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{"id":7,"date":"2023-02-16T18:28:08","date_gmt":"2023-02-16T18:28:08","guid":{"rendered":"https:\/\/x-math.mathi.uni-heidelberg.de\/?page_id=7"},"modified":"2023-02-17T07:52:51","modified_gmt":"2023-02-17T07:52:51","slug":"presentations","status":"publish","type":"page","link":"https:\/\/x-math.mathi.uni-heidelberg.de\/","title":{"rendered":"X-MATH WiSe22"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Introduction<\/h2>\n\n\n\n<p>X-MATH (eXperimental MATHematics) is an online asynchronous symposium showcasing projects organized at Heidelberg and Magdeburg. You can interact with the presenting teams during <strong>Feb 20\u201324<\/strong> over <strong>Slack<\/strong>; <a href=\"https:\/\/forms.gle\/jrLZ2cfM43nmoJgs6\">register here<\/a> to receive the Slack invite. This symposium is organized by the <a href=\"https:\/\/hegl.mathi.uni-heidelberg.de\/\">Heidelberg Experimental Geometry Lab (HEGL)<\/a>. For questions or comments, please contact <em>hegl [at] mathi [dot] uni [dash] heidelberg [dot] de<\/em>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Presentations<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Magdeburg<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">RISE Project: Programming a Geometric Realization of non-affine Coxeter groups<\/h4>\n\n\n\n<p><strong>Slack<\/strong>: #wise22-rise-project<br><strong>Team<\/strong>: Marco Lotz, Mireia Taus<br><strong>Abstract<\/strong>: This video presents the project Mireia Taus and I implemented as part of a 2020 DAAD-funded internship. Using the python packages &#8220;hyperbolic&#8221; and &#8220;drawSvg&#8221; we visualized two-dimensional Coxeter complexes of non-affine Coxeter groups in the Poincar\u00e9 disk model and coloured the complex according to the reflection length of the chambers.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"RISE: Programming a Geometric Realization of non-affine Coxeter groups\" width=\"1290\" height=\"726\" src=\"https:\/\/www.youtube.com\/embed\/gukCOLjQHaE?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Heidelberg<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Physics-Based Graph Layout in Hyperbolic Space<\/h4>\n\n\n\n<p><strong>Slack<\/strong>: #wise22-graph-layout<br><strong>Team<\/strong>: David Li, Anna Roth<br><strong>Abstract<\/strong>: In Euclidean space, a physics simulation has been successfully used to find graph layouts that show the symmetries of a given graph without being explicitly specified. In this project, we developed an analogous simulation on the Poincare disc for visualizing some graphs with hyperbolic symmetries.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Physics-Based Graph Layout in Hyperbolic Space\" width=\"1290\" height=\"726\" src=\"https:\/\/www.youtube.com\/embed\/DlnY57v0iY8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Rolling Knots<\/h4>\n\n\n\n<p><strong>Slack<\/strong>: #wise22-rolling-knots<br><strong>Team<\/strong>: Leon-Josip Dzojic, Matilde Sciortino, Pirmin Kupffer<br><strong>Abstract<\/strong>: In 1980, M. H. Freedman conjectured that every generic smooth knot in 3-dimensional Euclidean space has a tritangent plane, i.e., a plane tangent to three distinct points. However, ten years later, A. M. Amilibia, J. J. N. Ballesteros, and H. R. Morton used trefoil knots to construct a family of counterexamples to this conjecture. A. Eget, S. K. Lucas, and L. Taalman later improved the roll-ability of Morton&#8217;s family of trefoil knots by reducing the center of mass&#8217;s height deviation. In this project our goal was to understand the proof by Morton, find new families of tritangentless knots and optimize them with respect to smooth roll-ability.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Rolling Knots\" width=\"1290\" height=\"726\" src=\"https:\/\/www.youtube.com\/embed\/tVvVp2xmY9w?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Geometric Deep Learning<\/h4>\n\n\n\n<p>Coming soon!<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Math and Data Science for Social Good<\/h4>\n\n\n\n<p>Coming soon!<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Political Geometry<\/h4>\n\n\n\n<p><strong>Slack<\/strong>: #wise22-political-geometry<br><strong>Team<\/strong>: Ay\u015feg\u00fcl Pek\u00f6zsoy, Leonard Sp\u00e4th, Klaus Stier<br><strong>Abstract<\/strong>: In this project, we analyzed the cross-party cooperation between US senators from 1973-2022 using co-sponsorship data. Our results show significant changes in cross-party cooperation over time.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Political Geometry\" width=\"1290\" height=\"726\" src=\"https:\/\/www.youtube.com\/embed\/4M5MOmsc70c?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Continuous Cellular Automata<\/h4>\n\n\n\n<p><strong>Slack<\/strong>: #wise22-cellular-automata<br><strong>Team<\/strong>: Adrian Becker<br><strong>Abstract<\/strong>: Lenia is a family of cellular automata that generalize Conway&#8217;s game of life to a continuous domain. In this project, we implemented two Lenia systems and optimized our implementations with mathematics and GPU programming tricks.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Continuous Cellular Automata\" width=\"1290\" height=\"726\" src=\"https:\/\/www.youtube.com\/embed\/XJGdVjrYN8s?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">An Interactive Web-Based Animation Application for Graph Algorithms<\/h4>\n\n\n\n<p><strong>Slack<\/strong>: #wise22-alvis<br><strong>Team<\/strong>: Tillmann Fehrenbach<br><strong>Abstract<\/strong>: In this project, we built an interactive system, ALVIS, for visualizing graph algorithms in the web browser. We here give an overview of the project and the web technologies used.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Animating Graph Algorithms in the Browser\" width=\"1290\" height=\"968\" src=\"https:\/\/www.youtube.com\/embed\/kYmf50rFFis?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Hyperbolic Billiards<\/h4>\n\n\n\n<p><strong>Slack<\/strong>: #wise22-hyperbolic-billiards<br><strong>Speaker<\/strong>: Jannis Heising<br><strong>Abstract<\/strong>: In this project, we study billiard orbits in hyperbolic polygons. Using symbolic dynamics, we visualize tiles in a parameter space corresponding to triangles with particular closed orbits. We are currently refining our method for describing these orbit tiles and exploring relations with billiards in Euclidean triangles.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Polygonal Hyperbolic Billiards\" width=\"1290\" height=\"726\" src=\"https:\/\/www.youtube.com\/embed\/kRkI6fIxUIA?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Root Systems and their Weyl Groups<\/h4>\n\n\n\n<p>Coming soon!<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Quasicrystals and the Cut-and-Project Method<\/h4>\n\n\n\n<p><strong>Slack<\/strong>: #wise22-quasicrystals<br><strong>Team<\/strong>: Noah Koopman, Ingmar Lowack<br><strong>Abstract<\/strong>: In 1981, N. G. de Bruijn introduced a novel method for generating Penrose tilings by projecting particular points from a five-dimensional lattice onto the two-dimensional plane. Since then, it has been discovered that the de Bruijn method, now commonly known as the cut-and-project method, can be used to generate many families of aperiodic tilings. In this project, we implement and optimize the cut-and-project method for some families of aperiodic tilings.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Generating Quasicrystals with the Cut and Project Method\" width=\"1290\" height=\"726\" src=\"https:\/\/www.youtube.com\/embed\/hwMAOFb6yvA?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Visualizing Poncelet\u2019s Porism<\/h4>\n\n\n\n<p><strong>Slack<\/strong>: #wise22-poncelet-porism<br><strong>Team<\/strong>: Adrian Becker, Miriam Compton, Lukas Schmidt<br><strong>Abstract<\/strong>: Poncelet&#8217;s porism is a deceptively simple result in geometry that states that whenever a polygon is inscribed in one conic section and circumscribes another, the polygon must be part of an infinite family of polygons that are all inscribed in and circumscribe the same two conics. [<a href=\"https:\/\/en.wikipedia.org\/wiki\/Poncelet%27s_closure_theorem\">Wikipedia<\/a>] In this project, we learned the proof of the result and produced relevant visualizations.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Poncelets Porism\" width=\"1290\" height=\"726\" src=\"https:\/\/www.youtube.com\/embed\/Jc33XZzhDW8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n","protected":false},"excerpt":{"rendered":"<p>Introduction X-MATH (eXperimental MATHematics) is an online asynchronous symposium showcasing projects organized at Heidelberg and Magdeburg. You can interact with the presenting teams during Feb 20\u201324 over Slack; register here to receive the Slack invite. This symposium is organized by the Heidelberg Experimental Geometry Lab (HEGL). For questions or comments, please contact hegl [at] mathi [dot] uni [dash] heidelberg [dot] de. Presentations Magdeburg RISE Project: Programming a Geometric Realization of non-affine Coxeter groups Slack: #wise22-rise-projectTeam: Marco Lotz, Mireia TausAbstract: This video presents the project Mireia Taus and I implemented as part of a 2020 DAAD-funded internship. Using the python packages\u2026<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-7","page","type-page","status-publish","hentry"],"blocksy_meta":{"styles_descriptor":{"styles":{"desktop":"","tablet":"","mobile":""},"google_fonts":[],"version":5}},"_links":{"self":[{"href":"https:\/\/x-math.mathi.uni-heidelberg.de\/wp-json\/wp\/v2\/pages\/7","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/x-math.mathi.uni-heidelberg.de\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/x-math.mathi.uni-heidelberg.de\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/x-math.mathi.uni-heidelberg.de\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/x-math.mathi.uni-heidelberg.de\/wp-json\/wp\/v2\/comments?post=7"}],"version-history":[{"count":29,"href":"https:\/\/x-math.mathi.uni-heidelberg.de\/wp-json\/wp\/v2\/pages\/7\/revisions"}],"predecessor-version":[{"id":69,"href":"https:\/\/x-math.mathi.uni-heidelberg.de\/wp-json\/wp\/v2\/pages\/7\/revisions\/69"}],"wp:attachment":[{"href":"https:\/\/x-math.mathi.uni-heidelberg.de\/wp-json\/wp\/v2\/media?parent=7"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}