- Nathan Vaughn (Undergrad Researcher, graduated May 2015, currently a graduate student at University of Michigan) – Bifurcations in Thin-Film Traveling Waves – Resulting in Publication “A numerical study of traveling waves for a model of thin films in cylindrical domains”
- Anya Katsevich (Undergrad Researcher, graduated May 2017, currently a graduate student at the Courant Institute) – Honors Thesis on “The hydrodynamic limit of a crystal surface jump diffusion with Metropolis-type rates”
Metropolis rates in crystal evolution problems and spin systems, coarse graining, numerics and convergence. Results now partially contained in this publication.
- Alan Luner (Undergrad Researcher, graduated May 2018) – Working on using Finite Element solvers to understand properties of fluid flow in different geometries and to construct nonlinear solutions to problems related to Density Functional Theory.
- Isabel Bors (Undergrad Researcher, graduated May 2020) – Behavior of eigenfunctions under spectral flow-type perturbations. Honors Thesis resulted in a joint publication.
- Rebecca Olson (Graduated May 2020) and Alex McEntarffer (expected graduation May 2021) – Markov Chain Monte Carlo simulations on graph models for optical scattering devices.
- Marichi Gupta (expected graduation December 2021) – Honors Thesis on nodal set crossings in eigenfunctions and their stability under domain deformation.
- Matt Harris (Master’s Degree Awarded May 2013, currently a consultant at Deloitte) – Master’s Thesis on “Numerically Computing Bound States” – Note, techniques are all correct and applicable, but the geometric potential in H^2 takes an attractive character in the simulations and it should take a repulsive character, which leads an incorrect prediction in that case as explained clearly in recent work with Borthwick, Donninger and Lenzmann.
- David Webb (Ph.D. student, Graduated August 2017, now an instructor at Shorter University) – “Nonlinear Dirac Equations”
- Quentin Robinson (Ph.D. student, Graduated August 2018, now at North Carolina Central University) – Periodic Capillary Waves in Fluids, Forced KdV models, Experiments and Full Euler simulation “Surface Disturbances Generated by Fluid Flow Past an Obstacle or Over Topography as Predicted by the Korteweg-De Vries and the Euler Equations”
- Yuan Gao (Ph.D. student, Graduated May 2019, co-advised with Katie Newhall, now at Wells Fargo) – Metropolis dynamics of random spin systems. “Metropolis dynamics of random spin systems”
- Sterling Swygert (Ph.D. student, Graduated May 2019, now at Pearson) – “Analysis of Thin Films Related to Flows in Cylindrical Geometries”
- Dmitro Golovanich (Ph.D. student, Graduated May 2021) – Potential perturbations of non-self-adjoint problems related to stability theory and NLS dynamics with potentials.
- Wesley Hamilton (Ph.D. student, Graduated May 2021) – Data analysis and spectral properties of graph Laplacians.
- Grace Conte (Ph.D. student, expected graduation May 2021) – Adjoint continuation on quantum graphs.
- Gary Moon (Ph.D. student, expected graduation May 2022) – Well-posedness for vortex sheet water wave models in the presence of geometry, stabilization/control of water waves, numerical algorithms for water waves.
- Graham Cox – (Funded by Chris Jones, now at Memorial University in Newfoundland) Maslov Index in high dimensional PDE, Dirichlet-to-Neumann maps.
- Tom Beck (Now at Fordham University) – Properties of low energy eigenfunctions.
- Zach Boyd – (Funded by Peter Mucha, now at BYU) Graph Theory, Spectral Clustering, Markov Chains