Sidebar image

Research Opportunities for Undergradates



NSF-funded summer computational research in Barnett group

Dear math (or physics or CS or Engs) majors,

I am looking for an excellent student, preferably a junior, to help with research projects in computational mathematics this summer. It will be full time work for the summer term, and there is $4k of NSF funding available. It will involve developing/coding/testing new methods for the numerical solution of PDEs and eigenvalue (resonance) problems such as the Helmholtz equation (which models linear waves) in 2D and 3D, with applications to solar cells, acoustics, quantum mechanics, radar, optical devices, etc. It might turn into a senior thesis, or a publication. There are some analysis directions it could go in too, depending on interest, and would involve some interaction with grad students and postdocs (ie the rest of the group), and training. An ideal student would have solid Matlab or C programming skill (and enjoyment!), have taken Math 22,23, and some from: 26, 46, 63, 76, 50, 53, 116/126; or the NEW upcoming 56 which I teach this spring...

Contact me if interested, with a brief summary of your relevant background.

Advisor: Dr Alex Barnett Rm 206, Kemeny Hall

Minimal surfaces in the rototranslation group

Recently, there has been a great deal of interest in the study of minimal surfaces in a new setting, that of sub-Riemannian geometry. Projects in this area would include extending and developing techniques for the construction of minimal surfaces in the roto-translation group.

More information/requirements

Advisor: Prof. Pauls

Applications of minimal surface theory to the neuroscience of vision

Interest in minimal surfaces in the rototranslation group stem from, in a large part, a new model of the function of the primary visual cortex. Building on work of Patrick Karas '07, we wish to develop perceptual tests and predictions from this model for the purposes of validation and revision.

More information/requirements

Advisor: Prof. Pauls

Minimal surface theory and digital image processing

A new model of the function of primary visual cortex via minimal surface theory provides a new approach to problems in digital image reconstruction. In this project, students would develop and implement (in MATLAB) image disocclusion algorithms based on this model.

More information/requirements

Advisor: Prof. Pauls

[Past projects]