Exotic boundary Dehn twists after two stabilizations

Any reasonable exotic phenomena in simply connected 4-manifolds are unstable. It is an open question if there is a universal upper bound to the number of stabilizations needed. The case of 1 stabilization was proven in works of Lin and Guth-K., but whether we need more than two stabilizations has been open because it is significantly harder. In this talk, we discuss my recent proof with Park and Taniguchi that two stabilizations are indeed not enough for exotic diffeomorphisms.