RTG: Combinatorics and Algebra

这个在明尼苏达大学的RTG是三个PI之间的合作努力在组合学和两个代数。 由这些PI监督的许多本科生，博士生和博士后需要在PI的研究计划中共同的现代数学领域进行广泛的培训，如表示论，代数几何，拓扑学和数学物理。 除了继续之前的RTG在组合学中最成功的功能，如强大和不断增长的夏季REU计划，目前的赠款将资助令人兴奋的新举措，如高调的组合学开放问题会议，首次举办EDGE夏季计划，以加强代表性不足的群体的研究生教育，以及组合学和代数组之间的更多联合研讨会。 它还将继续推广到明尼苏达州的区域邻近机构，并将通过提供丰富的课程，明尼苏达大学天才青年数学计划（UMTYMP）为我们的高中学生服务。RTG将利用明尼苏达州代数和组合学小组之间的交叉施肥，为我们的本科生，研究生和博士后提供更丰富的指导经验。 PI现在已经学会了使他们的夏季REU计划不仅为本科生提供令人兴奋和身临其境的研究体验，而且还为培训我们的格拉德生和博士后提供指导艺术的实验室。 PI的主题课程（例如，在Hecke代数的表示论中，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人口，沿着有才华的本科生，介绍现代数学和物理学中许多最热门的话题。博士后将获得独特的机会，教有才华的高中生，研究生将学习宝贵的组织技能，在主办年度研究生组合学会议。这个奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。

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.