Title:  Aperiodic Tilings and Tiling Spaces
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Abstract: The talk will focus on tilings of the plane that are almost periodic.
Such tilings serve as models of ideal quasi-crystals and have symmetry
properties unseen in periodic tilings (which model ideal crystals).
I will illustrate the subject by recounting Penrose's discovery of his
famous example and follow with an explanation of the concept of a tiling
space.
This is to frame some new results about linear and nonlinear symmetries
of aperiodic tilings and about their topological rigidity.