You can have a website.

(you could make it beautiful, unlike this one)

That website could link to your publications, if you are clever enough to have some.

Or link to stuff you find interesting.

If all else fails, self-indulgently promote your own blog posts.

You could put some PDFs up online, or some pictures in the same way.
Use it as somewhere to test out your coding skills (as this so very ably demonstrates...).
Or just use it as an online version of your CV. That's a pretty good idea if you can't think of any other way to use it.
The ITS website has more information on using your own webspace.
Or maybe you'd like something completely different.