Every summer, many of our students participate in various summer research programs. Students work as full participants in the processes of creating a research plan, executing a research project, and preparing results for presentation in a public forum. Learn more about the research done by your fellow mathematics and statistics students.
This week's panelists include:
- Owen Brown '27 did summer research at the Summer@ICERM 2026 program focused on DNA graph theoretical modeling of DNA self-assembly. Self-assembly is the process where a set of components combine to form an organized structure without external direction or energy input. Double stranded DNA molecules have unique properties that make them a useful material for the self-assembly of nanostructures. These nanostructures can be modeled with discrete graphs, turning DNA self-assembly into an interesting mathematical puzzle. These nanostructures have wide-ranging applications, such as containers for the transport and release of nano-cargos, templates for the controlled growth of nano-objects, and in drug-delivery methods. His research this summer explored several graph families, utilizing graph theoretical and combinatorial properties of DNA self-assembly to optimize the nanostructure construction for laboratories. This presentation will explain the graph theoretical model for DNA self-assembly and feature an example that Owen worked on this summer, Kayak Paddle Graphs.
- Quang Doan '28 - Worked with Prof. Gee as part of this year's Summer Science Scholars. This project explores optimal path planning for an undetected survivor in a zombie apocalypse who must reach a safe zone within a set deadline. He developed a path planning model in which local slope determines the survivor's speed, while terrain type and zombie density determine the cost of movement. Because the zombies diffuse randomly, their density is modeled by the 2D diffusion equation (PDE). With the solution to the PDE, he then derived a time-dependent Hamilton-Jacobi-Bellman (HJB) equation and solve it numerically backward in time. He tested the model on real elevation and terrain data from Gambier, OH, using an initial zombie population inspired by Kenyon College student activity patterns. Evaluating the model under different deadlines generates distinct optimal evacuation paths. Specifically, shortening the deadline generates a path approaching the time-optimal trajectory, whereas increasing the deadline makes the solution converge to the safest path. Overall, when the deadline is long enough, he predicted it is optimal to take a slower path that avoids high-density zombie regions at the expense of time.
Join us on Monday, Sept. 14, at 3:10 pm in Hayes Hall 109 to hear these exciting presentations and perhaps learn how you too can get involved in summer research programs. We hope to see you there!