I study knots and surfaces in low-dimensional contact and symplectic topology. My research centers on the construction and classification of exact Lagrangian fillings of Legendrian knots. I often use techniques from cluster theory to study these objects.
Decompositions of Augmentation Varieties via Weaves and Rulings (preprint 2025), with Johan Asplund, Orsola Capovilla-Searle, Caitlin Leverson, Wenyuan Li, and Angela Wu.
Exact Lagrangian Fillability of 3-braid Closures (preprint 2025), with Jiajie Ma.
Legendrian Doubles, Twist-Spuns, and Clusters, (preprint 2025), with Agniva Roy.
Legendrian Loops and Cluster Modular Groups, (preprint 2024).
Augmentations, Fillings, and Clusters for 2-bridge Links, Selecta Math. (accepted), (2025), with Orsola Capovilla-Searle and Daping Weng.
Lagrangian Fillings in A-type and their Kálmán Loop Orbits, Rev. Mat. Iberoam. 39-5 (2023), 1681–1723.
Weave Realizability for D-type, Algebraic & Geometric Topology 23-6 (2023), 2735--2776.
Constructing Lagrangian Fillings of Twist-spun Torus Links (in preparation; draft available upon request), with Vincent Chen, Patton Galloway, and Luciana Wei.
Spring 2025 Southeastern AMS Sectional: Invariants in Geometric Topology, Low Dimensions and Beyond - Non-orientable Exact Lagrangian Fillings and Cluster Structures
Spring 2024 Southeastern AMS Sectional: Special Session on Interactions of Contact and Symplectic Manifolds - Legendrian Doubles and Twist-spun Tori.
CMS 2023 Winter Meeting: Cluster Algebras in Representation Theory - Cluster Modular Groups of Braid Varieties.
Incheon National University 15th International Symposium on National Sciences - An Introduction to Cluster Structures from Legendrian Links.
LSU Geometry and Topology Seminar - Legendrian Loops and Cluster Modular Groups.
Geometric Topology Grad and Postdoc Seminar - An introduction to Legendrian Weaves.
Clusters and braids seminar, AIM program on link homology - Legendrian Weave Calculus and Clusters (video).