Can WordPress do the job?

I have to build a website for a department at a university. The university wants me to use Joomla or otherwise TYPO3, because other department websites are using those. From the first look, I did not like any of those, so I started looking for alternatives. I know Joomla could do the job, but I find it very hard to use if you are new to it and TYPO3 looks just very outdated. My favorite is wordpress.

Here is what I need:
• The website will have static pages, with general information about the department
• each professor needs a page, with information about his work, his classes and his team (research assistants, etc.). That means that somehow I have to assign certain people to a professor, so that they are only displayed on that page (Maybe like a group).
• the professors need to upload files (e.g. lecture slides as pdf) to their own page, that their students can download later. these downloads could have some kind of password protection.
• a professor’s page should be like a profile page, where the professor can edit his own information (with custom fields). the same has to work for his team members. They have to be able to upload own profile pictures. and I have to be able to display these profile pictures anywhere I want (e.g. an page with an overview of the professors)
• I need a people search for the website

I will not be at the university forever, so I need to build a website with a CMS that can be managed and updated easily after I am gone. I am building this website for just one department (7 professors + about 35 people). But if it works, I want to use this for other departments, too.

I looked at WordPress and I think it is great. But can I realize this project with WordPress? Or with WordPress MU + BuddyPress? I just want to convince my superiors that the era of Joomla has ended because there is a much better OpenSoure CMS.