Gabe Flanagin

Developing reaction–diffusion models for infectious disease spread in wildlife populations with terrain-influenced movement, in collaboration with graduate student Alex Escoto. Current work investigates computational methods for domains with complex topography and heterogeneous land cover, as well as control strategies for limiting disease spread, including culling, vaccination, and predator introduction.

Investigating boundary integral methods for elliptic interface problems under the supervision of Zhen Chao, with applications to electrostatic models and PDEs on complex geometries. Current work focuses on numerical implementation, validation, and analysis of interface formulations.

First-author study using density functional theory to investigate the structural and electronic properties of I–V–VI₂ chalcogenide semiconductors. Develops a novel model relating local bonding motifs and electronic properties to the global geometric structure arising from different cation orderings.

Gave an introduction to reaction-diffusion based models used to study the spatial spread of infectious diseases in wildlife. Also introduced and numerically solved optimal control problems trying to minimize the spread of such diseases. Currently working with collaborator to submit novel results which generalize these models to complex domains with terrain that influences animal movement.

Studied and implemented a max-plus algebra based algorithm for approximating solutions to Hamilton–Jacobi–Bellman equations. Proved the method is applicable to a broader class of functions than previously shown and generalized semiconvexity results underlying the approach.