activity
20202026
most citedOn Newton polytopes of Lagrangian augmentations

4 citations · 4 across the 7 of their papers we have counts for

collaborators

8 papers

math.SG2026

On Ruling polynomials of Legendrian links

Orsola Capovilla-Searle, Yu Pan

The ruling polynomial is a Legendrian invariant that is closely related to the augmentation variety of the Legendrian. We characterize all graded and ungraded ruling polynomials, a…

math.SG2025

Decompositions of augmentation varieties via weaves and rulings

Johan Asplund, Orsola Capovilla-Searle, James Hughes +3

The braid variety of a positive braid and the augmentation variety of a Legendrian link both admit decompositions coming from weaves and rulings, respectively. We prove that these…

math.SG2023

Augmentations, Fillings, and Clusters for 2-Bridge Links

Orsola Capovilla-Searle, James Hughes, Daping Weng

We produce the first examples relating non-orientable exact Lagrangian fillings of Legendrian links to cluster theory, showing that the ungraded augmentation variety of certain max…

math.SG2023★ 4 cited

On Newton polytopes of Lagrangian augmentations

Orsola Capovilla-Searle, Roger Casals

This note explores the use of Newton polytopes in the study of Lagrangian fillings of Legendrian submanifolds. In particular, we show that Newton polytopes associated to augmented…

math.SG2023

Lagrangian cobordism of positroid links

Johan Asplund, Youngjin Bae, Orsola Capovilla-Searle +3

Casals-Gorsky-Gorsky-Simental realized all positroid strata of the complex Grassmannian as augmentation varieties of Legendrians called positroid links. We prove that the partial o…

math.SG2022

Obstructions to reversing Lagrangian surgery in Lagrangian fillings

Orsola Capovilla-Searle, Noémie Legout, Maÿlis Limouzineau +3

Given an immersed, Maslov-, exact Lagrangian filling of a Legendrian knot, if the filling has a vanishing index and action double point, then through Lagrangian surgery it is po…