{"id":11412,"date":"2024-10-08T09:00:20","date_gmt":"2024-10-08T14:00:20","guid":{"rendered":"https:\/\/www.wisconsin.edu\/all-in-wisconsin-new\/?post_type=campus_story&p=11412"},"modified":"2024-10-08T09:00:20","modified_gmt":"2024-10-08T14:00:20","slug":"from-piano-to-proofs-uwl-alum-and-mathematician-breaks-ground-on-40-year-old-knot-theory-mystery","status":"publish","type":"campus_story","link":"https:\/\/www.wisconsin.edu\/all-in-wisconsin\/story\/from-piano-to-proofs-uwl-alum-and-mathematician-breaks-ground-on-40-year-old-knot-theory-mystery\/","title":{"rendered":"From piano to proofs: UWL alum and mathematician breaks ground on 40-year-old knot theory mystery"},"content":{"rendered":"
\n
\"Photo<\/a>
Isaac Sundberg, a postdoctoral fellow at the Max Planck Institute for Mathematics in Germany, graduated from UWL in 2016 with a major in mathematics and a minor in computer science. Sundberg studies low-dimensional topology with a focus on 4D knot theory. Photo courtesy of Archives of the Mathematisches Forschungsinstitut Oberwolfach.<\/figcaption><\/figure>\n

For 40 years, mathematicians around the world grappled with a challenging problem in knot theory. Today, that problem has been solved, thanks to the groundbreaking work of Isaac Sundberg, a 2016 graduate of UW-La Crosse\u2019s mathematics program.<\/p>\n

Sundberg, now a post-doctoral fellow at the Max Planck Institute for Mathematics in Germany, has made significant strides in knot theory, a branch of mathematics within topology. Their recent research, which has garnered attention from esteemed math and science publications like\u00a0Quanta Magazine<\/a>\u00a0and\u00a0AMS: Math in the Media<\/a>, identifies a pair of Seifert surfaces that retain distinct differences even when projected into the fourth dimension.<\/p>\n

\u201cFor decades, mathematicians debated whether certain Seifert surfaces, which exhibit three-dimensional differences, would preserve those differences when extended to 4D,\u201d Sundberg explains. \u201cI never anticipated solving it in my lifetime. When it happened, the problem consumed my thoughts. I couldn\u2019t sleep.\u201d<\/p>\n

The breakthrough emerged from Sundberg’s use of Khovanov Homology, a modern tool in mathematics. \u201cIt has been a question of mine how far can we push this tool to discover new 4D phenomena,\u201d says Sundberg.<\/p>\n<\/div>\n

\n

Piano prelude<\/h3>\n

Sundberg\u2019s journey into mathematics began unexpectedly. Originally a piano student at UWL, they shifted focus to mathematics after a series of academic pivots, including studies in physics and computer science.<\/p>\n

\"\"
Sundberg, left, teaches mathematics. Inspired by UWL faculty members, Sundberg sought to emulate their support and teaching excellence by going on to earn a graduate degree in mathematics.<\/em><\/figcaption><\/figure>\n

 <\/p>\n

Tushar Das, UWL professor of Mathematics & Statistics, recalls first meeting Sundberg at the La Crosse People\u2019s Food Co-op. The two talked about their common love for playing piano.<\/p>\n

\u201cI had played since I was a child and had very similar plans at around Isaac\u2019s age, my mother being a piano teacher in Calcutta was a great boon. So I gently suggested to Isaac that I was confident that he would find mathematics at least as beautiful, challenging, and creative as I did, and that he should take some math classes to confirm my suspicions,\u201d says Das.<\/p>\n

Sundberg\u2019s interest in topology was sparked by a special topics class organized by UWL Professors Whitney George and Das pro-bono after several students expressed interest. This introduced them to the field\u2019s unique approach to geometric problems.<\/p>\n

The class would meet once or twice a week in seminar format, and the group would work through textbook problems together. Unlike a typical math lecture where a faculty member leads the discussion, here the math students presented the problems they were learning and where they were struggling to the professors.<\/p>\n

\u201cIt was amazing because that is how math research works,\u201d says Sundberg. \u201cIt gave me a taste of how to dig into something on my own and explain it to someone else.\u201d<\/p>\n

Often other faculty and students would join the seminars, which led to enhanced curiosity, engagement, and confidence throughout, says Das. These seminar classes eventually led to George and Das creating a brand new MTH 415 Topology course that is now offered each spring semester.<\/p>\n

This exposure to topology led Sundberg to develop a deep passion for the field that often involves visualizing complex problems rather than relying on numerical calculations. As a UWL student, Sundberg would take a walk through the woods or draw a picture to work out a particular problem. \u201cI got hooked on doing these problems in my head, and it grew into a passion of mine,\u201d says Sundberg.<\/p>\n

During their undergraduate years, Sundberg collaborated with Robert Allen, UWL\u2019s interim associate dean of the College of Science and Health, on Sundberg\u2019s first published mathematics paper.<\/p>\n

\u201cRobert was an amazing, supportive role model,\u201d says Sundberg. \u201cI learned about the whole process of mathematics research \u2014 coming up with questions, trying to solve them, developing proofs others can read, and turning that into a document that can be published.\u201d<\/p>\n

Inspired by UWL faculty members such as Allen, George, Das, Eddie Kim, and former faculty member Ted Wendt, Sundberg sought to emulate their support and teaching excellence. This led Sundberg to graduate school in mathematics and eventually a post-doctoral fellowship at the Max Planck Institute, one of the world\u2019s premier mathematics research institutions. They also maintain a part-time teaching position at the University of Bonn.<\/p>\n

Sundberg\u2019s recent achievement in solving the knot theory problem was a moment of fulfillment. \u201cIt was surreal to solve a problem I had dreamed about for so long,\u201d they reflect.<\/p>\n

The collaborative effort, which included contributions from friend and colleague Maggie Miller, resulted in a significant paper that addresses the longstanding mathematical question.<\/p>\n

In July, Sundberg returned to the U.S. for a visit, reconnecting with family, friends, and UWL faculty. \u201cThe Mathematics Department at UWL provided incredible support throughout my journey,\u201d says Sundberg. \u201cThey encouraged me through failures and successes alike. They are role models who support you throughout your career. I wouldn\u2019t be here without them.\u201d<\/p>\n

What is topology?<\/h3>\n

Knot theory, within the branch of mathematics called Topology, was something Sundberg had never heard of until studying mathematics as an undergraduate at UW-La Crosse. Not the typical math of numbers and equations, topology is the study of geometric objects and how their properties are preserved through deformations, such as stretching, twisting, and bending.<\/span><\/span><\/p>\n

Learn more about\u00a0UWL Mathematics & Statistics<\/a>.\u00a0<\/span><\/span><\/p>\n<\/div>\n

\n

Written by UW-La Crosse<\/p>\n

Link to original story: https:\/\/www.uwlax.edu\/news\/posts\/from-piano-to-proofs\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

For 40 years, mathematicians around the world grappled with a challenging problem in knot theory. Today, that problem has been solved, thanks to the groundbreaking work of Isaac Sundberg, a 2016 graduate of UW-La Crosse\u2019s mathematics program. Sundberg, now a post-doctoral fellow at the Max Planck Institute for Mathematics in Germany, has made significant strides […]<\/p>\n","protected":false},"author":15,"featured_media":11415,"comment_status":"closed","ping_status":"closed","template":"","institution":[104],"story_category":[],"class_list":["post-11412","campus_story","type-campus_story","status-publish","has-post-thumbnail","hentry","institution-uw-la-crosse"],"_links":{"self":[{"href":"https:\/\/www.wisconsin.edu\/all-in-wisconsin\/wp-json\/wp\/v2\/campus_story\/11412","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wisconsin.edu\/all-in-wisconsin\/wp-json\/wp\/v2\/campus_story"}],"about":[{"href":"https:\/\/www.wisconsin.edu\/all-in-wisconsin\/wp-json\/wp\/v2\/types\/campus_story"}],"author":[{"embeddable":true,"href":"https:\/\/www.wisconsin.edu\/all-in-wisconsin\/wp-json\/wp\/v2\/users\/15"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wisconsin.edu\/all-in-wisconsin\/wp-json\/wp\/v2\/comments?post=11412"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wisconsin.edu\/all-in-wisconsin\/wp-json\/wp\/v2\/media\/11415"}],"wp:attachment":[{"href":"https:\/\/www.wisconsin.edu\/all-in-wisconsin\/wp-json\/wp\/v2\/media?parent=11412"}],"wp:term":[{"taxonomy":"institution","embeddable":true,"href":"https:\/\/www.wisconsin.edu\/all-in-wisconsin\/wp-json\/wp\/v2\/institution?post=11412"},{"taxonomy":"story_category","embeddable":true,"href":"https:\/\/www.wisconsin.edu\/all-in-wisconsin\/wp-json\/wp\/v2\/story_category?post=11412"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}