Wordpress / Change Most Recent Posts by Category using an Ajax Call

We have a website - [login to view URL] In the right column, you can see Most Recent Videos - this is "Most Recent Posts" essentially. I'd like to have it set up so a User can click a category (see attached image) or pick a category via a Drop Down Menu and when they pick a new category, the <div> that contains the Most Recent posts will update with the posts from that category, WITHOUT doing an entire page refresh. I have attached a screenshot of how I'd like it. If you know of a plugin that can do this and you just have to modify it, that's fine - makes it easier for all of us.