The CSS posted above is specifically for the Blogum theme.
I wouldn't really recommend making the header area static... it takes up a ton of space and it seems like it would be annoying on small screens.
For the Twenty Eleven theme, I looked at the demo site as an example http://twentyelevendemo.wordpress.com/ and you could set the header as fixed with this CSS:
#branding {
position: fixed;
background: white;
max-width: 1000px;
}
You'd probably also want to get rid of the gab at the top of the page or the content shows through when you scroll:
#page {
margin: 0em auto;
}