Multiscale refinement subdivision are methods for taking coarsely sampled data and recursively creating very finely sampled data consistent with the coarse-scale data. They arise in intriguing ways from wavelet and pyramid algorithms in signal and image processing, from geometric modelling problems in computer aided design and manufacturing, from processing of surface data gathered by 3D scanners and, more recently, from a variety of emerging geometric representation problems which involve data taking values in nonlinear manifolds.

Subdivision algorithms typically look quite simple, but their simplicity is deceptive -- more often than not it is highly nontrivial to understand their properties. The speaker will discuss a number of recent results and some of the breakthrough results from the past 20 years or so, and discuss many challenging analysis problems that remain.