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.
