Topological Data Analysis (TDA) is a mathematical method used to study and quantify the structure of complex systems. This year's capstone projects focus on two applications of TDA: fluid flow and mixing through porous media, and the movement of T-cells in the immune system. For porous media, we analyze 3D images to understand how the internal structure of the material influences fluid mixing, which is important for processes such as groundwater filtration and environmental cleanup. For T-cells, we use computational simulations to investigate how cell movement and interactions affect immune response. In both projects, we use persistent homology, a technique from TDA, to identify topological features and explore their relationships with the physical behavior of these systems. For more details, see the poster and group reports below.
