Research in Differential Equations and Applied Mathematics

I have multiple undergraduate research projects that involve various aspects of analysis of differential equations, math modeling and scientific computation . Here are some example projects, but I am open to discussion about related projects based upon student interests:

1. Properties of eigenvalues and eigenfunctions in graphs and domains. Related undergraduate projects have resulted in the publications:
– https://arxiv.org/abs/2204.12009
– https://arxiv.org/abs/2006.13839

2. Properties of edge states in topological physics. Related projects with good follow-ups for undergrads are:
– https://arxiv.org/abs/2006.07762
– https://arxiv.org/abs/1904.10312
– https://arxiv.org/abs/1802.06812

3. Domain and graph partitioning. Related projects with good components for undergraduates are:
– https://arxiv.org/abs/2006.14482
– https://arxiv.org/abs/2201.00773

4. Analysis of nonlinear states and dynamics in models from quantum mechanics, material science and fluids. Related projects with good components for undergraduates are:
– https://arxiv.org/abs/2108.01786
– https://arxiv.org/abs/2003.07236
– https://arxiv.org/abs/1902.08685