This is the website of our weekly Hyperbolic & Dispersive PDE Seminar at Rutgers University. Welcome!
The topics covered by the seminar are very broad and also include, among others: General Relativity, Fluid Mechanics, Harmonic Analysis, Quantum Mechanics, Spectral Theory and Applied Mathematics, always with a strong emphasis on Analysis.
The seminar in Spring 2024 takes place at 3:50 pm on Thursdays in Hill 705.
Speaker: Sam Collingbourne Columbia University
Title: Uniform Boundedness for Linearised Gravity on Schwarzschild from the Canonical Energy
Abstract: In this talk, I will discuss a robust method for producing a conservation law for linearised gravity on a stationary spacetime: the canonical energy. Whilst its coercivity properties are obscure, I will argue that it can be used to obtain a uniform boundedness result for the gauge invariant Teukolsky variables on Schwarzschild. Remarkably, this does not rely on the (decoupled) Teukolsky equation itself or the transformation theory associated to it. Time permitting I will discuss how this makes it a good candidate method for exploring higher dimensional spacetimes where the decoupling and transformation theory fails. This work is joint with Gustav Holzegel.
Speaker: Hans Ringstrom KTH
Title: A quiescent regime for big bang formation
Abstract: Recently, many results concerning stable big bang formation have appeared. Most of the results concern stability of spatially homogeneous and isotropic solutions. However, a recent result of Fournodavlos, Rodnianski and Speck (FRS) covers the full regime in which stability is to be expected. On the other hand, it is restricted to the stability of spatially homogeneous and spatially flat solutions. In this talk, I will present a new result (joint work with Hans Oude Groeniger and Oliver Petersen) in which we identify a general condition on initial data ensuring big bang formation. The solutions need, in this case, not be close to symmetric background solutions. Moreover, the result reproduces previous results in the Einstein-scalar field and Einstein-vacuum settings. Finally, the result is in the Einstein-non-linear scalar field setting, and therefore yields future and past global non-linear stability of large classes of spatially locally homogeneous solutions.
Speaker: Lili He Princeton University
Speaker: Tristan Leger Princeton University
Speaker: Jonathan Luk Stanford University
Speaker: Michael Weinstein Columbia University