The HADES seminar on Tuesday, September 17th, will be at 2:00pm in Room 740.

Speaker: Zhongkai Tao

Abstract: Let be a probability measure on . The Fourier transform of the measure, defined by has been very useful in dynamical systems. A central question is the Fourier decay, that is, the uniform decay rate of . This was studied by Erdős and Salem almost a century ago. While polynomial Fourier decay, i.e.  for some , is expected in many situations, it is only recently that people can prove polynomial Fourier decay for nontrivial measures coming from dynamical systems, c.f. the works of Bourgain, Dyatlov, Li, Sahlsten, Shmerkin, Orponen, de Saxcé, Khalil, Baker, Algom, Rodriguez Hertz, Wang, etc. I will try to explain the key ideas in some recent developments: sum-product estimates, additive combinatorics and the use of dynamical systems.

The HADES seminar on Tuesday, September 10th, will be at 2:00pm in Room 740.

Speaker: Katie Marsden

Abstract: This talk will concern the three dimensional half-wave maps equation (HWM), a nonlocal geometric equation with close links to the better-known wave maps equation. In high dimensions, n≥4, HWM is known to admit global solutions for suitably small initial data. The extension of these results to three dimensions presents significant new difficulties due to the loss of a key Strichartz estimate. In this talk I will introduce the half-wave maps equation and discuss a global wellposedness result for the three dimensional problem under an additional assumption of angular regularity on the initial data. The proof combines techniques from the study of wave maps with new microlocal arguments involving commuting vector fields and improved Strichartz estimates.

The HADES seminar on Wednesday, 4 September, will be at 3:30pm in Evans 736. (Note the unusual space and time)

Speaker: Jingbo Wan (Columbia)

Abstract: We establish boundedness and polynomial decay results for the Teukolsky system in the exterior spacetime of slowly rotating and strongly charged sub-extremal Kerr-Newman black holes, with a focus on axially symmetric solutions. The key step is deriving a physical-space Morawetz estimate for the associated generalized Regge-Wheeler system, without relying on spherical harmonic decomposition. The estimate is potentially useful for linear stability of Kerr-Newman under axisymmetric perturbation and nonlinear stability of Reissner-Nordstrom without any symmetric assumptions. This is based on a joint work with Elena Giorgi.