Mar Gavriel tells us:
Most of the world is observing Yom Ha’Atzma’ut on Tuesday, because Yom HaZikaron is the day before Yom Ha’Atzma’ut and when Yom HaZikaron is due to be on a Sunday we push the whole lot up a day – Yom HaZikaron on Monday and Yom Ha’Atzma’ut on Tuesday – so as not to encourage people to drive to the memorials when it is still Shabbat.
Consideration 1: According to Rav Hershel Schachter (top bod at Yeshiva University), halakhic Yom Ha’Atzma’ut can never fall on any date other than 5 Iyyar, because that is the actual date on which the miraculous event occurred. So no pushing it off to Tuesday – if 5 Iyyar is a Monday, Yom Ha’Atzma’ut is a Monday, end of story.
So — on Monday, the main YU Beis Medresh minyan recited Selichot AND Hallel. Not something one generally sees.