The APDE seminar on Monday, 11/27, will be given by Rita Teixeira da Costa (Princeton) in-person in Evans 736, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu).

Title: The Teukolsky equation on Kerr in the full subextremal range |a|<M

Abstract: The Teukolsky equation is one of the fundamental equations governing linear gravitational perturbations of the Kerr black hole family as solutions to the vacuum Einstein equations. We show that solutions arising from suitably regular initial data remain uniformly bounded in the energy space without derivative loss, and satisfy a suitable “integrated local energy decay” statement. A corollary of our work is that such solutions in fact decay inverse polynomially in time. Our proof holds for the entire subextremal range of Kerr black hole parameters, |a|<M. This is joint work with Yakov Shlapentokh-​Rothman (Toronto).

The APDE seminar on Monday, 11/13, will be given by Thierry Laurens (UW Madison) in-person in Evans 736, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu).

Title: Sharp well-posedness for the Benjamin–Ono equation

Abstract: We will discuss a sharp well-posedness result for the Benjamin–Ono equation in the class of H^s spaces, on both the line and the circle.  This result was previously unknown on the line, while on the circle it was obtained recently by Gérard, Kappeler, and Topalov.  Our proof features a number of developments in the integrable structure of this system, which also yield many important dividends beyond well-posedness.  This is based on joint work with Rowan Killip and Monica Visan.

The APDE seminar on Monday, 11/06, will be given by Mihaela Ifrim (UW Madison) in-person in Evans 736, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu).

Title: The small data global well-posedness conjecture for 1D defocusing dispersive flows

Abstract: I will present a very recent conjecture which broadly asserts that small data should yield global solutions for  1D defocusing dispersive flows with cubic nonlinearities, in both semilinear and quasilinear settings. This conjecture was recently proved in several settings in joint work with Daniel Tataru.