9 citations · 16 across the 19 of their papers we have counts for
19 papers
Convex hypersurfaces and robust heterodimensional dynamics
Julian Chaidez, Michael Huang
We prove that any closed orientable hypersurface in a contact manifold of dimension five or greater is isotopic to a robustly non-convex hypersurface via an arbitrarily -small…
Conformally symplectic topology from a dynamical viewpoint
Julian Chaidez
This survey article discusses the emerging interaction between conformally symplectic topology and dynamics, with a focus on recent developments in convex hypersurface theory.
Pseudo-Anosov Reeb flows and contact structures
Julian Chaidez, Yijie Pan
We introduce the notion of a pseudo-Anosov contact structure, which admits a type of singular contact form with pseudo-Anosov Reeb flow. We prove that contact homology detects the…
On dynamical invariants of coadjoint orbits of 3D volume-preserving diffeomorphisms
Robert Cardona, Julian Chaidez, Francisco Torres de Lizaur
The helicity, or asymptotic linking number, is a functional of exact volume-preserving vector fields on 3-manifolds, invariant under volume-preserving transformations. It is known…
On Zoll Contact 5-Spheres
Julian Chaidez, Shira Tanny
We prove that any contact form on the standard contact 5-sphere with Zoll Reeb flow is strictly contactomorphic to a scaling of the standard Zoll contact form.
Contact homology and linearization without dga homotopies
Julian Chaidez
This article clarifies the status of linearized contact homology given the foundations of the contact dg-algebra established by Pardon. In particular, we prove that the set of isom…
Robustly non-convex hypersurfaces in contact manifolds
Julian Chaidez
We construct the first examples of hypersurfaces in any contact manifold of dimension 5 and larger that cannot be -approximated by convex hypersurfaces, contrasting sharply wi…
Elementary SFT Spectral Gaps And The Strong Closing Property
Julian Chaidez, Shira Tanny
We formulate elementary SFT spectral invariants of a large class of symplectic cobordisms and stable Hamiltonian manifolds, in any dimension. We give criteria for the strong closin…
Combed Trisection Diagrams and Non-Semisimple 4-Manifold Invariants
Julian Chaidez, Jordan Cotler, Shawn X. Cui
Given a triple of (possibly non-semisimple) Hopf algebras equipped with pairings satisfying a set of properties, we describe a construction of an associated smooth, scalar inva…
Legendrian embedded contact homology
Julian Chaidez, Oliver Edtmair, Luya Wang +2
We give a construction of embedded contact homology (ECH) for a contact -manifold with convex sutured boundary and a pair of Legendrians and contained in $\parti…
Newton-Okoukov bodies and symplectic embeddings into non-toric rational surfaces
Julian Chaidez, Ben Wormleighton
We develop new methods of both constructing and obstructing symplectic embeddings into non-toric rational surfaces using the theory of Newton-Okoukov bodies. Applications include s…
Contact homology and higher dimensional closing lemmas
Julian Chaidez, Ipsita Datta, Rohil Prasad +1
We develop methods for studying the smooth closing lemma for Reeb flows in any dimension using contact homology. As an application, we prove a conjecture of Irie, stating that the…
The Ruelle Invariant And Convexity In Higher Dimensions
Julian Chaidez, Oliver Edtmair
We construct the Ruelle invariant of a volume preserving flow and a symplectic cocycle in any dimension and prove several properties. In the special case of the linearized Reeb flo…
Lattice Formulas For Rational SFT Capacities
Julian Chaidez, Ben Wormleighton
We initiate the study of the rational SFT capacities of Siegel using tools in toric algebraic geometry. In particular, we derive new (often sharp) bounds for the RSFT capacities of…
ECH embedding obstructions for rational surfaces
Julian Chaidez, Ben Wormleighton
Let be a smooth rational surface or a possibly singular toric surface with ample divisor . We show that a family of ECH-based, algebro-geometric invariants $c^{\text{alg…
Computing Reeb dynamics on 4d convex polytopes
Julian Chaidez, Michael Hutchings
We study the combinatorial Reeb flow on the boundary of a four-dimensional convex polytope. We establish a correspondence between "combinatorial Reeb orbits" for a polytope, and or…
4-Manifold Invariants From Hopf Algebras
Julian Chaidez, Jordan Cotler, Shawn X. Cui
The Kuperberg invariant is a topological invariant of closed 3-manifolds based on finite-dimensional Hopf algebras. In this paper, we initiate the program of constructing 4-manifol…
Essential tori in spaces of symplectic embeddings
Julian Chaidez, Mihai Munteanu
Given two --dimensional symplectic ellipsoids whose symplectic sizes satisfy certain inequalities, we show that a certain map from the --torus to the space of symplectic emb…
Associative Arrays: Unified Mathematics for Spreadsheets, Databases, Matrices, and Graphs
Jeremy Kepner, Julian Chaidez, Vijay Gadepally +1
Data processing systems impose multiple views on data as it is processed by the system. These views include spreadsheets, databases, matrices, and graphs. The common theme amongst…