Another successful year for REU program highlights student achievements in mathematics

MINNEAPOLIS / ST. PAUL (11/1/2024) – Every summer, the Algebra and Combinatorics Research Experience for Undergraduates (REU) program brings undergraduate students from around the world to the University of Minnesota campus for an eight weeks of intensive training in collaborative mathematics research. The 2024 program marked the 23rd year of the REU, which has grown to be one of the most respected of its kind. With seven problem groups tackling distinct research questions, several outcomes stood out, demonstrating the power of mentorship and the dedication of the participating student mathematicians.

At the beginning of the program, students learn about prospective projects through mini introductory courses, then choose problems to work on for the first few weeks of the experience. Mentored by mathematics graduate students and faculty, the students collaborate to uncover solutions for their projects. The REU session also includes organized social activities, like trips to the theatre, professional sports events, and more, as well as mentorship and professional development from graduate student teaching assistants. This year's program mentors were Ayah Almousa, Christine Berkesch, Chris O’Neill, Pavlo Pylyavskyy, Victor Reiner, Shiyun Wang, and Kayla Wright – notably featuring a mentor from outside the University of Minnesota. Professor Chris O'Neill, a seasoned REU mentor and faculty member from San Diego State University, joined the program while on sabbatical.

One of the standout problem groups this year was led by Shiyun Wang, a Dunham Jackson Postdoctoral Associate. The group resolved an important special case of a conjecture posed by Wang, proving that a class of multivariate polynomials known as dual Schubert polynomials satisfies a significant property called the SNP (Saturated Newton Polytope) property. This property has been a topic of extensive recent study, and the students’ work not only confirmed this property for dual Schubert polynomials but also provided new insights into the structure of these mathematical objects. 

“As a mentor, I was impressed by the student's passion for math research, creative ideas, and hard work. Our collaboration and friendship will continue beyond this REU program, and we can make more extensions on the questions related to Postnikov-Stanley polynomials.” – Shiyun Wang, problem mentor

Though the Algebra and Combinatorics REU started in 2000, the program truly began to expand in 2011. The program has continued to grow over the years, both in size and scope. A significant boost came from securing an NSF Research Training Group grant, which enabled more faculty involvement and increased the number of research groups. As the applicant pool has become increasingly competitive – with 450 applications received for this year’s session – the program coordinators do their best to select students for whom the REU could be a transformative step in their academic careers. 

The University of Minnesota’s REU programs also play an important role as an introduction to higher education at Minnesota. “I think it's important to keep the program going as a pipeline for students to learn about mathematics research, but also to connect strong candidates with the possibility of a future in our PhD program,” REU facilitator Victor Reiner says. “There are really quite a few of our ex-REU students currently getting a PhD here – even more if you count those who have participated in Prof. Arnd Scheel’s Complex Systems REU program”

For the first time since its inception, the Algebra and Combinatorics REU program might not run in summer 2025 due to a gap in funding. To continue supporting talented students who aspire to make breakthroughs in their mathematics careers, the program organizers are seeking to build the program’s financial support system for the future. The outcomes of this year’s session demonstrate the undeniable importance of providing young mathematicians with research opportunities and mentorship. Program facilitators are optimistic that the REU has potential to resume in summer 2026 and beyond.