Topic: Catastrophe Theory

Accurate waveforms for a small black hole entering a much larger one remain difficult near merger. This talk presents a staged treatment of the first-order merger and ringdown that can isolate nonlinear contributions for later corrections. It also analyses the transition to plunge in rotating backgrounds, where catastrophe theory explains why equatorial and inclined trajectories share the same Painlevé equation. Together these approaches expose structure useful for extending self-force calculations.

Fate decisions in developing tissues involve cells transitioning between a set of discrete cell states. Geometric models, often referred to as Waddington landscapes, are an appealing way to describe differentiation dynamics and developmental decisions. We consider the differentiation of neural and mesodermal cells from pluripotent mouse embryonic stem cells exposed to different combinations and durations of signalling factors. We developed a principled statistical approach using flow cytometry data to quantify differentiating cell states. Then, using a framework based on Catastrophe Theory and