17 citations · 51 across the 15 of their papers we have counts for
15 papers
The entropy-degree theorem for Alexandrov spaces
P. Suárez-Serrato
We present the entropy-degree theorem for Lipschitz maps between Alexandrov spaces with curvature bounded below, extending the classical Besson--Courtois--Gallot entropy-rigidity r…
Modeling Social Systems: Transparency, Reproducibility, and Responsibility
Maximino Aldana, Roni Barak Ventura, Heather Z. Brooks +13
Mathematical models of complex social systems can enrich social scientific theory, inform interventions, and shape policy. From voting behavior to economic inequality and urban dev…
Volume entropy and rigidity for RCD-spaces
Chris Connell, Xianzhe Dai, Jesús Núñez-Zimbrón +3
We develop the barycenter technique of Besson--Courtois--Gallot so that it can be applied on RCD metric measure spaces. Given a continuous map from a non-collapsed RCD$(-(N-1),…
A conservative Turing complete flow
Pablo Suárez-Serrato
We present a Turing complete, volume preserving, smooth flow on the -sphere.
Turing approximations, toric isometric embeddings & manifold convolutions
P. Suárez-Serrato
Convolutions are fundamental elements in deep learning architectures. Here, we present a theoretical framework for combining extrinsic and intrinsic approaches to manifold convolut…
Areas on the space of smooth probability density functions on
J. C. Ruíz-Pantaleón, P. Suárez-Serrato
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…
Collapsing and group growth as obstructions to Einstein metrics on some smooth 4-manifolds
Haydeé Contreras Peruyero, Pablo Suárez-Serrato
We show that a combination of collapsing and excessive growth from the fundamental group impedes the existence of Einstein metrics on several families of smooth four-manifolds. The…
On Computational Poisson Geometry II: Numerical Methods
M. Evangelista-Alvarado, J. C. Ruíz-Pantaleón, P. Suárez-Serrato
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…
Maximal volume entropy rigidity for spaces
Chris Connell, Xianzhe Dai, Jesús Núñez-Zimbrón +3
For -dimensional Riemannian manifolds with Ricci curvature bounded below by , the volume entropy is bounded above by . If is compact, it is known that the e…
A note on collapse, entropy, and vanishing of the Yamabe invariant of symplectic 4-manifolds
Pablo Suárez-Serrato, Rafael Torres
We make use of -structures and technology developed by Paternain - Petean to compute minimal entropy, minimal volume, and Yamabe invariant of symplectic 4-manifolds, a…
On Higher Graph Manifolds
Chris Connell, Pablo Suárez-Serrato
In this short note we introduce higher graph manifolds and use a version of the barycenter technique to characterize when they undergo volume collapse. In the case when the pure pi…
Dynamics and zeta functions on conformally compact manifolds
Julie Rowlett, Pablo Suárez-Serrato, Samuel Tapie
In this note, we study the dynamics and associated zeta functions of conformally compact manifolds with variable negative sectional curvatures. We begin with a discussion of a larg…
A smooth codimension-one foliation of the five-sphere by symplectic leaves
Pablo Suárez-Serrato, Alberto Verjovsky
We construct a smooth codimension-one foliation on the five-sphere in which every leaf is a symplectic four-manifold and such that the symplectic structure varies smoothly. Our con…
An essential relation between Einstein metrics, volume entropy, and exotic smooth structures
Michael Brunnbauer, Masashi Ishida, Pablo Suárez-Serrato
We show that the minimal volume entropy of closed manifolds remains unaffected when nonessential manifolds are added in a connected sum. We combine this result with the stable coho…
Minimal entropy and geometric decompositions in dimension four
Pablo Suárez-Serrato
We show vanishing results about the infimum of the topological entropy of the geodesic flow of homogeneous smooth four manifolds. We prove that any closed oriented geometric four m…