I'm on my last semester of a math B.Sc. and about to start studying for a math M.Sc in the same institute. It now seems like a good time to start thinking of a PhD.

I'm interested in both algebra and algorithms. So I read a little in some computational algebra books (comp. group theory to be precise) and it looks like a great choice for me.

My questions:

1. Is this a "hot topic" in mathematics? Are there many serious people researching it?
2. Where are the major places in the world to research comp. algebra and to get a PhD?

Thank you!