Ergodic Theory Without Invariant Measures Ergodic theory deals with dynamical systems from a measurable point of view. One considers transformations of a probability space, like the rotation of a circle over a typically irrational angle. In general, one considers transformations that may or may not preserve the given probability measure, but that will always preserve sets of measure zero. Iterating […]
Approximating Real Numbers by Fractions How well can you approximate real numbers by rationals with denominators coming from a given set? Although this old question has applications in many areas, in general this question seems impossibly hard – we don’t even know whether e+pi is rational or not! If you allow for a tiny number of bad exceptions, then a beautiful […]
What Is the Best Super Power? If you could have any power as a super hero, what would it be? Would you choose to be able to use and interpret statistics? Statistics are an everyday part of life – in our social media feeds, news reports and conversations. It’s not always easy to know if we can trust the statistics […]
Symmetry and Enumeration of Fractals In this talk, it is discussed how a simple ‘iterated function system’ construction leads to large classes of self-similar fractals. It is described how a little group theory can be used to examine the symmetries of these fractals and to enumerate various classes, with pictorial examples.