REU Site: Undergraduate Research in Applied Analysis at West Virginia University

West Virginia University Research Corporation, Morgantown WV

Investigators

Abstract

This project is jointly funded by the Workforce program in the Division of Mathematical Sciences and the Established Program to Stimulate Competitive Research (EPSCoR). This Research Experiences for Undergraduates (REU) site award will support the mathematical training of ten students per year at West Virginia University in Morgantown, WV, for eight weeks during the summers of 2024, 2025, and 2026. The program will engage participants in applied analysis and partial differential equations research. While recruiting from a nationwide pool, special consideration will be given to underrepresented groups, students attending baccalaureate degree programs at colleges and universities in the Appalachian region and beyond, and, in general, institutions with limited research opportunities. Through weekly interactions, training, and mentoring, participants are expected to complete an independent research project, obtain first-hand experience with the rigors of and best practices in mathematical research, and familiarize themselves with mainstream expectations for graduate school and pursuing a career in mathematics. This program will also help strengthen STEM education and attract talent to West Virginia, thereby enhancing the region’s workforce and development. Participants' research projects will focus on utilizing tools from analysis and PDEs to address practical issues arising from physics and materials science. The projects include a diverse collection of topics based on the research interests of the faculty mentors: systems of conservation and balance laws with singular solutions, asymptotics for a basic cosmological model, and the director field model with electromagnetic waves. Research in hyperbolic conservation laws will focus on solving equations with special initial conditions and employ the characteristic method and, in general, various dynamical systems ideas with geometric flavor. These methods will help us gain quantitative and qualitative insights into more general problems with many applications, such as fluid mechanics, biosciences, and cosmology. The analysis of the director field model will advance our understanding of the interaction between elastic and electromagnetic waves in liquid crystals. Research on the sticky particles model will enhance our comprehension of the formation of large-scale structures in the universe by accretion of matter; more specifically, this part of the project will involve a discrete particle evolution approach to gain insight into the long-time behavior of stellar and galactic clusters. The proposed projects for this REU are based on interesting open problems and are designed to be accessible, while highly intellectually stimulating, for talented undergraduates. Additional information will be provided on the webpage: https://mathanddata.wvu.edu/students/undergraduate/applied-analysis-reu. 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.