Research Interests:
One of my favorite things to explore is finding ways to create visual representations of complicated algebraic structures. I particularly love the world of algebraic combinatorics, especially when there are connections to cluster algebras and representation theory. Here is my PhD thesis titled "Higher Dimer Models in Cluster Algebras and Categorification of Non-Orientable Surfaces." My thesis defense slides are here!
Published Papers:
Twists, Higher Dimer Covers, and Web Duality for Grassmannian Cluster Algebras [Journal of Algebra](joint with Esther Banaian, Elise Catania, Christian Gaetz, Miranda Moore, and Gregg Musiker)
Double and Triple Dimer Partition Functions in Gr(3,n) [Algebraic Combinatorics](joint with Moriah Elkin and Gregg Musiker)
Marked Non-Orientable Surfaces and Cluster Categories via Symmetric Representations [Math Z](joint with Véronique Bazier-Matte and Aaron Chan)
Matrix Formulae and Skein Relations for Quasi-Cluster Algebras [SIGMA](joint with Cody Gilbert and McCleary Philbin)
Mixed Dimer Configuration Model for Type D Cluster Algebras [Electronic Journal of Combinatorics] (joint with Gregg Musiker)
Mixed Dimer Configuration Model for Type D Cluster Algebras II: Beyond the Acyclic Case [to appear in Electronic Journal of Combinatorics] (joint with Gregg Musiker and Libby Farrell)
Friezes over Z[√2] [to appear in Involve] (joint with Esther Banaian, Libby Farrell, Amy Tao, and Joy Zhichun Zhang)
Preprints:
Local Statistics for the M_n Dimer Model (joint with Nickolas Anderson, Moriah Elkin, Elizabeth Kelley and Nicholas Ovenhouse)
A Geometric Model for Semilinear Locally Gentle Algebras (joint with Esther Banaian, Raphael Bennett-Tennenhaus, and Karin Jacobsen)
Quivers from Non-Orientable Surfaces (joint with Véronique Bazier-Matte, Linda He, Ruiyan Huang, and Hanyi Luo)
Triangulations of Almost-Complete Graphs (joint with Padraic Bartlett, Kim Pham and Landon Settle)
Selected Research Talks:
A Geometric Model for Semilinear Locally Gentle Path Algebras
Seminar on Homological Algebra and Related Topics at University of Buenos Aires
UMN Student Combinatorics and Algebra Seminar
UMN Adult Combinatorics and Algebra Seminar
Dimers, SL_k Webs and Grassmannian Cluster Algebras
University of Oregon Combinatorics Seminar
University of Connecticut Algebra Seminar
University of Oregon RATHCOTh Seminar
Aarhus Homological Algebra Seminar
Dimers: Combinatorics, Representation Theory and Physics
CMS Winter Meeting on Cluster Algebras in Representation Theory
Mixed Dimer Configurations for Type D Cluster Algebras
Graduate Online Combinatorics Colloquium (video here!!)
Quasi-Cluster Algebras and Non-Orientable Surfaces
UC Berekeley Pre-Talk and Talk for Combinatorics Seminar
Flash Talks in Representation Theory
Current Projects:
Caldero-Chapoton Map for Gentle Algebras
joint with Esther Banaian, Azzurra Ciliberti, Illaria Di Dedda, Khrystyna Serhiyenko and Yadira Valdivieso Diaz
Quasi-Cluster Modular Groups
joint with James Hughes
Plane Partitions and Jack Combinatorics
joint with Kyla Pohl and Ben Young