Within Teamwork.com, you can filter the projects assigned to a particular person.
Go to the People section of your site and select the relevant user to view their profile. While viewing their profile, go to the Projects tab.

To access the advanced filters panel, click the filters button in the top right.

Here you can choose filters such as project, tag, category and more. You also have extra check boxes to show only starred projects, hide projects that you are an observer, show only projects you are a memebe of and include archived projects.
Keyword Search
You can use the search bar to filter your results down to the search term entered.

Note: Saved filters are available on paid Teamwork.com subscriptions.
For more information, see: Filtering