One option is to listen to white noise or similar (I think brown noise sounds the best). It's unpleasant to have to drown out background noise but it works very well even for discussions nearby. There are various websites and apps that will play brown noise, or you can use speaker-test in Linux.

I used to have a roommate in college who insisted he needed the TV on at all times and wouldn't wear headphones. My pomodoro script that played white noise for 25 minutes was critical for being able to focus in my room that year.