Can I use an arbitrary webpage for my domain?

Not really, for a domain completely your own you need to set up apache or something simmilar on your own computer, and register a your static IP with a DNS service, then the DNS service that you pay for routes traffic going to yourdomain.com to that IP.

I think domain masking is what you want. The best part is the URL always shows as “mydomain”. Visitors do not know they are being shunted around.

But I haven’t tried it with an outside domain, so I’m not positive this is your solution. I do it with a couple of sites, but they are all hosted on the same machine.

GoDaddy – Forwarding or Masking Your Domain Name

@XOIIO I definitely don’t want to host it myself, but that shouldn’t have to be required.

@jaytkay That looks exactly like what I was looking for. Unfortunately, my domain name provider doesn’t seem to support it. Guess I’ll have to look for a different solution (a different host or domain name provider). Thanks anyway.

Yes, this is possible to do. It may or may not be easy depending on the way your webhost (the university service) is set up. You should be asking them about this, not us; for example, they can tell you whether or not your web-space has its own IP address. Probably they have had this exact question before from others.

Not really, I don’t think it has its own IP address. It’s not a university-wide service, just something implemented by a department of my faculty, and probably just in place because one of the students who works there thought it’d be cool.

The fact remains that the person who runs the web server is the one you need to talk to about this. Ask them to set you up a “virtual host” in Apache (I’m assuming that Apache is the web server they use, as it’s the most popular and arguably the best available. If they aren’t using it, point and laugh for me, will you?).
Setting up a vhost is pretty simple. It’s a matter of adding a few lines to a configuration file and reloading (or doing a graceful restart). The person who does it will need to know your domain name and the path to your webpage on the server.

Yeah, but since it’s mostly a side-project of someone I don’t really know and who is on holiday now, that’s not really an option, unfortunately :)