Research Experience for Undergraduates

The Department of Mathematics and Applied Mathematics will host a Research Experience for Undergraduates (REU) site in graph theory and computational mathematics.

The REU will provide 12-16 undergraduates a hands-on introduction to computational research endeavors and improve their problem-solving, communication and computer programming skills. Student teams will be formed to work on the research projects listed below.

The REU will be conducted online with most meeting times during 9:00 a.m. - 4:00 p.m. EDT. The program will run May 28 - July 19, 2024.

Selected students will receive a $5,200 stipend ($650 per week). Additionally, students will be funded to present their work at conferences after the REU.

Participants must be U.S. citizens or permanent residents, and must be undergraduates in fall of 2024. Applications are especially encouraged from students who identify with populations currently underrepresented in mathematics graduate programs, from schools with limited access to research opportunities and current freshmen and sophomores.

Projects

Graph Theory and Lie Theory

Mentors: Marco Aldi and Daniele Grandini

The goal of this project is to investigate a dictionary between graph theory and the theory of Lie algebras. The simplest form of this construction, due to Dani and Mainkar, assigns a Lie algebra to each graph. While it is known that these Lie algebras completely characterize the isomorphic class of the associated graph, the graph theoretic information is repackaged in a non-trivial way that is not yet completely understood. The focus of this project is to bridge this gap by systematically studying well-known graph-theoretic notions through the lenses of Lie theory. By doing so we aim at advancing our understanding of both areas of mathematics.

Modeling vector-borne diseases

Mentor: Suzanne Robertson

The community composition of vectors and hosts plays a critical role in determining the risk of an area for vector-borne disease. Mosquito species have different habitat preferences, competitive advantages, and ability to spread disease. We will use ordinary differential equation models to explore the impact of factors affecting mosquito population dynamics, such as rainfall, temperature, and socio-economic factors, on the outcome of competition between species and the resulting implications for vector-borne disease transmission.

Experiencing the Power of Data Science on Real-World Challenges

Mentors: David Chan, Yanjun Qian, Indranil Sahoo

In the era of big-data and information, understanding and mastering modern machine learning/artificial intelligence (ML/AI) based data analysis methods have become essential skills in academic research and industrial professions. These methods can find hidden patterns behind the sheer bulk of the collected data, providing critical clues to help people solve problems. For instance, the latent factor analysis (LFA) identifies potential factors that affect students performance during the COVID-19 pandemic from large-scale survey data; Markov chains (MC) dynamically model students; academic mindsets to predict the classroom learning outcome; integrating machine learning techniques to spatial-temporal modeling gives us quantitative descriptions of the climate crisis using large scale satellite data; natural language processing (NLP) extracts common concerns and opinions from comments collected from surveys and internet.

Over the course of this Research Experience, we will investigate the incorporation of these ML- based analytical methods to solve real-life problems using a variety of datasets. Students will not only learn the principles of these cutting-edge methods, but also get a hands-on experience of implementing them using software such as R or Python. Some of the datasets which the students may work on include:

1. Student support data during the beginning of COVID-19
2. Migrant support data
3. Weekly mindset data within a classroom during semester
4. Large-scale geographical data from satellites, including (but not limited to) data on desertification in the Sahara region during the recent half-century.