Vorträge in der Woche 03.11.2025 bis 09.11.2025

Donnerstag, 06.11.2025: The Conformal Method and Hamiltonian General Relativity

David Maxwell (Fairbanks, Alaska)

The conformal method is a workhorse tool for building solutions of the Einstein constraint equations, especially those with constant mean curvature. One frequent perspective on the technique is that it is simply a handy tool, a frequently effective mathematical artifice. In this talk we demonstrate instead that the conformal method is deeply rooted in the Hamiltonian approach to general relativity. We start with a careful analysis of the Gauss constraint $\mathrm{div} E = \rho$ of electromagnetism and describe an approach, grounded in Hamiltonian field theory, for generating its solutions. Then, after an unexpected detour into temporal wave gauge in general relativity, we exhibit a modern understanding of conformal method as an immediate generalization of the toy-model approach to the Gauss constraint. If time permits, we discuss how these ideas led to recent advances in formulating the conformal method in the non-vacuum setting, with applications to charged fluids.