{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/129871"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/129871","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Cluster algebras from surfaces and their bases","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","abstract_has_math":false,"creators":["Kang, Wonwoo"],"institution":"University of Illinois Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Kedem, Rinat","Yong, Alexander","Di Francesco, Philippe","Kelley, Elizabeth"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-07-15","date_published":"2025-07-15","updated_at":"2026-07-22T22:25:06Z","subjects":["Cluster Algebra","Combinatorics"],"languages":["en","eng"],"rights":["Copyright 2025 Wonwoo Kang"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/129871","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kedem, Rinat","Yong, Alexander","Di Francesco, Philippe","Kelley, Elizabeth"]},{"key":"dc:creator","label":"Author","values":["Kang, Wonwoo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-07-15","2025-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Cluster Algebra","Combinatorics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2025 Wonwoo Kang"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/129871"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","The student, Wonwoo Kang, accepted the attached license on 2025-07-14 at 16:54.","The student, Wonwoo Kang, submitted this Dissertation for approval on 2025-07-14 at 16:56.","This Dissertation was approved for publication on 2025-07-15 at 11:13.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22531 on 2025-10-20 at 16:57:53","In this dissertation, we establish results concerning the combinatorial interpretation of cluster algebras from surfaces. We examine cluster algebras from surfaces and their associated skein relations, providing explicit formulas for these relations. This work demonstrates that the bangle and bracelet sets form spanning sets for cluster algebras from punctured surfaces. Furthermore, for surfaces with boundary and closed surfaces of genus 0, we show that bangle set and bracelet set constitute bases. The material presented here is based on a collaboration with Esther Banaian and Elizabeth Kelley."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Cluster algebras from surfaces and their bases"]}]}],"canonical_facts":{"dc:contributor":["Kedem, Rinat","Yong, Alexander","Di Francesco, Philippe","Kelley, Elizabeth"],"dc:creator":["Kang, Wonwoo"],"dc:date":["2025-07-15","2025-08"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","The student, Wonwoo Kang, accepted the attached license on 2025-07-14 at 16:54.","The student, Wonwoo Kang, submitted this Dissertation for approval on 2025-07-14 at 16:56.","This Dissertation was approved for publication on 2025-07-15 at 11:13.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22531 on 2025-10-20 at 16:57:53","In this dissertation, we establish results concerning the combinatorial interpretation of cluster algebras from surfaces. We examine cluster algebras from surfaces and their associated skein relations, providing explicit formulas for these relations. This work demonstrates that the bangle and bracelet sets form spanning sets for cluster algebras from punctured surfaces. Furthermore, for surfaces with boundary and closed surfaces of genus 0, we show that bangle set and bracelet set constitute bases. The material presented here is based on a collaboration with Esther Banaian and Elizabeth Kelley."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/129871"],"dc:language":["en","eng"],"dc:rights":["Copyright 2025 Wonwoo Kang"],"dc:subject":["Cluster Algebra","Combinatorics"],"dc:title":["Cluster algebras from surfaces and their bases"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:06Z"}