Summer School for Young Researchers on Representations of Finite Groups

该项目将支持美国的旅行-研究生参加国际会议“在卡斯特罗的代表：暑期学校。该会议针对早期职业数学家（特别是研究生），将于2020年9月7日至12日在西班牙Castro Urdiales的Centro Internacional de Encuentros Matematicos（CIEM）举行。暑期学校的主要目的是培训年轻的研究人员，并鼓励他们掌握该学科领域。 它将开始三天的介绍性讲座，随后是三天的更先进的讲座，介绍学生在数学领域的代表性理论的一些当前热点问题。会议有三名组织者和五名发言人，代表六个国家。因此，通过允许美国-这项赠款将鼓励在该领域开展重要的国际合作和建立联系。 特别鼓励在数学领域代表性不足的妇女和其他群体的成员参加，因为在研究生涯早期建立同行网络已被证明对保持活跃和在该领域的可见性特别重要。暑期学校将鼓励性格理论和模块理论这两个相关（但有时看似遥远）领域之间的交叉授粉。 表征理论领域的许多最新进展和开放性成果都清楚地表明，将双方的技术结合起来有很大的好处。 介绍性讲座是为研究生和博士后设计的，他们有良好的代数背景，但没有表示论的先验知识。他们将从两个不同的角度来讨论一般理论：一个是关注更多的数值，特征理论的观点，另一个是关注同调，模理论的观点。 这些课程将有一个强大的重点放在到达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表征理论的一些当前方向，以及这两种观点如何在该地区的一些基本知识中发挥作用。 在整个暑期学校，讲座将与讨论和问题的演讲者和组织者领导的会议交替进行。 通过为学生提供一个密集的介绍性系列课程和讲座在该地区当前的热门话题，暑期学校的目的是激励年轻的研究人员利用他们的才能，以推进该地区的知识状态，并激励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奖反映了NSF的法定使命，并已被认为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。

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.