The question whether a singularity is removable by coordinate transformation has been of central importance in General Relativity since Schwarzschild's discovery of black hole solution in 1916. However, beyond ad-hoc coordinate constructions, General Relativity lacks a unifying theory for identifying when singularities are removable, and it lacks a general procedure for removing them.

B. Temple and I recently discovered a system of elliptic partial differential equations, the RT-equations, which provides a definitive theory for identifying and removing singularities above a threshold regularity, (including cusp and shock wave singularities in GR, but not yet those at black hole horizons). That is, based on the RT-equations, we developed a necessary and sufficient condition for when a singularity in an affine connection (the basic object of a geometry) in $L^p$ is removable by coordinate transformation, together with a computable procedure for removing the singularity by regularizing the connection all the way up to its essential (highest possible) regularity.

More generally, the RT-equations apply to singular connections on vector bundles of Yang-Mills gauge theories, and imply that connections with $L^p$ curvature can always be regularized to one derivative above $L^p$; based on this, we gave the first extension of Uhlenbeck compactness from Riemannian to Lorentzian geometry.

Bio: Moritz Reintjes received a Ph.D. from the University of California in Davis, a Master degree (Diplom) from the University of Regensburg in Germany (where he grew up) and a B.Sc. (Honours) from the University of Cape Town. He held post-doctoral positions at the University of Regensburg (2011-2012), the Max Planck Institute for Gravitational Physics (2012), the University of Michigan - Ann Arbor (2013), the Instituto de Matematica Pura e Aplicada in Rio de Janeiro (2013-2016), the Instituto Superior Tecnico in Lisbon (2017 - 2018) and the University of Konstanz (2019 - 2021). He joined the City University of Hong Kong as an Assistant Professor in 2021. In 2025 he was awarded the Hong Kong Mathematical Society Young Scholars Award for his contributions to the discovery and analysis of the RT-equations.