- Nathan Vaughn (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 (graduated May 2017, NSF postdoc at MIT) – 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 (graduated May 2018, now a graduate student in Applied Math at Johns Hopkins) – 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 (graduated May 2020) – Behavior of eigenfunctions under spectral flow-type perturbations. Honors Thesis resulted in a joint publication.
- Rebecca Olson (graduated May 2020), Alex McEntarffer (graduated May 2021), Nifu Dan (graduated May 2023), and Zhihao Chen (graduated May 2023) – Markov Chain Monte Carlo simulations on graph models for optical scattering devices.
- Marichi Gupta (graduated December 2021, now a consultant with McKinsey) – Honors Thesis on nodal set crossings in eigenfunctions and their stability under domain deformation. Resulting in a joint publication.
- Stepan Malkov (graduated May 2022, now a grad student at UCLA) – Honors Thesis on existence of stationary states in Dirac models motivated by topological physics lattice models.
- Laura Hinson (graduated May 2022, now headed to Law School at UVA) – Reading on spectral flows and numerically computing nodal deficiency of eigenfunctions on the disk.
- Xiangyu Zeng (graduated May 2023, co-advised with Nicolas Fraiman) – Properties of spectral clustering algorithms and their application on genetic data sets
- Zhihao Chen (graduated May 2023, co-advised with Jingfang Huang) – Properties of volume and boundary layer potential integrals near the boundary of a domain
- Joseph Stellman (expected graduation May 2025) – Transmission/Reflection coefficients for truncated periodic potentials
- Andrew Sun (expected graduation May 2024 from Duke, co-advised with Jonathan Mattingly and Greg Herschlag) – Mixing and spectral analysis of transition state models with applications in quantifying Gerrymandering
- Maddy Vinal (expected graduation May 2025, co-advised with Shahar Kovalsky and Caroline Moosmueller) – Optimal transport on graphs with alternative metrics and applications to biological data sets
- Henry Woodbury (expected graduation May 2025, co-advised with Maddie Brown) – Behavior of low energy eigenfunctions under boundary deformations in the setting of Neumann boundary conditions
- Abel Abraham (expected graduation May 2024, advised by Pedro Saenz and Jian Wang) – Bouncing droplets with bottom topography
- Matt Harris (Master’s student, graduated 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 Institute for Defense Analyses) – 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, now an Analyst at Ramirez Asset Management) – Potential perturbations of non-self-adjoint problems related to stability theory and NLS dynamics with potentials.
- Wesley Hamilton (Ph.D. student, graduated May 2021, now at MathWorks) – Data analysis and spectral properties of graph Laplacians.
- Grace Conte (Ph.D. student, graduated August 2022, now at Johns Hopkins APL) – Adjoint continuation on quantum graphs.
- Gary Moon (Ph.D. student, graduated May 2022, now a postdoc at University of Oklahoma) – Well-posedness for vortex sheet water wave models in the presence of geometry, stabilization/control of water waves, numerical algorithms for water waves.
- Ben Trigsted (Master’s student, graduated May 2022, now with Keyrus Consulting) – Large data well-posedness and singularity formation in degenerate diffusion models in material science.
- Andrew Lyons (Ph.D. student, expected graduation 2025) – Properties of nodal sets and nodal domains under perturbation
- Tim Van Hoose (Ph.D. student, expected graduation 2027) – Nonlinear bound states and stochastic partial differential equations
Research Playground Endeavors through UNC PDE RTG:
- Corbin Balitactac, Ben Bechtold, and Jeremy Wall (RTG Research Playground Researchers, co-mentored with Casey Rodriguez) – Spectral stability and local well-posedness of Cosserat Rods near steady stationary states
- 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
- Jian Wang – (Current, Mentored by Hans Christianson) – Damped fractional wave equations and applications to water waves
- James Rowan – (Current) – Nonlinear bound states in water waves and continuum mechanics
- Dan Weser – (Current, Mentored by Arunima Bhattacharya) – Regularity of level sets for optimizers of sub-domain detection algorithms
- Emmanuel Fleurantin (Current, NSF postdoc at George Mason with Chris Jones) – Gap eigenvalues for the linearized Schrödinger operator in 3d