## On the existence of minimal Heegaard splittings

Dan Ketover

Princeton University; Member, School of Mathematics

October 2, 2018

In the 80s Pitts-Rubinstein conjectured that certain kinds of Heegaard surfaces in three-manifolds can be isotoped to index 1 minimal surfaces. I'll describe in detail a proof of their conjecture and some applications. This is joint work with Liokumovich and Song.