Ian Morris is in Canada this week (19-23 January) attending and speaking at the BANFF International Mathematics Research Centre in the Canadian mountains just west of Calgary.  The conference is on “Random Dynamical Systems and Multiplicative Ergodic Theorems“.  On Thursday Ian spoke on “The transfer operator for the binary Euclidean algorithm“.  The video of his talk is here.  A abstract of the talk follows: statistical properties of the classical Euclidean algorithm — such as the average number of steps required to process a pair of integers both of which are less than N — can be studied via the thermodynamic formalism of the Gauss map acting on the unit interval. To investigate similar properties for the binary Euclidean algorithm one must instead study the thermodynamic formalism of an IID random dynamical system on the interval. Ian will describe a recent result on the transfer operator of the binary Euclidean algorithm which can be applied to resolve conjectures of R.P. Brent, B. Vallee and D.E. Knuth.