Change archive layout

Yes, you can do this. The layout (the output of the shortcode) is controlled by template.wppa_publication_list.php in the /includes directory. What you do is copy this file into your active theme, then edit your copy as much as you want to.

The template file is heavily documented, so you can see what variables are set and what markup is being used. Just remember, do not edit the copy in the plugin folder as any updates will overwrite your changes. Copy the file into your theme first, then edit the copy there. The plugin will automatically detect the new file in the theme and load it instead.