Kleinian groups: history and recent results

Kleinian groups, first studied by Felix Klein and Henri Poincaré in the late 19th century, are discrete groups of isometries of hyperbolic 3-space. Since then, they’ve become central objects in mathematics, with deep connections to fields including number theory, complex analysis, and geometric topology. In this talk, I’ll share some of the historical development of Kleinian groups and aim to give a sense of what they are and why they matter. Along the way, I’ll highlight some examples and explain how these groups arise naturally in geometry and low-dimensional topology. I'll finish with more recent results and share connections to problems I worked on during my sabbatical in Australia and New Zealand.