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hdp page update based on Gaetan suggestions

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mwinter 1 year ago
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portfolio-nuxt/pages/a_history_of_the_domino_problem.vue
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The tilings sonified and visualized in <span class="italic">a history of the domino problem</span> are rare because there is no systematic way to find them. This is due to the fact that they are <NuxtLink to='https://en.wikipedia.org/wiki/Aperiodic_tiling'><span class="italic">aperiodic</span></NuxtLink>. One can think of an aperiodic tiling as an infinite puzzle with a peculiar characteristic: given unlimited copies of dominoes with a finite set of color/pattern combinations for the edges, on can form a tiling that expands infinitely. However, in that solution, any repeating structure in the tiling will eventually be interrupted. This phenomenon is one of the most intriguing aspects of the work. As the music and the visuals are derived from the tilings, the resulting textures are always shifting ever so slightly.
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<p>
The original Domino Problem asked if there exists an algorithm/computer program that, when given as input a finite set of dominoes with varying color combinations for the edges, can output a binary answer, `yes' or `no', whether or not copies of that set can form an infinite tiling. The problem was first posed by Hao Wang in 1961, who conjectured that the answer is positive and that such an algorithm does exist. The existence of aperiodic tilings would mean that such an algorithm <span class="italic">does not</span> exist. However, in 1966, his student, Robert Berger, proved him wrong by discovering an infinite, aperiodic tiling constructed with copies of a set of 20,426 dominoes. The resolution of Wang's original question led to new questions and mathematicians took on the challenge of finding the smallest set of dominoes that would construct an infinite aperiodic tiling. Over the past 60 years, this number has been continually reduced with the contributions of many different mathematicians until the most recent discovery of a set of 11 dominoes along with a proof that no smaller sets exist. It is a remarkable narrative/history of a particular epistemological problem that challenged a group of people not only to solve it, but to understand it to the extent possible.
The original Domino Problem asked if there exists an algorithm/computer program that, when given as input a finite set of dominoes with varying color combinations for the edges, can output a binary answer, `yes' or `no', whether or not copies of that set can form an infinite tiling. The problem was first posed by Hao Wang in 1961, who conjectured that the answer is positive and that such an algorithm does exist. The existence of aperiodic tilings would mean that such an algorithm <span class="italic">does not</span> exist. However, in 1964, his student, Robert Berger, proved him wrong by discovering an infinite, aperiodic tiling constructed with copies of a set of 20,426 dominoes. The resolution of Wang's original question led to new questions and mathematicians took on the challenge of finding the smallest set of dominoes that would construct an infinite aperiodic tiling. Over the past 60 years, this number has been continually reduced with the contributions of many different mathematicians until the most recent discovery of a set of 11 dominoes along with a proof that no smaller sets exist. It is a remarkable narrative/history of a particular epistemological problem that challenged a group of people not only to solve it, but to understand it to the extent possible.
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<div class="mb-5 text-3xl italic font-bold">
a few thoughts on how things fit together...
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<div class="mb-5">
(free entrance)
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<br>
<div class="mb-5">
in collaboration with MAREIKE YIN-YEE LEE
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Exact Gallery hours to be announced soon!
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<div class="mb-5">
Lichthof Ost, HU Berlin, Campus Mitte, Unter den Linden 6, U Bahn Unter den Linden oder Museuminsel
Lichthof Ost, HU Berlin Hauptgebäude, Campus Mitte, Unter den Linden 6 (U-Bahn Unter den Linden oder Museuminsel)
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<div class="mb-5">
Exhibition Opening - 17 Nov 2023 | 19 Uhr
<span class="font-bold">Exhibition Opening - 17 Nov 2023 | 19 Uhr</span>
<br>
Lichthof Ost, HU Berlin, Campus Mitte, Unter den Linden 6, U Bahn Unter den Linden oder Museuminsel
Lichthof Ost, HU Berlin Hauptgebäude, Campus Mitte, Unter den Linden 6 (U-Bahn Unter den Linden oder Museuminsel)
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<div class="mb-5">
Exhibition Closing - 31 Nov 2023 | 19 Uhr
<span class="font-bold">Exhibition Closing - 31 Nov 2023 | 19 Uhr</span>
<br>
Lichthof Ost, HU Berlin, Campus Mitte, Unter den Linden 6, U Bahn Unter den Linden oder Museuminsel
Lichthof Ost, HU Berlin Hauptgebäude, Campus Mitte, Unter den Linden 6 (U-Bahn Unter den Linden oder Museuminsel)
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<div class="mb-5">
Lecture-Concert
<span class="font-bold">Public lecture + Concert (free entrance)</span>
<br>
with mathematician JARKKO KARI moderated by GAETAN BOROT
with Prof. JARKKO KARI (Turku University), moderated by Prof. Dr. GAËTAN BOROT (HU Berlin)
<br>
performance by KALI ENSEMBLE
<br>
22 Nov 2023 | 19:30 Uhr
<br>
Reuter-Saal, HU Berlinm Universitätsgebäude am Hegelplatz, Dorotheentsraße 24, U Bahn Unter den Linden oder Museuminsel
Fritz-Reuter-Saal, HU Berlin Universitätsgebäude (am Hegelplatz), Dorotheentsraße 24 (U-Bahn Unter den Linden oder Museuminsel)
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<div class="mb-5">
Concert
<span class="font-bold">Concert</span>
<br>
performance by KALI ENSEMBLE
<br>
23 Nov 2023 | 20 Uhr
<br>
KM28
<NuxtLink to='https://www.km28.de/'>KM28</NuxtLink>
<br>
Karl-Marx-Str. 28, 12043 Berlin (U-Bahn Karl-Marx-Platz)
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<br>
<div class="mb-5">
<span class="font-bold">From Wang Tiles to the Domino Problem: A Tale of Aperiodicity</span>
<br>
<br>
Karl-Marx-Str. 28, 12043 Berlin, U Bahn Karl-Marx-Platz
This presentation delves into the remarkable history of aperiodic tilings and the domino problem. Aperiodic tile sets refer to collections of tiles that can only tile the plane in a non-repeating, or non-periodic, manner. Such sets were not believed to exist until 1964 when R. Berger introduced the first aperiodic set consisting of an astonishing 20,426 Wang tiles. Over the years, ongoing research led to significant advancements, culminating in 2015 with the discovery of a mere 11 Wang tiles by E. Jeandel and M. Rao, alongside a computer-assisted proof of their minimality. Simultaneously, researchers found even smaller aperiodic sets composed of polygon-shaped tiles. Notably, Penrose's kite and dart tiles emerged as early examples, and most recently, a groundbreaking discovery was made - a solitary aperiodic tile known as the "hat" that can tile the plane exclusively in a non-periodic manner. Aperiodic tile sets are intimately connected with the domino problem that asserts how certain tile sets can tile the plane without us ever being able to establish their tiling nature with absolute certainty. Moreover, aperiodic tilings hold a distinct visual aesthetic allure. In today's musical presentation, their artistic appeal transcends the visual domain and extends into the realm of music. -Jarkko Kari
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Jarkko J. Kari is a Finnish mathematician and computer scientist, known for his contributions to the theory of Wang tiles and cellular automata. Kari is currently a professor at the Department of Mathematics, University of Turku.
Jarkko Kari received his MSc and PhD degrees in mathematics from the University of Turku in Finland in 1986 and 1990, respectively. He then worked for the Academy of Finland, and for Iterated Systems Inc. and the University of Iowa in the USA. Since year 2000 he has been a professor of mathematics at the University of Turku. His research interests include automata theory and the theory of computation, with emphasis on cellular automata, tilings and symbolic dynamics. Jarkko Kari has supervised twelve PhD theses, published over one hundred peer reviewed research articles and edited twenty conference proceedings and special issues on these topics. He serves in the editorial boards of eight scientific journals, and is currently a co-editor-in-chief of the journal Natural Computing. Jarkko Kari is a member of the Finnish Academy of Science and Letters since 2014.
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<NuxtLink class="text-3xl font-bold" to='https://www.mathematik.hu-berlin.de/de/forschung/forschungsgebiete/mathematische-physik/borot-mp-homepage'>Gaetan Borot - mathematician | organizer | moderator</NuxtLink>
<NuxtLink class="text-3xl font-bold" to='https://www.mathematik.hu-berlin.de/de/forschung/forschungsgebiete/mathematische-physik/borot-mp-homepage'>Gaëtan Borot - mathematician | organizer | moderator</NuxtLink>
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<nuxt-img class="w-full" src="/hdp_images/gaetan.jpg"/>
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Gaëtan Borot was trained at École Normale Supérieure (Paris) in theoretical physicist and progressively moved to pure mathematics. He received his PhD from Universite d'Orsay / CEA Saclay in 2011. After a postdoctorate in Geneva and a visiting scholarship at MIT, he worked as a Group Leader at the Max Planck Institute for Mathematics in Bonn. Since 2020, he holds a bridge professorship between the Institute of Mathematics and the Institute of Physics of the Humboldt University of Berlin. He has worked on enumerative geometry, combinatorics, random matrix theory and mathematical aspects of quantum field theory, and likes to investigate the unexpected relations between seemingly different problems. He is also interested in scientific outreach.
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