How to arrange a multi-topic academic homepage
My opinion...Perhaps instead of trying to sort the 'topics' or 'content' on the site, you could instead sort by user with a menu bar on the home page. 

Have separate tabs/buttons in the menu linking to separate pages: 1 for "Students"; 1 for "researchers/peers"; and 1 for "prospective employers". 

That way, you can put exactly what you want that particular audience to see (even if some content is the same across audiences) on individual pages. You will have 1 site, with 3 distinct sets of content arranged by topic independently of each other. On each of those 3 pages, there can then be a specific menu or something for the content on that specific page, for that audience, arranged by either a topic, date, tags, whatever.