Director of Research (if dissertation) or Advisor (if thesis)
Kedem, Rinat
Doctoral Committee Chair(s)
Yong, Alexander
Committee Member(s)
Di Francesco, Philippe
Kelley, Elizabeth
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Cluster Algebra, Combinatorics
Abstract
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.
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