The APDE seminar on Monday, 3/3, will be given by Gustav Holzegel (University of Münster) in-person in Evans 736, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Sung-Jin Oh (sjoh@math.berkeley.edu).

Title: Quasi-linear wave equations on black hole backgrounds

Abstract: After a brief introduction to the geometric features of black holes, I will discuss recent joint work with Dafermos, Rodnianski and Taylor introducing a new scheme to prove small data global existence results for quasilinear wave equations on sub-extremal Kerr black hole backgrounds. In the slowly rotating case (see arXiv:2212.14093), a key ingredient is a new purely physical, highly degenerate, spacetime estimate at the top order which avoids understanding the detailed structure of trapped geodesics. In the full sub-extremal case (see arXiv:2410.03639) this estimate needs to be tailored to a finite number of wave packets defined by an appropriate frequency decomposition in the azimuthal and stationary frequencies. The relation to the stability problem for black holes will also be discussed.