Only giving this very minor and not-useful feedback because you say "The Stack Overflow" for and I make Stack Overflow's mobile apps:

This app is a good idea. It'd look a lot more professional and believable if it had some minor changes like "Don't have the selected tab's text color be black on navy blue", or "give your list items consistent margin and padding".

Both of these minor suggestions, and more, are also listed in the Material Design guidelines: https://developer.android.com/design/index.html