Noticias en español
Tree Embedding Problem for Digraphs.
Abstract: The \textit{tree embedding problem} focuses on identifying the minimal conditions a graph $G$ must satisfy to ensure it contains all trees with $k$ edges. Here, a graph $G$ consists of a set $V$ of elements called vertices, and a set $E$ of (unordered) pairs of vertices, called edges. We say that a graph $G$ is a tree if, for any pair of vertices, there is exactly one path connecting them. Erd\H{o}s and Sós conjectured that any graph $G$ with $n$ vertices and more than $(k-1)n/2$ edges contains every tree with $k$ edges. This conjecture has been generalized into the Antitree...
Read MoreHecke groups in geometry.
Abstract: This talk discusses two geometric aspects of the so-called Hecke groups, defined by E.Hecke in the 1920s, and which are a generalisation of the modular group SL(2,Z) of 2×2 matrices with integer coefficients and determinant 1. Hecke groups will be used here as a pretext to talk about my research field, namely hyperbolic geometry and translation surfaces (no prior knowledge on these fields are required). More precisely, we will see that these groups are examples of lattice Fuchsian triangle groups, and that they also arise as Veech groups of translations surfaces. At the end we...
Read MoreSecond-order dynamical systems associated with a class of quasiconvex functions.
Abstract: In this talk, we examine second-order gradient dynamical systems for smooth strongly quasiconvex functions, without assuming the usual Lipschitz continuity of the gradient. We establish that these systems exhibit exponential convergence of the trajectories towards an optimal solution. Furthermore, we extend our analysis to the broader quasiconvex setting by incorporating Hessian-driven damping into the second-order dynamics. Finally, we demonstrate that explicit discretizations of these dynamical systems result in gradient-based methods, and we prove the linear convergence of these...
Read MoreAn overview of some coloring parameters for (n,m)-graphs.
Abstract: Graph coloring is one of the most famous problems in graph theory. The most natural question to ask in this framework is whether or not a given family of graphs has a finite chromatic number. As graph homomorphisms generalize coloring, we study the notion of homomorphisms for (n,m)-graphs. Due to their various types of adjacencies, the (n,m)-graphs manage to capture complex relational structures and are useful for mathematical modeling. For instance, the Query Evaluation Problem (QEP) in graph databases, the immensely popular databases that are now used to handle highly...
Read MoreNew developments in the study of the elasticity equation for the analysis of inverse problems applied in Geoscience.
Abstract: This talk presents the analysis of an elasticity equation with interface conditions as a way to understand the formation of subduction earthquakes and how it is possible to determine geophysical characteristics of some tectonic plates from surface measurements. First, two different numerical methods based on finite elements are analyzed to solve the forward problem by comparing their algorithmic complexity and some properties necessary to solve an inverse problem. Then, the inverse problem of recovering the coseismic slip (one of the interface conditions) from surface measurements...
Read MoreA journey through discourses and practices.
Summary: Our experiencing and, thus, our practices are co-enabled by entwined fields of knowledge, fields of power and forms of subjectivity. Through the articulation of different research pieces, and one protagonist, in this SIPo session we will tackle the following question: how free are we? Our protagonist is a student enrolled in Chile’s Secondary Technical VocationalEducation and Training (S-TVET) system. All research pieces used to drive then narrative of the presentation are the result of a postdoctoral research endeavor. These include research articles published in indexed...
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