2023 NREUP Projects

Bucknell University

Project Title: NREUP--Bucknell
Project Director: Nathan Ryan
Project Summary: Participants in the NREUP--Bucknell will formulate and verify conjectures in number theory. Specifically, they will be using random matrix theory to study important features of the Riemann zeta function and other L-functions. We will accomplish this by using the computer algebra systems SageMath and PARI/GP to generate a lot of data to support conjectures that come from applying random matrix theory to the Riemann zeta function and L-functions of modular forms. Students will learn various computational techniques (e.g., computational linear algebra, high throughput computing, etc.), contribute to a mathematical database sponsored by the NSF, write papers to be submitted to mathematical or computational journals and share their results at conferences. A special feature of this NREUP is that it will be run in both English and Spanish.

California State University at Monterey Bay

Project Director: Steven Kim
Project Summary: Students are curious how mathematics and statistics are applied to real-world problems. The summer research program at CSU Monterey Bay is designed for students who have completed multivariate calculus, discrete mathematics, linear algebra, and preferably introductory statistics and some programming course. (If there is any gap in the preparations, students will be trained via a 3-week mini-course.) The common theme of the summer research program is sequential decisions using data and statistical models. Students will study and develop probability models and statistical methods for making a series of decisions based on the most updated information available to decision makers. Applied areas include, but not limited to, toxicology, kinesiology, exercise science, bioinformatics, and sports analytics.

DePaul University*

Project Title: DePaul NREUP
Project Directors: Emily Barnard
Project Summary: Building on the success of our 2022 summer NREUP, this proposal is to renew our National Research Experience for Undergraduates Program (NREUP) at DePaul University for Summer 2023. This year we have intentionally chosen a project on graph b-colorings with questions that are low-floor and high-ceiling to accommodate students at varying places in their educational careers. Several papers have been written on this topic in recent years. Many of these papers have focused on regular graphs with large diameter, leaving many open problems related to non-regular graphs or regular graphs with small diameter. Our REU aims to address some of these questions. Since many of our students will be local to the Chicagoland area, we will also use graph theory to discuss equity issues in Chicago. Our main goal is to create opportunities for our students to conduct original research and to open the door to graduate programs and careers in mathematics.

Louisiana State University at Alexandria

Project Title: The Summer Undergraduate Research Experiences at LSUA
Project Director: Prakash Ghimire
Project Summary: The Summer Undergraduate Research Experiences at LSUA will allow four undergraduate students to work on research problems in the field of non-associative algebra for eight weeks in summer 23. More specifically, students will characterize the linear commuting maps of the algebra of strictly block upper triangular matrices and the linear triple centralizers of the algebra of dominant block upper triangular matrices. Students will also learn mathematics writing software LATEX and research paper writing skill. We expect students to submit at least one research paper in professional journals and present their findings at the LSUA annual scholar day and MAA Louisiana/Mississippi section meeting.

State University of New York (SUNY) New Paltz

Project Title: NREUP at SUNY New Paltz: The mathematics of incorporating human behavior in epidemic modeling
Project Directors: Anca Radulescu, Moshe Cohen
Project Summary: SUNY New Paltz will conduct a 7-week summer program involving participation of four mathematics undergraduates from underrepresented groups in distinct, focused and challenging research experiences. All four projects will stem from the crucial importance to scientifically address the relationship between epidemic patterns and the population response. Research activities will focus in particular on capturing and analyzing the coupling between the pandemic dynamics and the population response, and will encompass both theoretical and data-driven modeling of this coupled system. Results of this research will inform the scientific community in its work to understand and fight current and future pandemics. Students participating in this program will gain valuable research experience with 1) traditional methods in dynamical systems; 2) statistics and big data analytics, and 3) harnessing the major impact of statistics and big data on applications. Additionally, students will receive professional development experience by preparing their work for publication and presenting their results at mathematics conferences.

Texas A&M University-San Antonio

Project Title: Summer Research Program on Lattice Reduction Theory
Project Director: Jingbo Liu
Project Summary: This summer research program provides a mentoring structure for historically underrepresented undergraduate mathematics students from South Texas and promotes active engagement in mathematical research on the reduction theory of lattices (mainly Lagrange reduction, Minkowski reduction, HKZ reduction, and LLL reduction) that deepens and extends certain topics covered in a standard undergraduate linear algebra course. The reduction theory of lattices is not only an essential component of contemporary algebraic number theory, but also has significant applications to lattice-based cryptography and wireless communications, among other high technology fields. The four students will study the relation between the smallest value of the parameter in the LLL algorithm which generates the shortest LLL-reduced basis vector and the determinant of the lattice, and the relation between the smallest value of that parameter in the LLL algorithm and the rank of the lattice, respectively. To accomplish this research, these students will be immersed in intensive short courses on relevant topics in modern algebra, number theory, lattice theory, and statistics, plus training in LaTeX and other software; they will also be engaged in daily experience of independent research by reading papers, giving presentations, and having group discussions. The four student researchers are expected to continue their research on the lattice reduction theory in the following school years with their mentor, to give research presentations at important regional and national conferences, and to publish the work in high/good-quality mathematical research journals.

University of Massachusetts, Dartmouth*

Project Title: Mixed model implicit and IMEX Runge–Kutta methods
Project Directors: Zheng Chen, Yanlai Chen, Scott Field, Alfa Heryudono, Sigal Gottlieb
Project Summary: The focus of the proposed program is to bring together a small and focused group of undergradu- ate mathematics majors from underrepresented groups to engage in dynamic, exciting, supportive research collaborations. We will select two students from UMass Dartmouth and two students from Spelman College who will work closely with other UMassD faculty members. The research topics will build on the mixed precision Runge–Kutta methods of Z. Grant, and applied to mixed model simulations. Investigations of interest will include analytical and numerical studies of stability using different spatial discretizations. Through this program, we aim to build enthusiasm for advanced degrees and careers in mathematics, and the support of a strong peer network closely mentored and guided by faculty mentors. Through the supportive community we will build, our students will feel enabled and empowered to continue their mathematics education and explore career options in this field.

*Funding provided by the Tondeur Fund.