Seminários

The clustering words for the Burrows-Wheeler transform, which are used in data compression, are intrinsically linked with interval exchange transformations, either discrete or continuous, through a combinatorial condition on bispecial words we call the order condition. We use it to answer a question of M. Lapointe about the clustering of return words for interval exchanges, in the most general framework, and extend the results to concatenations of such words. Clustering can also be used to investigate which words can be produced by generalized interval exchanges but not by standard ones. Joint work with L.Q. Zamboni

We address a question of do Carmo in six-dimensional Riemannian manifolds with bounded curvature, extending results from lower dimensions. In particular, we show that every complete, finite-index, non-minimal CMC hypersurface immersed in a closed Riemannian manifold with nonnegative sectional curvature is compact.

We also study the general case of a Riemannian manifold with bounded curvature and derive partial results. In particular, we show that a complete, finite-index CMC hypersurface immersed in the hyperbolic space $\mathbb{H}^6$ with mean curvature $|H|>7$ is compact. This gives a partial answer to a question posed by Chodosh in his survey for the ICM.

Iterated holomorphic correspondences on Riemann surfaces generalise rational maps and Kleinian groups. There are now a range of examples of ‘matings’: correspondences F with the property that the surface can be partitioned into a disjoint union of subsets, restricted to each of which F is conformally conjugate to a rational map, its inverse, or to generators of a Kleinian group. However, in every example up till now the group constituents have been (2,q,infinity)-triangle groups, and consequently the correspondence F has been reversible. We present a new construction, realising matings between composite maps and (p,q,infinity)-triangle groups with arbitrary p and q. Joint work with L. Lomonaco.

In this talk I will review the Chow and étale motivic cohomology groups of smooth complete intersections with Hodge structures of level one, classified by Deligne and Rapoport, with particular attention to fivefolds. We will see how these results can be extended to algebraic cycles on other smooth Fano manifolds with Hodge structures of level one. As an application of this, we will prove the integral Hodge conjecture for smooth quartic double fivefolds using the étale motivic approach. Specifically, we will examine their unramified cohomology groups with torsion coefficients. This is based on joint work with Iván Rosas-Soto. 

In this talk, I will prove the SL2 version of Kapranov’s theorem for tropical limits of hyperbolic amoebas of complex analytic surfaces obtained jointly with Peter Petrov, the simplicity of which motivated the development of corresponding non-Abelian version of classical phase tropicalization. In particular, I will deduce an explicit formula for SL2 phase valuation map $SL_2(\mathbb{K})\rightarrow SL_2(\mathbb{K}),$ where $\mathbb{K}$ is the field of convergent Hahn series with complex coefficients,  and sketch an exhaustive description of images of algebraic surfaces under this map, which is the subject of a work in progress with Andrei Benguş-Lasnier, as well the reproduction and extension of the  known case of algebraic curves in the special linear group described previously with Grigory Mikhalkin in the phase-forgetful setup.

In this talk, based on joint work with M. F. Elbert (UFRJ) and B. Nelli (Università di L’Aquila), we approach the one-parameter family of rotational constant mean curvature (CMC) spheres in $\mathbb H^n \times \mathbb R$ and $\mathbb S^n \times \mathbb R$, with particular emphasis on their stability and isoperimetric properties.

Our results include a proof of the uniqueness of the regions enclosed by rotational CMC spheres in $\mathbb H^n \times \mathbb R$ as solutions of the isoperimetric problem, thereby filling a gap in the original argument of Hsiang and Hsiang. We also show that all CMC spheres in $\mathbb H^n \times \mathbb R$ are stable, as are those in $\mathbb S^n \times \mathbb R$ with sufficiently large mean curvature.

We also establish the existence of a one-parameter family of CMC spheres in $\mathbb S^n \times \mathbb R$ that are stable but non-isoperimetric, in the sense that they do not bound isoperimetric regions. Finally, we emphasize that these results are essentially a consequence of the nesting property of rotational CMC spheres in $\mathbb H^n \times \mathbb R$, and of those in $\mathbb S^n \times \mathbb R$ with sufficiently large mean curvature.

Cerâmica é um dos tipos mais comuns de vestígios humanos encontrados em contextos arqueológicos. A análise da cerâmica arqueológica tem grande potencial informativo, e sua reconstrução é uma tarefa demorada e altamente dependente de profissional encarregado.
Neste trabalho, apresentamos uma abordagem baseada em deep learning para automatizar esse processo. Dada uma nuvem de pontos de um fragmento em uma posição padronizada, o método prevê a transformação geométrica que move o fragmento para sua posição relativa dentro do sistema de coordenadas do vaso. Duas redes neurais convolucionais profundas são treinadas para prever os parâmetros da transformação euclidiana 3D. 
Live @ https://www.youtube.com/live/UobZeoKpFmM

When the injectivity radius of the surface is finite, it is known that horocycle trajectories are closed or have non minimal  closure, except if the surface is "convex-cocompact" .

If we add the condition that the injectivity radius is >0, then all ergodic measure m, invariant by the horocycle flow are quasi-invariant i.e. the image of m by any time of the geodesic flow is absolutely continuous with respect to m.

In this talk, I will explain how to construct a hyperbolic surface admitting a non-trivial minimal set for the horocyclic flow and a conservative and ergodic invariant measure which is not quasi-invariant. This is joint work with J. Farre, O. Landesberg, and Y. Minsky.

The dynamics of area-preserving flows on surfaces is a well-understood topic, and there exists a canonical invariant decomposition of the phase space into a region (a collection of topological annuli) where the dynamics is integrable, and a finite number of pieces of positive genus where the dynamics is quasi-minimal (closely resembling the dynamics of an irrational flow on a torus).

In this work, we show that a very similar canonical decomposition remains valid when dealing with conservative homeomorphisms with zero topological entropy. We present this decomposition while also exhibiting examples of different phenomena that may arise, as well as several properties of the “quasi-minimal” regions.

Part of the work involves proving a Thurston–Nielsen–type reduction result, showing that maps homotopic to Dehn twists and with zero entropy actually possess invariant “Dehn-like” annuli. Time permitting, we will also discuss some applications to Reeb flows on three-dimensional manifolds.

Joint Work with P. Le Calvez, P.-A. Guihéneuf, and A. Passeggi

In this presentation, I will give an overview of key aspects of accurate simulation of the visibility of distortions in VR and AR. Next, I will discuss our work in the Visible Difference Predictor (VDP) line of vision science-based metrics, and future research directions.

Live @ https://www.youtube.com/live/SZ_GKjnKuHE