Slides

Here are slides from some of my previous talks.

Title and link to .pdf	Description
Geometric Methods in Hyperbolic PDEs	This is a brief overview of some of my recent work on global stability problems for various hyperbolic PDEs. The talk focuses on the role that geometry plays in the analysis.
The Stability of the Euler-Einstein System with a Positive Cosmological Constant	This is an extension of the results addressed in the next talk. The new result is the elimination of the assumption that the fluid is irrotational.
The Stability of the Irrotational Euler-Einstein System with a Positive Cosmological Constant	This talk concerns joint work with Igor Rodnianski. We showed that a well-known family of FLRW family of solutions to the Euler-Einstein system is globally future-stable when the cosmological constant is positive, when the speed of sound verifies certain assumptions, and when the fluid is irrotational. The FLRW solutions lie at the heart of some of the most fundamental predictions of cosmology.
The Global Stability of the Minkowski Spacetime Solution to the Einstein-Nonlinear Electromagnetic System in Wave Coordinates	This talk concerns a global stability result for the trivial solution to the coupled Einstein-nonlinear electromagnetic system in 1 + 3 dimensions. The result is an extension of the well-known Christodoulou-Klainerman proof of the stability of Minkowski spacetime. As in the next talk, the nonlinear electromagnetic matter models are interesting because of their connection to the electromagnetic divergence problem.
The Nonlinear Stability of the Maxwell-Born-Infeld System	This talk addresses a global stability result for the 0 solution to the Maxwell-Born-Infeld system of electrodynamics, which is a nonlinear version of Maxwell's equations. This system plays a role in physicists' efforts to fix the electromagnetic divergence problem. This problem is the disappointing fact that the motion of an electron due to its own self-influence is ill-defined in standard Maxwell theory.