James Michael Hughes

Assistant Research Professor of Mathematics

james.hughes@duke.edu

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Selected Publications

Decompositions of augmentation varieties via weaves and rulings

Preprint · August 27, 2025 Link to item Cite

Legendrian doubles, twist spuns, and clusters

Preprint · May 23, 2025 Link to item Cite

Legendrian loops and cluster modular groups

Preprint · March 19, 2024 Cite

Weave-realizability for D–type

Journal Article Algebraic & Geometric Topology · September 7, 2023 Full text Cite

Augmentations, Fillings, and Clusters for 2-Bridge Links

Preprint · August 22, 2023 Link to item Cite

Lagrangian fillings in $A$-type and their Kálmán loop orbits

Journal Article Revista Matemática Iberoamericana · July 4, 2023 We compare two constructions of exact Lagrangian fillings of Legendrian positive braid closures, the Legendrian weaves of Casals–Zaslow, and the decomposable Lagrangian fillings of Ekholm–Honda–Kálmán, and show that they coinci ... Full text Cite

Exact Lagrangian fillability of 3-braid closures

Journal Article Bulletin of the London Mathematical Society Open Access Link to item Cite

Exact Lagrangian fillings of twist-spun torus links

Journal Article We construct exact Lagrangian fillings of Legendrian torus links Λ(k,n−k) that are fixed by a Legendrian loop that acts by 2πℓ/n rotation. Using these rotationally symmetric fillings, we produce fillings of the corresponding Legendrian twist-spun tori. Our ... Open Access Link to item Cite