Pablo Suárez-Serrato

On the Influence of Social Bots in Online Protests

Social bots can affect online communication among humans. We study this phenomenon by focusing on #YaMeCanse, the most active protest hashtag in the history of Twitter in Mexico. Accounts using the hashtag are classified using the BotOrNot bot detection tool. Our preliminary analysis suggests that bots played a critical role in disrupting online communication about the protest movement.

Minimal entropy and geometric decompositions in dimension four

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-manifold has zero minimal entropy if and only if it has zero simplicial volume. We also show that if a four-manifold M admits a geometric decomposition in the sense of Thurston and does not have geometric pieces modelled on hyperbolic four-space H 4 , the complex hyperbolic plane H 2 or the product of two hyperbolic planes H 2 H 2 then M admits an F ‐structure. It follows that M has zero minimal entropy and collapses with curvature bounded from below. We then analyse whether or not M admits a metric whose topological entropy coincides with the minimal entropy of M and provide new examples of manifolds for which the minimal entropy problem cannot be solved. 37B40, 57M50; 22F30, 53D25

Poisson Structures on Smooth 4–Manifolds

We show that every closed oriented smooth 4-manifold admits a complete singular Poisson structure in each homotopy class of maps to the 2-sphere. The rank of this structure is 2 outside a small singularity set, which consists of finitely many circles and isolated points. The Poisson bivector vanishes on the singularities, where we give its local form explicitly.

A note on collapse, entropy, and vanishing of the Yamabe invariant of symplectic 4-manifolds

Abstract We make use of F -structures and technology developed by Paternain–Petean to compute minimal entropy, minimal volume, and Yamabe invariant of symplectic 4-manifolds, as well as to study their collapse with sectional curvature bounded from below. A la Gompf, we show that these invariants vanish on symplectic 4-manifolds that realize any given finitely presented group as their fundamental group. We extend to the symplectic realm a result of LeBrun which relates the Kodaira dimension with the Yamabe invariant of compact complex surfaces.

The volume flux group and nonpositive curvature

We show that every closed nonpositively curved manifold with non-trivial volume flux group has zero minimal volume, and admits a finite covering with circle actions whose orbits are homologically essential. This proves a conjecture of Kedra–Kotschick–Morita for this class of manifolds.

Dynamics and Zeta functions on conformally compact manifolds

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 larger class of manifolds known as convex co-compact manifolds with variable negative curvature. Applying results from dynamics on these spaces, we obtain optimal meromorphic extensions of weighted dynamical Zeta functions and asymptotic counting estimates for the number of weighted closed geodesics. A meromorphic extension of the standard dynamical Zeta function and the prime orbit theorem follow as corollaries. Finally, we investigate interactions between the dynamics and spectral theory of these spaces. -

Topological rigidity of higher graph manifolds

In this short note we prove the Borel conjecture for a family of aspherical manifolds that includes higher graph manifolds.

Affine Configurations and Pure Braids

We show that the fundamental group of ordered affine-equivalent configurations with at least five points in the real plane is isomorphic to the pure braid group in as many strands, modulo its centre. In the case of four points, this fundamental group is free with 11 generators.