Summer School for Young Researchers on Representations of Finite Groups

有限群表示青年研究人员暑期学校

• 批准号: 2001077
• 负责人: Mandi Schaeffer Fry
• 金额: $ 1万
• 依托单位: Metropolitan State University of Denver
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-06-01 至 2021-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2001077&HistoricalAwards=false
• 关键词: Summer; Young; Researchers; Representations; Finite

This project will support travel of U.S.-based graduate students to attend the international conference "Representations in Castro: A Summer School." The conference is aimed at early-career mathematicians (especially graduate students) and is to be held September 7-12, 2020, at the Centro Internacional de Encuentros Matematicos (CIEM) in Castro Urdiales, Spain. The summer school is primarily for the purpose of training young researchers and encouraging their mastery of the subject area. It will begin with three days of introductory lectures, followed by three days of more advanced lectures introducing the students to some current hot topics in the mathematical area of representation theory. The conference has three organizers and five speakers, representing a total of six countries. Hence, by allowing U.S.-based students to attend the summer school, this grant will stimulate important international collaboration and networking in the area. Women and members of other groups underrepresented in mathematics are especially encouraged to participate, as building a network of peers early in one's research career has been shown to be especially crucial for staying active and visible in the field. The summer school will encourage cross-pollination between the two related (but sometimes seemingly distant) fields of character theory and module theory. Many of the recent advances and open conjectures in the area of representation theory have made it clear that there is a strong benefit to combining the techniques from both sides. The introductory lectures are designed for graduate students and postdocs with a good background in algebra but no prior knowledge in representation theory. They will cover the general theory from two different points of view: one focusing on the more numerical, character-theoretic point of view, and the other on the homological, module-theoretic point of view. These courses will have a strong focus on arriving at some of the key definitions and concepts in block theory. The second part of the summer school will be aimed at showing the students some of the current directions of representation theory and how both perspectives play a role in some of the fundamental conjectures in the area. Throughout the summer school, lectures will be alternated with discussion and problem sessions led by the speakers and organizers. By providing students with an intensive introductory series of courses and lectures on current hot topics in the area, the summer school aims to motivate young researchers to use their talents to advance the state of knowledge in the area and to inspire a new generation of well-rounded representation theorists. The conference website is https://sites.msudenver.edu/castrosummerschool/2019/09/17/hello-world/.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.

该项目将支持美国研究生的旅行，参加国际会议“卡斯特罗的代表性：暑期学校”。该会议针对早期的数学家（尤其是研究生），将于2020年9月7日至12日在西班牙卡斯特罗·乌尔迪亚斯（Castro Urdiales）举行的Centro Interno Internacional de Encuentros Matematicos（CIEM）。暑期学校主要是为了培训年轻研究人员并鼓励他们对学科领域的掌握。 它将从三天的入门讲座开始，然后进行三天的更高级讲座，向学生介绍代表理论数学领域的一些当前热门话题。该会议有三名组织者和五名演讲者，共有六个国家。因此，通过允许美国的学生上暑期学校，该赠款将刺激该地区重要的国际合作和网络。 特别鼓励妇女和其他人数不足的数学人数参与，因为已经证明，在研究生涯的早期建立同龄人网络对于保持活跃和在该领域的活跃和可见特别重要。暑期学校将鼓励性格理论和模块理论的两个相关（但看似遥远）的领域之间的交叉授粉。 代表理论领域的许多最新进展和开放式猜想清楚地表明，结合双方技术有很大的好处。 介绍性讲座是专为代数背景良好的研究生和博士后设计的，但没有代表理论的先验知识。他们将从两种不同的角度涵盖一般理论：一种关注更数值，特征理论的观点，另一个关注同源，模块理论的观点。 这些课程将重点关注块理论中的一些关键定义和概念。暑期学校的第二部分将旨在向学生展示当前代表理论的一些方向，以及两种观点如何在该地区的某些基本猜想中发挥作用。 在整个暑期学校中，讲座将与演讲者和组织者领导的讨论和问题会议交替。 通过为学生提供有关该地区当前热门话题的大量介绍性课程和讲座，暑期学校旨在激励年轻的研究人员利用自己的才华来推进该地区的知识状态，并激发新一代的全面代表理论家。会议网站是https://sites.msudenver.edu/castrosummerschool/2019/09/17/hello-world/.this Award反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的评估来通过评估来获得支持的。