Cluster algebras from surfaces and their bases

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Kang, Wonwoo

Contributors dc:contributor

• Kedem, Rinat
• Yong, Alexander
• Di Francesco, Philippe
• Kelley, Elizabeth

• Cluster Algebra
• Combinatorics

Statement dc:rights

• Copyright 2025 Wonwoo Kang

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/129871

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F129871