The APDE seminar on Monday, 4/3, will be given by Jared Wunsch (Northwestern) in-person in Evans 732, 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: Wave propagation on rotating cosmic string backgrounds

Abstract: A rotating cosmic string spacetime has a singularity along a timelike curve corresponding to a one-dimensional source of angular momentum. Such spacetimes are not globally hyperbolic: there exist closed timelike curves near the “string”. Nonetheless, I will describe joint work with Katrina Morgan in which we explore the possibility of obtaining forward solutions to the wave equation, appropriately interpreted.

The APDE seminar on Tuesday, 4/4 (Special Time and Location), will be given by Sergiu Klainerman in-person in Evans 740, and will also be broadcasted online via Zoom from 3:40pm to 4:40pm PST. To participate, email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu).

Title: Nonlinear global stability of Kerr black holes with small angular momentum

Abstract: I will be talking about recent results which settle the stability conjecture of Kerr black holes in the case of small angular momentum.

The APDE seminar on Monday, 3/20, will be given by Federico Pasqualotto (UC Berkeley) in-person in Evans 732, 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: Singularity formation in the Boussinesq equations

Abstract: In this talk, I will first review existing results on singularity formation in incompressible and inviscid fluids. I will then describe a new mechanism for singularity formation in the Boussinesq equations. The initial data we choose is smooth except at one point, where it has Hölder continuous first derivatives. Moreover, the singularity mechanism is connected to the classical Rayleigh–Bénard instability. This is joint work with Tarek Elgindi (Duke University).

The APDE seminar on Monday, 3/13, will be given by Theo Drivas (Stony Brook) 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: Irreversible phenomena in 2D perfect fluids

Abstract: We discuss a number of results that reveal a form of irreversibility in the two-dimensional Euler equations governing the motion of an incompressible and inviscid (perfect) fluid. Specifically, we establish results on aging, wandering, and filamentation in perfect fluids. The main tool in establishing these results is an all-time stability of twisting result for 2d Hamiltonian flows, which allows us to deduce infinite-time results in settings where only static bounds are available.