Renormalization Operator for Conformal Dimension of Sierpinski Carpet
Talk by Dr. Jarek Kwapisz (Mathematical Sciences, MSU)
9/9/2019 Wilson Hall 1-144 4:10-5:00pm
Abstract: Fractals, sets with fractional dimension, arise in a variety of theoretical and applied contexts, often as the limiting self-similar objects in geometry or dynamics. Last 30+ years have seen a concerted effort to construct a version of Calculus on such sets and lead to a realization that the standard notion of Hausdorff dimension has to be supplanted by the so-called conformal dimension. The catch is that the latter remains unknown even for some simple looking classical fractals, including the Sierpinski Carpet. I will contrast the two notions of dimension and propose an approach to computing the conformal dimension of the carpet.