M-theory singularities: Going beyond Dynkin diagrams

<!--HTML-->M-theory on an ADE singularity gives rise to an ADE gauge theory at low energies. However, the “T-brane” phenomenon completely shatters this picture, and reveals that simply resolving singularities, and uncovering a Dynkin diagram is insufficient to understand what’s really going on. I will demonstrate how exploiting 3d mirror symmetry sheds light on T-branes, and gives us a new definition of the phenomenon for all ADE algebras. For the E-series, we will see how non-Lagrangian theories actually simplify the problem.