Katherine E. Stange

Primitive integral Apollonian circle packings are fractal arrangements of tangent circles with integer curvatures. The curvatures form an orbit of a 'thin group,' a subgroup of an arithmetic group having infinite index in its Zariski closure. The...

I will begin with the familiar Farey sequences: the subdivisions of the real line obtained by recursively taking the mediant (a+c)/(b+d) of fractions a/b and c/d. I will take this starting point as an excuse for an ecclectic tour which may include...