Date:	Tue, October 1, 2013
Time:	15:45
Place:	Research I Seminar Room

Abstract: We discuss the dynamics of certain entire functions, for instance those of finite order and bounded type. Of particular interest is the escaping set: that is the set of points that converge to infinite under iteration. A classical conjecture of Eremenko (and an even more classical question of Fatou) says that this set, union infinity, is path connected. This conjecture was proved a few years ago by two Jacobs graduate students (for the functions mentioned above). We outline the proof and indicate how we think this statement could possibly be generalized to functions beyond those of finite type.

If time remains, we will also indicate how this leads to the following ``dimension paradox'': there is a collection of disjoint curves (presumably C^\infty -- anyone interested in proving this?) that together have (Hausdorff) dimension 1 and that connect some ``endpoint'' in C to infinity, so that every point in the complex plane is either on exactly one such curve, or it is the endpoint of one or several such curves. So, paradoxically, ``almost every'' point in C (in a much stronger sense than just Lebesgue measure) is an endpoint of one or several curves, but the union of all these curves only has dimension 1.