arXiv subjects

P. Suárez-Serrato

Publications and source records attributed to P. Suárez-Serrato.

14 recordsLinked to original sources

arXiv2026

The entropy-degree theorem for Alexandrov spaces

We present the entropy-degree theorem for Lipschitz maps between Alexandrov spaces with curvature bounded below, extending the classical Besson--Courtois--Gallot entropy-rigidity results to this singular setting. The proof requires a new degree theorem for Alexandrov spaces, developed using the Ambrosio--Kirchheim theory of integral currents, showing the equivalence between analytical and topological degrees. Applications include geometric obstructions for negatively curved Einstein metrics on 4-orbifolds, volume bounds for cone-manifolds, quantitative inequalities for hyperbolic convex cores, and lower bounds on the asymptotic translation lengths of end-periodic surface homeomorphisms. We show that entropy-volume minimization under uniform lower curvature bounds obstructs to the formation of metric singularities in Gromov--Hausdorff limits, prove an Alexandrov boundary rigidity theorem, and establish volume minima for cone manifolds and cone orbifolds.

math.DG↗

arXiv2025

Space filling positionality and the Spiroformer

Transformers excel when dealing with sequential data. Generalizing transformer models to geometric domains, such as manifolds, we encounter the problem of not having a well-defined global order. We propose a solution with attention heads following a space-filling curve. As a first experimental example, we present the Spiroformer, a transformer that follows a polar spiral on the $2$-sphere.

cs.LG↗

arXiv2025

SymFlux: deep symbolic regression of Hamiltonian vector fields

We present SymFlux, a novel deep learning framework that performs symbolic regression to identify Hamiltonian functions from their corresponding vector fields on the standard symplectic plane. SymFlux models utilize hybrid CNN-LSTM architectures to learn and output the symbolic mathematical expression of the underlying Hamiltonian. Training and validation are conducted on newly developed datasets of Hamiltonian vector fields, a key contribution of this work. Our results demonstrate the model's effectiveness in accurately recovering these symbolic expressions, advancing automated discovery in Hamiltonian mechanics.

cs.LG↗

arXiv2024

Zero entropy on entire Grauert tubes

On a real analytic Riemannian manifold a Grauert tube is an uniquely adapted complex structure defined on the tangent bundle. It is called entire if it may be defined on the whole tangent bundle. Here, we show that the geodesic flow of an analytic manifold with entire Grauert tube has zero topological entropy. Several consequences then follow. We find that Grauert tubes of convex analytic hypersurfaces of ${\bf R}^3$ are generically finite. We give a complete classification of 3-manifolds with entire Grauert tube, showing that these are precisely the 3-manifolds that admit good complexifications. Assuming a manifold has entire Grauert tube, we offer classification statements for several families of smooth 4-manifolds, determine all such simply connected 5-manifolds, and offer new topological restrictions for certain manifolds with infinite fundamental groups. Using these results we present an example of a simply connected and rationally elliptic 5-manifold which nonetheless does not admit any metric with entire Grauert tube.

math.DG↗

arXiv2024

Poisson structures on wrinkled fibrations

We provide local formulæ for Poisson bivectors and symplectic forms on the leaves of Poisson structures associated to wrinkled fibrations on smooth $4$--manifolds.

math.SG↗

arXiv2024

Asymptotic dimension and geometric decompositions in dimensions 3 and 4

We show that the fundamental groups of smooth $4$-manifolds that admit geometric decompositions in the sense of Thurston have asymptotic dimension at most four, and equal to 4 when aspherical. We also show that closed $3$-manifold groups have asymptotic dimension at most 3. Our proof method yields that the asymptotic dimension of closed $3$-dimensional Alexandrov spaces is at most 3. We thus obtain that the Novikov conjecture holds for closed $4$-manifolds with such a geometric decomposition and closed $3$-dimensional Alexandrov spaces. Consequences of these results include a vanishing result for the Yamabe invariant of certain $0$-surgered geometric $4$-manifolds and the existence of zero in the spectrum of aspherical smooth $4$-manifolds with a geometric decomposition.

math.GT↗

arXiv2022

Areas on the space of smooth probability density functions on $S^2$

We present symbolic and numerical methods for computing Poisson brackets on the spaces of measures with positive densities of the plane, the 2-torus, and the 2-sphere. We apply our methods to compute symplectic areas of finite regions for the case of the 2-sphere, including an explicit example for Gaussian measures with positive densities.

math.SG↗

arXiv2021

Turing approximations, toric isometric embeddings & manifold convolutions

Convolutions are fundamental elements in deep learning architectures. Here, we present a theoretical framework for combining extrinsic and intrinsic approaches to manifold convolution through isometric embeddings into tori. In this way, we define a convolution operator for a manifold of arbitrary topology and dimension. We also explain geometric and topological conditions that make some local definitions of convolutions which rely on translating filters along geodesic paths on a manifold, computationally intractable. A result of Alan Turing from 1938 underscores the need for such a toric isometric embedding approach to achieve a global definition of convolution on computable, finite metric space approximations to a smooth manifold.

math.DG↗

arXiv2021

On Computational Poisson Geometry II: Numerical Methods

We present twelve numerical methods for evaluation of objects and concepts from Poisson geometry. We describe how each method works with examples, and explain how it is executed in code. These include methods that evaluate Hamiltonian and modular vector fields, compute the image under the coboundary and trace operators, the Lie bracket of differential 1-forms, gauge transformations, and normal forms of Lie-Poisson structures on $\mathbf{R}^{3}$. The complexity of each of our methods is calculated, and we include experimental verifications on examples in dimensions two and three.

math.DG↗

arXiv2019

On Computational Poisson Geometry I: Symbolic Foundations

We present a computational toolkit for (local) Poisson-Nijenhuis calculus on manifolds. Our python module $\textsf{PoissonGeometry}$ implements our algorithms, and accompanies this paper. We include two examples of how our methods can be used, one for gauge transformations of Poisson bivectors in dimension 3, and a second one that determines parametric Poisson bivector fields in dimension 4.

math.DG↗

arXiv2019

BoostNet: Bootstrapping detection of socialbots, and a case study from Guatemala

We present a method to reconstruct networks of socialbots given minimal input. Then we use Kernel Density Estimates of Botometer scores from 47,000 social networking accounts to find clusters of automated accounts, discovering over 5,000 socialbots. This statistical and data driven approach allows for inference of thresholds for socialbot detection, as illustrated in a case study we present from Guatemala.

cs.CY↗

arXiv2018

Contour Parametrization via Anisotropic Mean Curvature Flows

We present a new implementation of anisotropic mean curvature flow for contour recognition. Our procedure couples the mean curvature flow of planar closed smooth curves, with an external field from a potential of point-wise charges. This coupling constrains the motion when the curve matches a picture placed as background. We include a stability criteria for our numerical approximation.

math.DG↗

arXiv2018

Socialbots whitewashing contested elections; a case study from Honduras

We analyze socialbots active tweeting in relation to Juan Orlando Hernández, the recently re-elected president of Honduras. We find a clear bimodal separation between humans and bots, using Botometer and its classifiers. Around one hundred separate communities of socialbots are identified and visualized, detected through the analysis of temporally coordinated retweets.

cs.CY↗

arXiv2017

Socialbots supporting human rights

Socialbots, or non-human/algorithmic social media users, have recently been documented as competing for information dissemination and disruption on online social networks. Here we investigate the influence of socialbots in Mexican Twitter in regards to the "Tanhuato" human rights abuse report. We analyze the applicability of the BotOrNot API to generalize from English to Spanish tweets and propose adaptations for Spanish-speaking bot detection. We then use text and sentiment analysis to compare the differences between bot and human tweets. Our analysis shows that bots actually aided in information proliferation among human users. This suggests that taxonomies classifying bots should include non-adversarial roles as well. Our study contributes to the understanding of different behaviors and intentions of automated accounts observed in empirical online social network data. Since this type of analysis is seldom performed in languages different from English, the proposed techniques we employ here are also useful for other non-English corpora.

cs.CY↗