36 citations · 166 across the 32 of their papers we have counts for
38 papers
Vanishing of higher Legendrian homology for rainbow closures
Roger Casals, Alexander Simons
We show that the higher Legendrian homology of any Legendrian link given by the rainbow closure of a positive braid must necessarily vanish. The result is proven in the most genera…
Categorical Lusztig cycles and weave schobers
Roger Casals, Merlin Christ
We establish the foundations of categorical weave calculus, developing the diagrammatic calculus of weaves and braid varieties within the study of Calabi-Yau triangulated categorie…
Comparing cluster algebras on braid varieties
Roger Casals, Pavel Galashin, Mikhail Gorsky +3
Braid varieties parametrize linear configurations of flags with transversality conditions dictated by positive braids. They include and generalize reduced double Bruhat cells, posi…
Demazure weaves for reduced plabic graphs (with a proof that Muller-Speyer twist is Donaldson-Thomas)
Roger Casals, Ian Le, Melissa Sherman-Bennett +1
First, this article develops the theory of weaves and their cluster structures for the affine cones of positroid varieties. In particular, we explain how to construct a weave from…
A Lagrangian filling for every cluster seed
Roger Casals, Honghao Gao
We show that each cluster seed in the augmentation variety is inhabited by an embedded exact Lagrangian filling. This resolves the matter of surjectivity of the map from Lagrangian…
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…
Conjugate Fillings and Legendrian Weaves
Roger Casals, Wenyuan Li
First, we show that conjugate Lagrangian fillings, associated to plabic graphs, and Lagrangian fillings obtained as Reeb pinching sequences are both Hamiltonian isotopic to Lagrang…
Cluster structures on braid varieties
Roger Casals, Eugene Gorsky, Mikhail Gorsky +3
We show the existence of cluster -structures and cluster Poisson structures on any braid variety, for any simple Lie group. The construction is achieved via weave calc…
Microlocal Theory of Legendrian Links and Cluster Algebras
Roger Casals, Daping Weng
We show the existence of quasi-cluster -structures and cluster Poisson structures on moduli stacks of sheaves with singular support in the alternating strand diagram o…
Stein traces and characterizing slopes
Roger Casals, John Etnyre, Marc Kegel
We show that there exists an infinite family of pairwise non-isotopic Legendrian knots in the standard contact 3-sphere whose Stein traces are equivalent. This is the first example…
Positroid Links and Braid varieties
Roger Casals, Eugene Gorsky, Mikhail Gorsky +1
We study braid varieties and their relation to open positroid varieties. We discuss four different types of braids associated to open positroid strata and show that their associate…
Dynamical Quantization of Contact Structures
Roger Casals, Gabriel Herczeg, Andrew Waldron
We construct a dynamical quantization for contact manifolds in terms of a flat connection acting on a Hilbert tractor bundle. We show that this contact quantization, which is indep…
Branched covering simply-connected 4-manifolds
David Auckly, R. Inanc Baykur, Roger Casals +3
We prove that any closed simply-connected smooth 4-manifold is 16-fold branched covered by a product of an orientable surface with the 2-torus, where the construction is natural wi…
Braid Loops with infinite monodromy on the Legendrian contact DGA
Roger Casals, Lenhard Ng
We present the first examples of elements in the fundamental group of the space of Legendrian links in the standard contact 3-sphere whose action on the Legendrian contact DGA is o…
Algebraic Weaves and Braid Varieties
Roger Casals, Eugene Gorsky, Mikhail Gorsky +1
In this manuscript we study braid varieties, a class of affine algebraic varieties associated to positive braids. Several geometric constructions are presented, including certain t…
Lagrangian Skeleta and Plane Curve Singularities
Roger Casals
We construct closed arboreal Lagrangian skeleta associated to links of isolated plane curve singularities. This yields closed arboreal Lagrangian skeleta for Weinstein pairs and We…
Legendrian Weaves: N-graph Calculus, Flag Moduli and Applications
Roger Casals, Eric Zaslow
We study a class of Legendrian surfaces in contact five-folds by encoding their wavefronts via planar combinatorial structures. We refer to these surfaces as Legendrian weaves, and…
Full Ellipsoid Embeddings and Toric Mutations
Roger Casals, Renato Vianna
This article introduces a new method to construct volume-filling symplectic embeddings of 4-dimensional ellipsoids by employing polytope mutations in toric and almost-toric varieti…
Infinitely many Lagrangian fillings
Roger Casals, Honghao Gao
We prove that all maximal-tb Legendrian torus links (n,m) in the standard contact 3-sphere, except for (2,m),(3,3),(3,4) and (3,5), admit infinitely many Lagrangian fillings in the…
The Legendrian Whitney trick
Roger Casals, Dishant M. Pancholi, Francisco Presas
In this article, we prove a Legendrian Whitney trick which allows for the removal of intersections between codimension-two contact submanifolds and Legendrian submanifolds, assumin…
Non-simplicity of isocontact embeddings in all higher dimensions
Roger Casals, John B. Etnyre
In this article we show that in any dimension there exist infinitely many pairs of formally contact isotopic isocontact embeddings into the standard contact sphere which are not co…
Transverse universal links
Roger Casals, John B. Etnyre
We show that there exists a transverse link in the standard contact structures on the 3-sphere such that all contact 3-manifolds are contact branched covers over this transverse li…
Loose Engel structures
Roger Casals, Álvaro del Pino, Francisco Presas
This article introduces the notion of a loose family of Engel structures and shows that two such families are Engel homotopic if and only if they are formally homotopic. This impli…
Classification of Engel Knots
Roger Casals, Álvaro del Pino
For any Engel 4-fold, we show that the scanning map from the space of Engel knots to the space of formal Engel knots is a weak homotopy equivalence when restricted to the complemen…