Title: Inner Steiner formula for polytopes with an application to self-affine fractal tilings
Speaker: Andrei Ratiu (Istanbul Bilgi University)
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 "complex dimensions" 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.