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.
