RTG: Combinatorics and Algebra

明尼苏达大学的RTG是组合学的三位pi和代数的两位pi的合作成果。这些pi指导的许多本科生、博士生和博士后需要在pi研究项目中共同的现代数学领域进行广泛的培训，例如表示理论、代数几何、拓扑学和数学物理。除了延续之前RTG在组合学方面最成功的特点，例如强大且不断增长的夏季REU计划，当前的拨款将资助令人兴奋的新计划，例如备受瞩目的组合学开放问题会议，首次主办EDGE夏季计划，以加强代表性不足群体的研究生教育，以及组合学和代数组之间的更多联合研讨会。它还将继续扩展到明尼苏达州的区域邻近机构，并将通过为明尼苏达大学天才青年数学计划（UMTYMP）提供丰富课程来服务我们的高中生。RTG将利用明尼苏达大学代数和组合组之间的交叉受精，为我们的本科生、研究生和博士后提供更丰富的指导经验。到目前为止，ppi已经学会了让他们的夏季REU项目不仅是本科生令人兴奋和身临其境的研究经历，而且是一个培养研究生和博士后指导艺术的实验室。pi的主题课程（例如，Hecke代数的表示理论，反射群，颤振，不变理论，自由分辨率，可积系统，簇代数，总正性和电网络）旨在向研究生和博士后人群以及有才华的本科生介绍现代数学和物理学中许多最热门的主题。博士后将有机会教授有才华的高中生，研究生将在主持年度研究生组合学会议中学习宝贵的组织技能。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，被认为值得支持。

This RTG at the University of Minnesota is a collaborative effort between three PIs in Combinatorics and two in Algebra. The many undergraduates, PhD students and postdocs supervised by these PIs require broad training in modern areas of mathematics in common to the PIs' research programs, such as representation theory, algebraic geometry, topology, and mathematical physics. In addition to continuing the most successful features of the previous RTG in Combinatorics, such as the strong and growing summer REU program, the current grant will fund exciting new initiatives, such as a high-profile Open Problems conference in Combinatorics, a first-time hosting of the EDGE summer program for enhancing graduate education of underrepresented groups, plus more joint seminars between the combinatorics and algebra groups. It will also continue the outreach to Minnesota's regional neighboring institutions, and will serve our high school students by providing enrichment courses to the University of Minnesota Talented Youth Math Program (UMTYMP).The RTG will take advantage of the cross-fertilization between the algebra and combinatorics groups at Minnesota to provide a richer mentoring experience for our undergraduates, graduate students and postdocs. The PIs have by now learned to make their summer REU program not only an exciting and immersive research experience for the undergraduates, but also a laboratory for training our grad students and postdocs in the art of mentorship. The PIs' topics courses (e.g., in representation theory of Hecke algebras, reflection groups, quivers, invariant theory, free resolutions, integrable systems, cluster algebras, total positivity and electrical networks) are designed to introduce a large cross-section of the graduate and postdoc population, along with talented undergraduates, to many of the hottest topics in modern mathematics and physics. Postdocs will be given unique opportunities to teach talented high school students, and graduate students will learn valuable organizational skills in hosting the annual Graduate Student Combinatorics Conference.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.