## The Simplicity Conjecture

Dan Cristofaro-Gardiner

Member, School of Mathematics

April 3, 2020

I will explain recent joint work proving that the group of compactly supported area preserving homeomorphisms of the two-disc is not a simple group; this answers the ”Simplicity Conjecture” in the affirmative. Our proof uses new spectral invariants, defined via periodic Floer homology, that I will introduce: these recover the Calabi invariant of monotone twists.