# Inner Steiner formula for polytopes with an application to self-affine fractal tilings

Algebra/Geometry/Topology Seminar

#### by Andrei Ratiu

Institution: Istanbul Bilgi University
Date: Mon 10th May 2010
Time: 2:15 PM
Location: Babel Middle Theatre

Abstract: The recent construction by Lapidus and Pearse of the tubular zeta-function of a self-similar tiling as a certain meromorphic function whose poles are the â€œcomplex dimensionsâ€ of the tiling and whose sum of residues gives the volume of its inner neighborhood, is an important breakthrough in the theory of fractals. As a first step beyond the world of self-similar fractals, we define the tubular zeta-function of a self-affine tiling and apply it to a higher-dimensional analogue of McMullen's generalized Sierpinski carpets. We use the fact that the volume of the inner tube of a polytope is a piecewise polynomial function, which would be the inner counterpart of the well-known classical Steiner formula for convex bodies.