REU Site: Algebra, Combinatorics, and Statistics

The Department of Mathematics at Texas State University will host an 8-week summer REU titled "REU Site: Algebra, Combinatorics, and Statistics" in the summers of 2025, 2026 and 2027. The program will continue the successful REU program run by Texas State University during the previous six years under the same title. The chosen participants will come from a selective pool of applicants, and the program will directly involve them in research projects guided by faculty mentors. Beyond successful research outcomes, the objectives of the program are to introduce students to all aspects of mathematical research and the broader mathematical community. At the same time, students will develop mentoring relationships with faculty as they consider pursuing graduate degrees and a career in mathematics. In addition to closely mentored work on a research project, professional training will be provided in various skills including literature review; the use of software such as GAP, Sage, Macaulay2 and R; presentation skills; and mathematical exposition. Students will be encouraged to present their work at local, regional, and national conferences in the subsequent academic year. The research projects include a diverse collection of topics based on the research interests of the faculty mentors. Specific projects include commutative algebra arising from graphs and matroids, algebraic and combinatorial aspects of higher dimensional tilings, chip firing on signed graphs and hypergraphs, combinatorial problems arising from group theory, arithmetic properties of group invariants, linear and permutational representations of groups, statistical analysis of biological data, and deep ReLU neural networks. All projects are tackling problems of high current interest. Some of the projects will lead to publications in respected research journals and thereby advance their respective fields. The REU site has a permanent webpage at https://www.math.txst.edu/research-conferences/summerreu.html. 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.