Applied or theoretical math, and what specialty?
If you like applied math verging on engineering, you might check out Varian's industrial products division. This division is growing, and they are having trouble convincing people to relocate from Palo Alto, where I believe most of the R&D is still done. They make coupled-cavity standing-wave particle accelerators for cargo inspection. There is a bit of interesting math in the coupled-cavity tuning which they may not do properly (I used to work for a competitor, where I found we had been slightly mistuning cavities for decades.) There would be more complex math in their image reconstructions, especially if they are doing tomography.
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