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Dynamical Systems and Analysis Seminar - Ashwin Bhat

Speaker: Ashwin Bhat (University of Birmingham) Title: Constructing Non-Rectifiable Delone Sets Abstract: Delone sets, also known as separated nets, are point sets in Euclidean space that are both relatively dense and uniformly discrete. They model aperiodic structures, which have been of great interest since Dan Shechtman first observed quasicrystals, an achievement that ultimately won him the Nobel Prize in Chemistry in 2011. Since then, many lines of research have emerged regarding the structural properties of Delone sets. An interesting question posed independently by Furstenberg and Gromov asks whether all Delone sets in a given dimension are bi-Lipschitz equivalent. McMullen, as well as Burago and Kleiner, answered this question in the negative for dimensions two and above by transforming it into a continuous problem concerning the prescribed Jacobian equation. In this talk, we discuss their method of "encoding" a non-realisable density into a Delone set, and examine how modern versions of this technique are implemented in metric geometry. Room: Frank Adams 1 Further information: https://personalpages.manchester.ac.uk/staff/yotam.smilansky/dynamics_analysis