示论）和数论之间有着明确关系的最著名的例子之一是朗兰兹纲领。 主要发言人，代表一些最有影响力的名字和趋势，目前在两个领域的群论和数论，将给予会谈讨论有关的朗兰兹计划的新成果，以及新成果代数群，置换群，概率方法表示理论和字的增长，局部-全球的结构特征理论，以及其他连接群论/表示论和数论两个领域的主题。会议网站是：https://sites.google.com/view/tiep60conference/This奖反映了NSF的法定使命，并已被认为是值得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的支持。