UW-PIMS Mathematics Colloquium: Katherine E. Stange

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 such topics as continued fractions, topographs, hyperbolic geometry, ergodic theory, and even Apollonian circle packings. In particular, I'd like to generalize these classical connections to the case of Gaussian integers and beyond.