Research
Research
Cluster Algebra
Representation Theory
My research is about finding out combinatorial interpretation of cluster algebra. I am interested in a combinatorial formula that allows for the Laurent expansion of a cluster variable within any cluster algebra originating from a punctured orbifold. The other thing I'm interested in is a combinatorial expansion formula that provides skein relations for elements within a cluster algebra derived from a punctured surface, specifically for cluster algebras of surface type.
Accelerated Evaluation of Ollivier-Ricci Curvature Lower Bounds: Bridging Theory and Computation (with H. Park)
preprint: arXiv: 2405.13302 (pdf)
Skein relations for punctured surfaces (with E. Banaian and E. Kelley)
Submitted, preprint available at: arXiv: 2409.04957 (pdf)
Skein relations for punctured surfaces (with E. Banaian and E. Kelley), Seminaire Lotharingien de Combinatoire in the proceedings for Formal Power Series and Algebraic Combinatorics 2024, Issue 91B
Skein Relations for Punctured Surfaces(Notes).
Given at: DA Seminar, Yonsei University (April 2024)
Pusan National University (May 2024)
IBS (June 2024) (Youtube)
Seminar in Cluster Algebra, Michigan State University (October 2024)
UCLA Combinatorics Forum, UCLA (Novermber 2024)
UConn Algebra Seminar, University of Connecticut (February 2025)
Skein Relations for Punctured Surfaces, International Conferences on Formal Power Series and Algebraic Combinatorics(FPSAC 2024), Ruhr-Universität Bochum, July 2024