{"id":24496,"date":"2023-04-21T17:38:34","date_gmt":"2023-04-21T17:38:34","guid":{"rendered":"https:\/\/www.uwb.edu\/news\/?p=24496"},"modified":"2023-07-10T21:55:55","modified_gmt":"2023-07-10T21:55:55","slug":"determined-to-solve-complicated-problems","status":"publish","type":"post","link":"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems","title":{"rendered":"Determined to solve complicated problems"},"content":{"rendered":"\n
\"\"
Harper Hults, senior in the School of STEM<\/figcaption><\/figure>\n\n\n\n

When Harper Hults was in kindergarten, the teacher noticed they looked bored while coloring by numbers and asked if they would like to start first-grade math and learn how to count by two. \u201cI just remember being like okay, sure, whatever,\u201d Hults recalled. \u201cThe worksheets in the first-grade classroom had potatoes on them, and I thought that was cool.\u201d<\/p>\n\n\n\n

Hults excelled in the higher-level classroom, and looking back now, said it was the start of what has been more than a decade-long pursuit to study mathematics. \u201cI suppose I have always been \u2018good\u2019 at math, but I really love language and communication, too. That\u2019s what I am really interested in. To me, math is just the most precise language we have access to.\u201d<\/p>\n\n\n\n

Currently a major both in Mathematics and in Computer Science & Software Engineering at the University of Washington Bothell, Hults next plans to attend graduate school to \u201ctake a crack\u201d at solving some of life\u2019s most complex questions.<\/p>\n\n\n\n

\u201cI just laugh at myself because I am so fascinated by how consciousness works and how we describe the human experience, which are some of the hardest questions to answer in the world,\u201d they said. \u201cPhilosophers have spent hundreds of years describing consciousness qualitatively, but in order for a paradigm shift, we need a formulation that admits tractable analysis \u2014 which is what I eventually want to do.\u201d<\/p>\n\n\n\n

Already, Hults has undertaken a daunting task: to prove that the Markov partition for one of the most famous tilesets, the Penrose tiles, is valid. \u201cFrench mathematician Sebastien Labb\u00e9 did this for another notable tileset \u2014 which is a collection of rectangular images \u2014 a few years ago,\u201d Hults said. \u201cOur research is all about figuring out how to replicate it. What conditions allowed Labb\u00e9 to do that?\u201d<\/p>\n\n\n\n

Dare to be daunted<\/h2>\n\n\n\n

Through the Research Experience for Undergraduates at UW Bothell last summer, followed by a Mary Gates Research Scholarship in autumn quarter, Hults set off on a quest to find answers.<\/p>\n\n\n\n

In the REU, a 10-week program during which students participate in research projects and professional development activities, Hults began to study tiling theory, which looks at the covering of a surface, often a plane, using one or more geometric shapes called tiles, with no overlaps and no gaps.<\/p>\n\n\n\n

Hults focused on Penrose tiles, which are aperiodic, meaning they don\u2019t tile the plane in a globally repeating manner. The goal was to study the dynamical properties of the Penrose tiles in part with the help of Wang tiles, which are also aperiodic. To do this, Hults had to find a Markov partition \u2014 a tool used in dynamical systems theory \u2014 that captured the structure of the Penrose and Wang tilings in a dynamical system.<\/p>\n\n\n\n

Distortion to clarity<\/h2>\n\n\n\n

Coming up with the Markov partition was a guessing game that involved Hults and other students in the REU cohort putting numbers into a script and analyzing the results.<\/p>\n\n\n\n

Depending on the numbers, the tiling image on the screen would come out in varying degrees of distortion. The more distorted the image, the farther away they were from the desired numbers, which define a vector lattice that determines the shape of the Markov partition.<\/p>\n\n\n\n

The students went to work to find the right numbers. It took several weeks and dozens of distorted images, but finally, in mid-July, the team found them. The \u201cmagic\u201d numbers were put into the script, and the screen came out crystal clear, indicating it was the Markov partition.<\/p>\n\n\n\n

\u201cIt was really cool to see the noise resolve, and all of a sudden this beautiful mathematical object appeared,\u201d Hults said. \u201cBut honestly, it just deepened the mystery for me. We found that there are many different parameters that produce Markov partitions, and the next step was understanding how they were all related.\u201d<\/p>\n\n\n\n

A continuing quest<\/h2>\n\n\n\n

Hults was able to continue the team\u2019s research through the Mary Gates Research Scholarship, a competitive program that enhances the educational experiences of undergraduate students through research guided by faculty. They received the scholarship in autumn quarter and used it to prove that the partition would work on all the infinite variations of Penrose tiling.<\/p>\n\n\n\n

In order to prove this, Hults spent countless hours combing through Sebastian Labb\u00e9\u2019s research and codebase. \u201cHe has huge amounts of code that he has written for this stuff, but his documentation is kind of shallow, so I spent a lot of time just reading the source code.\u201d<\/p>\n\n\n\n

Making sense of these documents has been the most challenging part of the entire project as Labb\u00e9\u2019s work is a mixture of topology, dynamical systems theory, combinatorics and computer science. \u201cIt is really complicated, messy math, and I have been teaching most of it to myself.\u201d<\/p>\n\n\n\n

Understanding it is vital to proving the partition is valid, though, as Labb\u00e9\u2019s papers contain all the theorems for proving the validity of Markov partitions. \u201cLearning how to read those research papers has definitely been a big hurdle, but I am grateful because it pushed me to self-teach on a level I never had before,\u201d Hults said.<\/p>\n\n\n\n

Persevere to payoff<\/h2>\n\n\n\n

Casey Mann, professor of Mathematics in UW Bothell\u2019s School of STEM<\/a>, served as Hults\u2019 adviser in the Mary Gates program. \u201cHarper has taken on some very advanced topics in our research,\u201d he said, \u201cand I am very impressed by their ability to see the important ideas that lie beneath the layers of technical definitions, notation and jargon. This, along with their tenacity, curiosity and ability has allowed us to make good progress on our project.\u201d<\/p>\n\n\n\n

Indeed, after nearly a year of research paired with unwavering determination, Hults applied some of Labb\u00e9\u2019s research to their own work and cracked the code.<\/p>\n\n\n\n

\u201cPenrose tilings have this nice self-similar structure that carries over from Penrose to Wang, so then by effect you get a bunch of nice properties of the Wang tilings. I used these properties to unequivocally prove the validity of results from my REU team and my original research to confirm the Markov partition for the Penrose shift,\u201d Hults said.<\/p>\n\n\n\n

\u201cIt\u2019s been really satisfying to see everything come together and have my perseverance pay off. I\u2019m excited for what comes next!\u201d<\/p>\n\n\n\n

Hults will be presenting their research at the Undergraduate Research Symposium on May 19. \u201cI\u2019m just really grateful to the Mary Gates Endowment for enabling me to spend my time doing research. Symbolic dynamical systems theory is super interesting to me, and I\u2019m going to use it in my future. I\u2019m happy that I\u2019ve been lucky enough to spend so much time learning about it.\u201d<\/p>\n","protected":false},"excerpt":{"rendered":"

Senior Harper Hults spent the past year on a daunting mathematical task: to prove the Markov partition for one of the most famous tilesets in the world, the Penrose tiles, is valid.<\/p>\n","protected":false},"author":16,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_is_archived":false,"_archived_contact_email":"","footnotes":""},"categories":[202,245,211,197,200,214,204],"tags":[],"school":[421],"class_list":["post-24496","post","type-post","status-publish","format-standard","hentry","category-campus-news","category-donors","category-honors-and-awards","category-news-releases","category-profiles","category-research","category-students","school-school-of-stem"],"acf":{"related_links":{"toggle_visibility":false,"link_1":null,"link_2":null,"link_3":null,"link_4":null,"link_5":null},"highlight_box":{"toggle_visibility":false,"title":"","content":"","button":null,"button_style":"angled-purple-button","button_screen_reader_text":""},"contact_type_1":{"toggle_visibility":true,"contact_title":"","email":"","phone":"","box":"","address_line_1":"","address_line_2":"","location":""},"contact_type_2":{"toggle_visibility":false,"contact_title":"","email":"","phone":"","box":"","address_line_1":"","address_line_2":"","location":""},"social_media":{"toggle_visibility":false,"facebook_url":"","instagram_url":"","linkedin_url":"","twitter_url":"","youtube_url":""},"blog_archive_sidebar_visibility":false},"yoast_head":"\nDetermined to solve complicated problems - News<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Determined to solve complicated problems - News\" \/>\n<meta property=\"og:description\" content=\"Senior Harper Hults spent the past year on a daunting mathematical task: to prove the Markov partition for one of the most famous tilesets in the world, the Penrose tiles, is valid.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems\" \/>\n<meta property=\"og:site_name\" content=\"News\" \/>\n<meta property=\"article:published_time\" content=\"2023-04-21T17:38:34+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-07-10T21:55:55+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.uwb.edu\/news\/wp-content\/uploads\/sites\/4\/2023\/05\/m2-hults-1.png\" \/>\n<meta name=\"author\" content=\"UWB Web\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"UWB Web\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems\"},\"author\":{\"name\":\"UWB Web\",\"@id\":\"https:\/\/www.uwb.edu\/news\/#\/schema\/person\/f75d5e6e475ec3bad5c3b86036641a79\"},\"headline\":\"Determined to solve complicated problems\",\"datePublished\":\"2023-04-21T17:38:34+00:00\",\"dateModified\":\"2023-07-10T21:55:55+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems\"},\"wordCount\":1113,\"image\":{\"@id\":\"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.uwb.edu\/news\/wp-content\/uploads\/sites\/4\/2023\/05\/m2-hults-1.png\",\"articleSection\":[\"Campus News\",\"Donors\",\"Honors and Awards\",\"News Releases\",\"Profiles\",\"Research\",\"Students\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems\",\"url\":\"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems\",\"name\":\"Determined to solve complicated problems - News\",\"isPartOf\":{\"@id\":\"https:\/\/www.uwb.edu\/news\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems#primaryimage\"},\"image\":{\"@id\":\"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.uwb.edu\/news\/wp-content\/uploads\/sites\/4\/2023\/05\/m2-hults-1.png\",\"datePublished\":\"2023-04-21T17:38:34+00:00\",\"dateModified\":\"2023-07-10T21:55:55+00:00\",\"author\":{\"@id\":\"https:\/\/www.uwb.edu\/news\/#\/schema\/person\/f75d5e6e475ec3bad5c3b86036641a79\"},\"breadcrumb\":{\"@id\":\"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems#primaryimage\",\"url\":\"https:\/\/www.uwb.edu\/news\/wp-content\/uploads\/sites\/4\/2023\/05\/m2-hults-1.png\",\"contentUrl\":\"https:\/\/www.uwb.edu\/news\/wp-content\/uploads\/sites\/4\/2023\/05\/m2-hults-1.png\",\"width\":571,\"height\":770},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.uwb.edu\/news\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Determined to solve complicated problems\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.uwb.edu\/news\/#website\",\"url\":\"https:\/\/www.uwb.edu\/news\/\",\"name\":\"News\",\"description\":\"Just another UW Bothell site\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.uwb.edu\/news\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.uwb.edu\/news\/#\/schema\/person\/f75d5e6e475ec3bad5c3b86036641a79\",\"name\":\"UWB Web\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.uwb.edu\/news\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/499869a0565f397f95a0641b3e7ac1cec2f5dd9ac0dc9dac3eaa2a158ab0c602?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/499869a0565f397f95a0641b3e7ac1cec2f5dd9ac0dc9dac3eaa2a158ab0c602?s=96&d=mm&r=g\",\"caption\":\"UWB Web\"},\"url\":\"https:\/\/www.uwb.edu\/news\/author\/uwbweb\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Determined to solve complicated problems - News","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems","og_locale":"en_US","og_type":"article","og_title":"Determined to solve complicated problems - News","og_description":"Senior Harper Hults spent the past year on a daunting mathematical task: to prove the Markov partition for one of the most famous tilesets in the world, the Penrose tiles, is valid.","og_url":"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems","og_site_name":"News","article_published_time":"2023-04-21T17:38:34+00:00","article_modified_time":"2023-07-10T21:55:55+00:00","og_image":[{"url":"https:\/\/www.uwb.edu\/news\/wp-content\/uploads\/sites\/4\/2023\/05\/m2-hults-1.png","type":"","width":"","height":""}],"author":"UWB Web","twitter_card":"summary_large_image","twitter_misc":{"Written by":"UWB Web","Est. reading time":"5 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems#article","isPartOf":{"@id":"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems"},"author":{"name":"UWB Web","@id":"https:\/\/www.uwb.edu\/news\/#\/schema\/person\/f75d5e6e475ec3bad5c3b86036641a79"},"headline":"Determined to solve complicated problems","datePublished":"2023-04-21T17:38:34+00:00","dateModified":"2023-07-10T21:55:55+00:00","mainEntityOfPage":{"@id":"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems"},"wordCount":1113,"image":{"@id":"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems#primaryimage"},"thumbnailUrl":"https:\/\/www.uwb.edu\/news\/wp-content\/uploads\/sites\/4\/2023\/05\/m2-hults-1.png","articleSection":["Campus News","Donors","Honors and Awards","News Releases","Profiles","Research","Students"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems","url":"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems","name":"Determined to solve complicated problems - News","isPartOf":{"@id":"https:\/\/www.uwb.edu\/news\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems#primaryimage"},"image":{"@id":"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems#primaryimage"},"thumbnailUrl":"https:\/\/www.uwb.edu\/news\/wp-content\/uploads\/sites\/4\/2023\/05\/m2-hults-1.png","datePublished":"2023-04-21T17:38:34+00:00","dateModified":"2023-07-10T21:55:55+00:00","author":{"@id":"https:\/\/www.uwb.edu\/news\/#\/schema\/person\/f75d5e6e475ec3bad5c3b86036641a79"},"breadcrumb":{"@id":"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems#primaryimage","url":"https:\/\/www.uwb.edu\/news\/wp-content\/uploads\/sites\/4\/2023\/05\/m2-hults-1.png","contentUrl":"https:\/\/www.uwb.edu\/news\/wp-content\/uploads\/sites\/4\/2023\/05\/m2-hults-1.png","width":571,"height":770},{"@type":"BreadcrumbList","@id":"https:\/\/www.uwb.edu\/news\/2023\/04\/21\/determined-to-solve-complicated-problems#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.uwb.edu\/news\/"},{"@type":"ListItem","position":2,"name":"Determined to solve complicated problems"}]},{"@type":"WebSite","@id":"https:\/\/www.uwb.edu\/news\/#website","url":"https:\/\/www.uwb.edu\/news\/","name":"News","description":"Just another UW Bothell site","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.uwb.edu\/news\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/www.uwb.edu\/news\/#\/schema\/person\/f75d5e6e475ec3bad5c3b86036641a79","name":"UWB Web","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.uwb.edu\/news\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/499869a0565f397f95a0641b3e7ac1cec2f5dd9ac0dc9dac3eaa2a158ab0c602?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/499869a0565f397f95a0641b3e7ac1cec2f5dd9ac0dc9dac3eaa2a158ab0c602?s=96&d=mm&r=g","caption":"UWB Web"},"url":"https:\/\/www.uwb.edu\/news\/author\/uwbweb"}]}},"_links":{"self":[{"href":"https:\/\/www.uwb.edu\/news\/wp-json\/wp\/v2\/posts\/24496","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.uwb.edu\/news\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.uwb.edu\/news\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.uwb.edu\/news\/wp-json\/wp\/v2\/users\/16"}],"replies":[{"embeddable":true,"href":"https:\/\/www.uwb.edu\/news\/wp-json\/wp\/v2\/comments?post=24496"}],"version-history":[{"count":10,"href":"https:\/\/www.uwb.edu\/news\/wp-json\/wp\/v2\/posts\/24496\/revisions"}],"predecessor-version":[{"id":28011,"href":"https:\/\/www.uwb.edu\/news\/wp-json\/wp\/v2\/posts\/24496\/revisions\/28011"}],"wp:attachment":[{"href":"https:\/\/www.uwb.edu\/news\/wp-json\/wp\/v2\/media?parent=24496"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.uwb.edu\/news\/wp-json\/wp\/v2\/categories?post=24496"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.uwb.edu\/news\/wp-json\/wp\/v2\/tags?post=24496"},{"taxonomy":"school","embeddable":true,"href":"https:\/\/www.uwb.edu\/news\/wp-json\/wp\/v2\/school?post=24496"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}