The MIT math department has something pretty much exactly like this, called PuMaGraSS (=Pure Math Grad Student Seminar): https://math.mit.edu/pumagrass/. I co-organized PuMaGraSS one year when I was a PhD student. It has been going on for quite a long time, not sure the complete history. There is also a separate, similar lunch seminar for applied math students, called SPAMS, if I recall correctly.

The MIT math department has something pretty much exactly like this, called PuMaGraSS (=Pure Math Grad Student Seminar): https://math.mit.edu/pumagrass/. I co-organized PuMaGraSS one year when I was a PhD student. It has been going on for quite a long time, not sure the complete history. There is also a separate, similar lunch seminar for applied math students, called SPAMS, if I recall correctly.

EDIT: Here is the SPAMS website: https://math.mit.edu/spams/. I guess since MIT breaks the pure and applied into two seminars it does not exactly match your request, but is pretty close.