Habrá 4 charlas para la comunidad universitaria
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The Way The World Fits Together (Tiling 1)
The Way The World Fits Together (Tiling 1)
Jueves 16 de abril, 1pm
Auditorio del IIMAS
The recently discovered “Hat” monotile reminds us that small gadgets, fitting together by local interactions can give rise to fantastic complexity, even in recreational mathematics! Across the sciences and mathematics, as fragments of formal logic, symbols in a computer language, or proteins, all producing irreducible complexity when combined by simple proscribed rules. We’ll discuss the source of this in combinatorial tiling puzzles. For a sample, try to decide whether or not you can use copies of the tile on the right to cover the entire plane!
Debido a la situación de clases virtuales de la Facultad de Ciencias, la siguiente charla cambia de día y lugar. Ahora será el martes 21 de abril en el Instituo de Matemáticas
The Magic Theorem
The Magic Theorem
Martes 21 de abril, 4pm
Auditorio Nápoles Gándara
Instituto de Matemáticas
Importante: traer tijeras y cinta adhesiva
Abstract: We are surrounded by an amazing variety of geometric repeating patterns, on our clothes, floors, buildings -- where there is a surface, people will decorate it. To a mathematician, though, there are only a few ways patterns are put together. In this presentation we'll learn how the Magic Theorem sorts out the possible symmetry types, using only a simple arithmetic count. We'll apply the Magic Theorem to recognize the mathematical type of repeating patterns -- and then we'll explore new methods of creating patterns using paper-and-scissors topology.
¿Te la perdiste en el IIMAS?, habrá una repetición de la siguiente plática:
The Way The World Fits Together (Tiling 1)
The Way The World Fits Together (Tiling 1)
Miércoles 22 de abril, 4pm
Auditorio Nápoles Gándara
Instituto de Matemáticas
The recently discovered “Hat” monotile reminds us that small gadgets, fitting together by local interactions can give rise to fantastic complexity, even in recreational mathematics! Across the sciences and mathematics, as fragments of formal logic, symbols in a computer language, or proteins, all producing irreducible complexity when combined by simple proscribed rules. We’ll discuss the source of this in combinatorial tiling puzzles. For a sample, try to decide whether or not you can use copies of the tile on the right to cover the entire plane!
Matching Rules For Rep-tiles (Tiling 2)
Matching Rules For Rep-tiles (Tiling 2)
Jueves 23 de abril, 4:30pm
Salón de Seminarios Graciela Salicrup
Instituto de Matemáticas
Four copies of this L-shape can be fitted together to form a larger L-shape; four of those can be fitted into a larger L still, and so on ad infinitum, in the end producing a non-periodic, hierarchical tiling of the plane. But this L-shape can form lots of other kinds of patterns too — how can we enforce this hierarchical structure? Today there are a few dozen specific examples (most famously the Penrose tiles and the Hat monotile) and a series of general constructions (Mozes '89, GS '98, Fernique-Ollinger '10), but these are not widely understood. We aim to demystify these methods with a simple to state and easy to prove lemma that applies to each of these constructions (pushing the hard work into showing the hypotheses of the lemma hold in whatever setting we are considering).
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