RTG: Combinatorics and Algebra

明尼苏达大学的这个RTG是组合学的三个PI和代数的两个PI合作的成果。由这些个人投资机构指导的许多本科生、博士生和博士后需要在现代数学领域进行广泛的培训，这些领域与个人投资机构的研究项目相同，如表示理论、代数几何、拓扑学和数学物理。除了延续前一届组合学RTG最成功的特点，例如强大且不断增长的夏季REU计划外，目前的赠款还将资助令人兴奋的新计划，如备受瞩目的组合学开放问题会议，首次主办EDGE夏季计划，以加强代表不足群体的研究生教育，以及组合学和代数小组之间更多的联合研讨会。它还将继续扩展到明尼苏达州邻近的地区机构，并将通过为明尼苏达大学天才青年数学项目(UMTYMP)提供丰富课程来服务于我们的高中生。RTG将利用明尼苏达州代数和组合学小组之间的交叉授课，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，PI已经学会了让他们的暑期REU项目不仅成为本科生令人兴奋和身临其境的研究体验，而且成为培训我们的研究生和博士后导师艺术的实验室。PI的主题课程(例如，Hecke代数的表示理论、反射群、箭图、不变理论、自由分解、可积系统、簇代数、全正性和电网络)旨在向研究生和博士后群体以及有才华的本科生介绍许多现代数学和物理中最热门的主题。博士后将获得教授有才华的高中生的独特机会，研究生将在主办年度研究生组合数学会议时学习宝贵的组织技能。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.