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start [2024/02/27 13:40] – 139.124.146.3 | start [2024/04/30 14:50] – 139.124.146.3 | ||
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+ | **April 30 2024: [[https:// | ||
+ | The recently discovered Hat is an aperiodic | ||
+ | monotile for the Euclidean plane, which needs a reflected | ||
+ | version for this property. The Spectre does not have this | ||
+ | (tiny) deficiency. We discuss the topological and dynamical | ||
+ | properties of the Hat tiling, how the CAP relates to it, and | ||
+ | what the long-range order of both tilings is. Finally, we | ||
+ | briefly describe the analogous structure for the Spectre tiling. | ||
- | **March 5 2024: [[https:// | ||
- | Let $S$ be a finite subset of $\mathbb{Z}^n$. A vector | + | **May 14 2024: [[https:// |
- | sequence | + | |
- | element of $S$ for all $i$. Gerver | + | In 2009, Shur published the following conjecture: |
- | $S\subset\mathbb{Z}^3$ there exists an infinite | + | |
- | $5^11+1=48,828,126$ points | + | https:// |
- | approach, | + | |
- | improve | + | **May 28 2024: [[https:// |
- | $S$-walk as the fixed point of iterating | + | |
- | letter alphabet. | + | **June |
+ | |||
+ | **June 25 2024: [[http:// | ||
+ | |||
+ | **July 9 2024: [[https:// | ||
+ | |||
+ | |||
+ | ==== Past talks 2024 ==== | ||
+ | |||
+ | **April 16 2024: [[https:// | ||
+ | |||
+ | {{ seminar2024: | ||
+ | |||
+ | Automatic structures | ||
+ | |||
+ | While existential quantifiers can be eliminated in linear time by application of a homomorphism, | ||
+ | We answer this question negatively. | ||
+ | |||
+ | In my talk, following a short introduction to the field of automatic structures, I will present the construction | ||
+ | |||
+ | |||
+ | Based on the paper: https:// | ||
+ | |||
+ | Authors: Christoph Haase, R.P. | ||
+ | |||
+ | Keywords: automatic structures, universal projection, tiling problems, state complexity. | ||
- | **March 19 2024: [[https:// | ||
**April 2 2024: John Campbell** // On the evaluation of infinite products involving automatic sequences// | **April 2 2024: John Campbell** // On the evaluation of infinite products involving automatic sequences// | ||
+ | |||
+ | {{ seminar2024: | ||
+ | |||
+ | {{ seminar2024: | ||
+ | |||
We explore and discuss some recently introduced techniques concerning the evaluation of infinite products involving automatic sequences. | We explore and discuss some recently introduced techniques concerning the evaluation of infinite products involving automatic sequences. | ||
- | **April 16 2024: [[https:// | ||
- | **April 30 2024: [[https://www.math.uni-bielefeld.de/baake/|Michael Baake]]** | + | **March 19 2024: [[https://diamweb.ewi.tudelft.nl/~cork/|Cor Kraaikamp]]** //An introduction to $N$-expansions with a finite set of digits// |
- | **May 14 2024: [[https:// | + | {{ seminar2024:20240319kraaikamp.pdf |slides}} |
- | **May 28 2024: [[https:// | + | {{ seminar2024:20240319kraaikamp.mp4 |video of the talk}} |
- | **June 11 2024: [[https:// | ||
- | **July 9 2024: [[https:// | + | In this talk $N$-expansions, |
+ | of digits, will be introduced. Although $N$-expansions were introduced as | ||
+ | recent as 2008 by Ed Burger and some of his students, quite a number of | ||
+ | papers have appeared on these variations of the regular continued fraction | ||
+ | expansion. By choosing a domain for the underlying Gauss-map which does | ||
+ | not contain the origin, a continued fraction with finitely many digits was | ||
+ | introduced by Niels Langeveld in his MSc-thesis. It turns out that these | ||
+ | continued fraction algorithms exhibit a very complicated and surprising rich | ||
+ | dynamical behavior. | ||
+ | This talk is based on joint work with Yufei Chen (Shanghai, Delft), Jaap | ||
+ | de Jonge (UvA, Amsterdam), Karma Dajani (Utrecht), Niels Langeveld | ||
+ | (Montan U., Leoben), Hitoshi Nakada (Keio, Yokohama), and Niels van der | ||
+ | Wekken (Netcompany). | ||
- | ==== Past talks 2024 ==== | + | **March 5 2024: [[https:// |
+ | |||
+ | {{ seminar2024: | ||
+ | |||
+ | {{ seminar2024: | ||
+ | |||
+ | |||
+ | Let $S$ be a finite subset of $\mathbb{Z}^n$. A vector | ||
+ | sequence $(z_i)$ is an $S$-walk if and only if $z_{i+1}-z_i$ is an | ||
+ | element of $S$ for all $i$. Gerver and Ramsey showed in 1979 that for | ||
+ | $S\subset\mathbb{Z}^3$ there exists an infinite $S$-walk in which no | ||
+ | $5^{11}+1=48,828,126$ points are collinear. Using the same general | ||
+ | approach, but with the aid of a computer search, we show how to | ||
+ | improve the bound to $189$. We begin by restating the infinite | ||
+ | $S$-walk as the fixed point of iterating a morphism defined for a $12$ | ||
+ | letter alphabet. | ||