REU Site: Algebra, Combinatorics, and Statistics

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This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). The Department of Mathematics at the Texas State University at San Marcos will host an eight-week REU Site in the summers of 2022, 2023, and 2024, involving nine students per year working in teams of three under the supervision of a faculty mentor. The selected participants will come from a diverse pool of applicants, and the faculty mentors will supervise the participants in research projects. Beyond successful research outcomes, the objectives of the program are to introduce students to aspects of mathematical research and the broader mathematical community. At the same time, the students will build mentoring relationships with faculty as they consider pursuing graduate degrees and a career in mathematics. Students will be part of an active community at the hosting institution. In addition to the REU, the participants will have various activities, participating in several summer programs and interacting with established mathematicians who visit the campus. A diverse body of participants is strongly desired, and priority will be given to applicants from groups that are underrepresented in the mathematical community. This includes minority students, women, as well as those students coming from institutions with limited resources to support independent research projects for their undergraduates. 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, shellability of simplicial complexes, algebraic and combinatorial aspects of higher dimensional tiling, graph theoretic problems arising from group theory, prime graphs of special classes of groups, arithmetical properties of group invariants, linear and permutational representations of groups, statistical analysis on DNA sequencing data, and survival analysis in data science. Participants will regularly meet with their research team and their mentors and spend some of the time learning the necessary background before and while pursuing original research. Students will be asked to present their findings in oral presentations and will be guided in summarizing their work in a mathematical research paper. In the course of the program, students will be trained in various skills, including literature review, using software such as GAP, Macaulay2, Sage, and R to make and check examples, oral presentation skills, and written mathematical communication using LaTeX. Communication with the participants will continue after the program ends, and students will be encouraged to present their work at local, regional, and national conferences in the subsequent academic year.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.