So here's the dilemma: I'm a pure math guy who's mostly interested in theoretical computer science, but also partly interested in theoretical machine learning. I've been accepted with similar funding yada yada to both UCLA and UC Irvine's CS PhD programs. The professor at UC Irvine more so matches my interests (graph theory, approximation algorithms, pure math-y stuff) and he's also highly distinguished, coming off a 15 year stint doing theory at Georgia Tech. The professor at UCLA is more engineering focused.
There's a few questions I need answers to influencing my decision:
How important is the prestige of a university compared to the prestige of one's research advisor when it comes to securing faculty positions?
How easy is it at UCLA (or in general) to either co-advise with another department (theory) or switch entirely, and would this affect funding offers?
Any advice would be greatly appreciated!