Speaker: Jorge Aguayo
Center for Mathematical Modeling, U. de Chile
Date: Monday, July 01, 2024 at 2:30 p.m. Santiago time

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 of deformations and tractions is analyzed, presenting a conditional stability result. Finally, we present an optimal control problem that allow us to recover a good approximation of the coseismic slip and the numerical analysis associated with the solution to the discretized optimal control problem. This talk will be complemented with some numerical experiments that show the efficiency of our numerical solvers and some realistic synthetic examples that simulate a subduction earthquake on the coast of Chile.

Venue: Multimedia, sexto piso, torre norte de Beauchef 851

Speaker: Fernando Bolaños
Center for Mathematical Modeling, U. de Chile
Date: Monday, June 17, 2024 at 2:30 p.m. Santiago time

Abstract:  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 journals (WoS and Scopus), cut-motion videos and a peer-reviewed book published by the Organization of Ibero-American States for Education, Science and Culture (OEI, for its acronym in Spanish). It is hoped that the space provided by SIPo can enable a conversation between researchers from different areas of knowledge where we can ponder on the underlying rationalities and logics behind our experiencing and practices.

Venue: Multimedia, sexto piso, torre norte de Beauchef 851

Speaker: Alejandra Muñoz Arancibia
Center for Mathematical Modeling, U. de Chile
Date: Monday, June 03, 2024 at 2:30 p.m. Santiago time

Abstract:  The Automatic Learning for the Rapid Classification of Events (ALeRCE) is a Chilean-led astronomical alert broker, and one of the seven brokers selected to receive the full alert stream from the Rubin Observatory. Since 2019 ALeRCE has been ingesting the public stream from the Zwicky Transient Facility, which contains hundreds of thousands of alerts per night, providing classifications and visualization for the astronomical objects detected.

In this talk I describe the ALeRCE project and its different science cases, showing how it has enabled the follow-up and study of young supernovae and other transient events. I highlight some of our discoveries, plus unforeseen benefits that we have found throughout our search. The advent of new surveys that target the dynamic sky, like the ones conducted now by the Asteroid Terrestrial-impact Last Alert System and soon by Rubin, opens a promising future for continuing the collaborative exploration of the changing universe.

Venue: Multimedia, sexto piso, torre norte de Beauchef 851

Speaker: Haritha Cheriyath
Center for Mathematical Modeling, U. de Chile
Date: Monday, May 06, 2024 at 2:30 p.m. Santiago time

Abstract:  Symbolic dynamics, initially used as a tool for analyzing general dynamical systems, has later caught more attention due to its independent applications in other areas including information theory and coding. From a given directed graph, we construct a symbolic space consisting of infinite paths on it. We are interested in studying its complexity by counting paths of fixed lengths. The topological entropy of this system is given by the growth rate of this complexity function.
When some of the edges are removed from the graph, the entropy of the new perturbed system drops. What if instead of edges, we make some paths to be forbidden? How much does the entropy drop when the lengths of these forbidden paths increase? These questions can be re-framed as enumeration of finite strings where a given collection of strings are forbidden. We explore more on this enumeration problem and if time permits, we discuss its applications in seemingly unrelated scenarios that include game theory and pattern matching algorithm.

Venue: Sala John Von Neumann, 7th floor, Beauchef 851

Speaker: Emeric Bouin
Université Paris-Dauphine
Date: Tuesday, April 23, 2024 at 2:30 p.m. Santiago time

Abstract: In this talk, I will present some facets of the best known equation in reaction-diffusion, which is called the Fisher KPP equation. I will explain where it comes from and what kind of results are interesting for mathematicians. Nobody needs knowledge in PDEs, the only thing to know is what is a Laplacian in R^d, or partial derivatives of order 2.

Venue: Sala John Von Neumann, 7th floor, Beauchef 851

Speaker: Nicolás Barnafi
Pontificia Universidad Católica de Chile
Date: Tuesday, April 09, 2024 at 2:30 p.m. Santiago time

Abstract:
In this talk, we will briefly introduce the nonlinear elasticity
equations to understand the language of large deformations modeling.
After this, we will focus on the much less studied “Inverse Elasticity
Problem”, whose solution is sometimes referred to as the reference
configuration, or stress-free configuration. This problem can be stated
as follows: Given a set of known external forces and a *deformed*
configuration, find an initial (or reference) configuration such that,
when the given forces are applied to it, we recover the deformed
configuration.

As we will see, the equations of nonlinear elasticity possess a certain
duality which allows, in a very “simple” manner, to formulate both the
direct and inverse problems, with almost no impact on the problem
structure. We will also see some numerical experiments to verify our
theoretical claims (if you want). If time allows it, I would also like
to discuss some ongoing work on nonlinear poroelastic media.

Venue: Sala John Von Neumann, 7th floor, Beauchef 851