Use mod_rewrite in your .htaccess file:
RewriteEngine on
RewriteOptions MaxRedirects=1
RewriteCond %{REQUEST_FILENAME} -f [NC,OR]
RewriteCond %{REQUEST_FILENAME} -d [NC]
RewriteRule .* - [L]
RewriteRule ^(.*)$ /foo.php/$1 [QSA,L]
Where foo.php is your script for showing the quick url pages.
Then in foo.php (or whatever you named it) you can catch the username in $_SERVER['PATH_INFO']
.
The first 5 lines turn on mod_rewrite and allow actual files/folders/scripts to be ignored by the rewrite rule. The last one rewrites all the urls that aren't fines/folders/scripts.