RTG in Combinatorics

这个RTG由明尼苏达大学组合学的四位pi指导：Gregg Musiker， Pavlo Pylyavskyy， Victor Reiner和Dennis Stanton。pi们坚信，年轻的组合数学家需要接触广泛的数学知识，包括传统的以及最近的主题，如聚类代数、总正性和热带几何，这一信念推动了这一计划。组合学非常适合培养年轻的研究人员，部分原因是它的主题和问题范围从那些基本的，可以介绍给本科生的到那些高度非基本的，与表示理论，代数几何，拓扑和数学物理有很深的联系。RTG的基石是集团的重组。这是一个成功的REU项目，其目标是通过让研究生和博士后充分参与进来，提高效率，培养更广泛的受众。此外，这笔资金将允许一个更大的博士后项目，以及博士后教授热门话题新课程的机会，以及在明尼苏达大学天才青年数学项目中教授有才华的高中生。它将资助更多的研究生和博士后参加会议的旅行，以便他们能够跟上发展并传播自己的研究，它将通过主办两种会议给他们提供组织经验：一系列中西部组合会议，以及重复主办2005年在明尼苏达州发起的年度研究生组合会议。RTG利用其pi之间的长期指导经验和新鲜观点，在明尼苏达大学创建了一个垂直整合的组合学培训环境。它建立在以往成功的本科生暑期研究培训的基础上，让研究生和博士后与本科生一起研究问题，同时让他们参与指导过程。此外，它将为博士后提供更广泛的教育机会和经验，并为研究生和博士后提供更多的机会，广泛地参加会议，并学会自己组织会议。RTG通过一系列中西部会议，向大明尼苏达地区的学校进行拓展讲座，包括卡尔顿学院的女性夏季数学项目，以及明尼苏达大学为高级高中生开设的青年数学天才项目，扩大了与明尼苏达州地区邻近机构的联系。

This RTG is directed by four PIs in Combinatorics at the University of Minnesota: Gregg Musiker, Pavlo Pylyavskyy, Victor Reiner, and Dennis Stanton. It is fueled by the strongly held conviction of the PIs that young mathematicians in combinatorics need exposure to a wide array of mathematics, including traditional as well more recent topics, such as cluster algebras, total positivity, and tropical geometry. Combinatorics is extremely well-suited for training young researchers partly because its topics and problems range from those which are elementary and can be introduced to undergraduates to those which are highly non-elementary and have deep connections to representation theory, algebraic geometry, topology, and mathematical physics. A cornerstone of the RTG is a reorganization of the group?s successful REU program, with the goals of greater efficiency and educating a broader audience, by thoroughly involving grad students and postdocs. In addition, the funding will allow for a larger postdoc program, as well as opportunities for postdocs to teach new course offerings in hot topics, and to teach talented high school students in the University of Minnesota Talented Youth Math Program. It will fund more travel to conferences for grad students and postdocs so that they can keep abreast of developments and disseminate their own research, and it will give them organizational experience via the hosting of two kinds of conferences: a series of Midwest Combinatorics Conferences, and a repeat-hosting of the annual Grad Student Combinatorics Conference which originated in Minnesota in 2005.The RTG leverages both the long-term mentoring experience and fresh perspectives among its PIs to create a vertically well-integrated training environment in combinatorics at the University of Minnesota. It builds on the previous success in summer training of undergraduates in research, by exposing graduate students and postdocs to research problems in parallel with the undergraduates, while involving them in the mentoring process. In addition, it will offer wider educational opportunities and experiences for postdocs, as well as more opportunities for both graduate students and postdocs to travel extensively to conferences, and learn to organize conferences themselves. The RTG expands outreach to Minnesota's regional neighbor institutions, through a series of Midwest conferences, outreach talks to schools in the greater Minnesota area, including the Summer Math Program for Women run at Carleton College, and through the University of Minnesota's Talented Youth Math Program for advanced high school students.