Title	Penrose tilings and Hurwitz theory of leaf spaces
Creator	Engel, Philip
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2019-05-28T16:00
Description	A group acting on an elliptic curve must have order N = 1, 2, 3, 4, or 6. We call the quotient an elliptic orbifold. Certain branched covers of the order N elliptic orbifold are in bijection with tiled surfaces, and form a lattice in the moduli space of N-ic differentials on Riemann surfaces. The enumerative theory of these branched covers suggests a phantom "elliptic orbifold" for all integers N. I will discuss work-in-progress with Peter Smillie proposing a definition for the Hurwitz theory of this non-existent object, and attempts to relate it to quasi-crystals in the moduli space of quintic differentials and the enumeration of Penrose-tiled Riemann surfaces.
Extent	37.0 minutes
Subject	Mathematics; Dynamical systems and ergodic theory; Algebraic geometry; Dynamical systems
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: University of Georgia
Series	BIRS Workshop Lecture Videos (Oaxaca de Juárez (Mexico))
Date Available	2021-01-16
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0395615
URI	http://hdl.handle.net/2429/77109
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Researcher
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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Penrose tilings and Hurwitz theory of leaf spaces Engel, Philip

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