Dynamical Systems and Analysis Seminar - Yotam Smilansky
| Dates: | 7 October 2024 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Yotam Smilansky (University of Manchester)
Title: Equivalence relations on aperiodic point sets
Abstract: A Delone set in Euclidean space is an infinite well-spaced (uniformly discrete and relatively dense) set of points. Examples range from perfectly ordered lattices through vertices of aperiodic Penrose tilings to random disordered configurations. A natural question concerns the intermediate behaviour: given a non-lattice Delone set, in what ways is it still "equivalent" to a lattice? I will introduce bounded displacement (BD) and biLipschitz (BL) equivalence relations on Delone sets, and describe fundamental results including the existence of BL-non-equivalent Delone sets (McMullen and Burago-Kleiner, independently, answering a question by Gromov) and criteria for BD and BL equivalence to a lattice (Laczkovich and Burago-Kleiner, respectively), both related to discrepancy estimates. I will then survey more recent advances, with special attention to aperiodic point sets arising through cut-and-project schemes and substitution tilings. No prior knowledge is assumed.
Room: Frank Adams 1
Further information: https://personalpages.manchester.ac.uk/staff/yotam.smilansky/dynamics_analysis
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Frank Adams 1
Alan Turing Building
Manchester
