Kaidan's a Sentinel, not an astrophysicist (Damnit, Jim-- wait, wrong character) so I don't think he'll be teaching himself five-space math for fun, but he can probably parse the overarching theories behind them. How they go about detecting the presence of a wormhole would be a big one, especially if they think something similar's brought people here.

Another thing he'd like to get information on would be a primer on Beta Colony -- history, current political outlooks, ties, newsfeeds, gossip rags, that sort of thing. His angle is in trying to get a sense of the culture of another major Nexus player to figure out if Cetaganda exists completely unchallenged in its possession of Barrayar, given that he's unlikely to be able to find information critical of them directly.

On the cultural front, I will definitely hit Ammay up! (Really, I can't blame Gail at all.)