Date/Time: 14 October 2022, 4:30pm ET Location: Millersville University, Wickersham Hall, Room 104 Zoom: https://millersville.zoom.us/j/98919210979 (contact any of the organizers if you need the Zoom Meeting ID or passcode) Speaker: Hannah Schwartz, Princeton University Title: Homotopy 4-spheres from a 5D perspective Abstract: The smooth, generalized Poincaré conjecture -- that all smooth homotopy spheres are diffeomorphic to the standard one -- remains unknown only in dimension four. In this talk, we will examine doubles of homotopy 4-spheres (also homotopy 4-spheres) by viewing these 4-manifolds as boundaries of 5-manifolds. Passing to a 5-dimensional perspective in this context is both practical and useful, since many handlebody calculus issues from dimension four can be avoided with an extra dimension. To convince you of this, I will sketch the proof of an (in-progress) result joint with Naylor and Gabai that certain Gluck twists are standard: in short, because they bound a 5-ball!