RTG: Combinatorics, Geometry, Representation Theory, and Topology at University of Oregon

这个研究训练小组是由七名教师在俄勒冈州的研究活动涵盖了广泛的主题，在几何，拓扑，表示理论和组合学领域的大学领导。 该奖项将支持至少4名博士后和20-30名有才华的研究生的培训，并将在夏季研究活动中吸引多达40名本科生。该奖项还将支持夏季研讨会系列在代表性理论和区域会议系列组合学和相关领域。这些研究人员将采取合作的方式来监督和指导早期职业数学家。除了研究培训外，该RTG的主要目标是通过以下几种机制扩大对数学的参与：灵活的博士后职位建立在远程培训和合作战略，通过将研究生纳入大学的监狱教育计划，合作指导战略和其他活动，为研究生发展技能，所有这些都旨在发展一个充满活力，有凝聚力，欢迎研究社区，旨在帮助学生和博士后充分发挥潜力。作为该奖项的一部分进行的项目将主要集中在代数和几何，等变拓扑，偏序集的几何和拓扑，以及正特征的上同调和表示理论中的派生类别。项目活动将促进这些不同主题之间的思想交流，目的是建立新的桥梁和联系。垂直整合的指导和学习机会将是RTG活动的关键组成部分，为早期职业参与者提供宝贵的技能。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

This Research Training Group is led by seven faculty members at the University of Oregon whose research activities cover a wide range of topics in the fields of geometry, topology, representation theory, and combinatorics. The award will support the training of at least four postdocs and 20-30 talented graduate students and will engage up to 40 undergraduates in summer research activities. The award will also support a summer workshop series in representation theory and a regional conference series in combinatorics and related areas. These researchers will undertake a collaborative approach to the supervision and mentoring of early career mathematicians. In addition to research training, a main goal of this RTG will be to broaden participation in mathematics through several mechanisms: flexible postdoc positions built on remote strategies for training and collaboration, development of skills for graduate students by incorporating them into the university’s prison education program, collaborative mentorship strategies, and other activities, all aimed at the development of a vibrant, cohesive, and welcoming research community designed to help students and postdocs reach their full potential. The projects conducted as part of this award will primarily focus on derived categories in algebra and geometry, equivariant topology, the geometry and topology of posets, and cohomology and representation theory in positive characteristic. The project activities will foster a flow of ideas among these various subjects, with the goal of creating new bridges and connections. Vertically integrated mentorship and learning opportunities will be key components of the RTG activities, offering valuable skillsets to the early-career participants.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.