Group actions, Mattila integral and simplexes inside fractal sets
SPEAKER | Alex Iosevich
DATE | May 9(Tue), 2017
TIME | 14:00
PLACE | 1503
ABSTRACT | We will describe how a simple group action viewpoint can be used to derive the classical Mattila integral and to study the distribution of simplexes inside compact subsets of Euclidean space of a given Hausdorff dimension. More general configuration are studied as well where the various notions of rigidity come into play along with Sard's theorem. A variety of interesting model multi-linear variants of generalized Radon transforms arise in this context and we shall discuss some steps towards the general theory of these objects.