I had a flyout at an academic place and they said “keep us informed about updates on your market “
I have an exploding industry offer. will the university care about that? As in, would they expedite their timeline?
They will care if they believe you'll accept it. Maybe it's not something with which you can bargain for a higher salary, but it may be something that leads them to speed up their process.
Thanks. I wouldn't bargain salary, but I would take the industry offer rather than be left without a job (the hypothetical third best option is discretely much worse than either)
“To be transparent with you, I have an offer from XXXX. Let me say that my main goal is to land an academic position.“
It's impossible to know if they will expedite the process, but you will certainly show interest and transparency. If you like them, they will expedite a bit.