Date:	Tue, October 13, 2015
Time:	14:15
Place:	Research I Seminar Room

Abstract: The Mandelbrot set is a classical but important object in Complex Dynamics. Some years ago Penrose and Bruin-Schleicher constructed a space - the "combinatorial model" - that captures its combinatorial structure. However, the natural map from the Mandelbrot set to this model (given by kneading sequences) is neither injective nor surjective.

After describing this model we present a way to modify it such that the new space constitutes an extension of the Mandelbrot set: It is a naturally defined compact topological Hausdorff space that contains the Mandelbrot set in a canonical way as a proper closed subset.

We also consider the question how to characterize the points in the combinatorial model (or in the extension) that actually correspond to points in the Mandelbrot set. The answer is known as the Admissibility Condition of Bruin and Schleicher. We give a geometric interpretation of this condition and sketch a way how this interpretation leads to a new proof of the condition.

The slides of the talk will be available at http://fels.tk.