7 years ago I started the StReeTs (Student Research Talks) series at George Mason University.
It is for graduate students and run by graduate students (although I personally ran it for the first few years to get things going). All subject areas are appropriate.
The seminar runs about twice a month. There generally is pizza and drinks (the department pays). Faculty generally do not attend (this is by design so students are not intimidated and are comfortable asking questions).
Talks are usually about 50 minutes with some time for questions at the end (there have been exceptions though; both longer and shorter talks).
Here is the website: https://streets-gmu.wikidot.com/
COVID has shaken the regularity, but it is still running.
Speakers mostly talk about their thesis work, but sometimes they talk about things they are learning about they find interesting that is not covered in foundational course work, and sometimes they bring in graduate students from local universities (our department reimburses local travel in those cases).
Our department is very friendly overall, and I think that students pick up on that, and so our seminars are pretty friendly too. This one is no exception.
One last thing, we also have the Mason Experimental Geometry Lab (MEGL) which is a community of vertically integrated research teams conducting research explorations and community engagement activities. We have, in the past, had collaborations between StReeTs and MEGL.