[yaantc]

You may consider the electronic design automation (EDA) industry. Basically, the tools used to design the ASIC we love.

The industry anticipates a job crisis, with elder people retiring, a shortage a new entrants (not see as sexy) and still a strong need. There's been initiatives around to bring more new blood in. A math PhD with an interest in optimization looks like a good fit.

There aren't so many employers (Cadence, Synopsys an Siemens/Mentor are the 3 bigs), but the domain is extremely technical with an history of pushing the envelope. SAT solving for example has progressed a lot thanks to EDA, and we not benefit from it in software with its SMT extension.

[ginnungagap]

This does sound very interesting! There was a chip design course during my masters that I always regretted not taking because it overlapped with something else