Details:
Dr. Olga Lukina (University of Leicester, UK), candidate for a tenure track position in Topology will speak on Thursday, April 12, at 4:00.
Title: Topology and dynamics of matchbox manifolds
Abstract: A matchbox manifold is a continuum where each point has a neighborhood homeomorphic to the product of a Euclidean disk and a totally disconnected space, and such that each path-connected component has a structure of a smooth manifold. Examples of matchbox manifolds include solenoids, closures of tilings with finite local complexity, attractors in dynamical systems, certain graphs constructions, and many others. In the cases when leaves have dimension at least 2, very little is known about the class of matchbox manifolds. In the talk, I will give an overview of a range of recent results of myself and my collaborators, which use topological tools such as inverse limit representations, graph constructions and others, to study properties and develop classifications of matchbox manifolds. I will outline a program of future research which arises from this recent work, and explain some interconnections with areas of mathematics such as geometric group theory, topological dynamics, and operator theory.
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