Abstract: 

Dynamical systems are an area of mathematics that studies how processes evolve over time. One of the main perspectives within this field is Ergodic Theory, which studies dynamical systems from the point of view of measure theory. Within ergodic theory, one of the main elements of study currently is the Lyapunov exponents.

Lyapunov exponents quantify the dependence of the system on its initial conditions. One of the central problems regarding Lyapunov exponents is the study of their continuity, that is, to understand how much the Lyapunov exponents change under small perturbations of the system’s parameters. This question is important because it allows us to better understand the behavior of dynamical systems with close parameters.

In this talk, we will introduce the concepts of Lyapunov exponents, dynamical systems, and linear cocycles. We will also discuss the possibility of obtaining continuity results and moduli of continuity for Lyapunov exponents in certain classes of dynamical systems.

Speaker: Aline Melo (PUCV)

Resumen: La extensión natural es una construcción clásica en teoría ergódica que asocia a cada sistema no-invertible un sistema invertible que lo extiende. En esta charla formalizaremos la noción de extensión invertible para el caso general de acciones de semigrupos que preservan una medida de probabilidad. Luego estudiaremos el problema de la existencia de extensiones invertibles, y analizaremos casos en los que se tiene y no se tiene unicidad de éstas.

Expositor: Miguel Donoso-Echenique (Universität Münster)

Abstract: In recent years, the integration of optimization techniques with machine learning paradigms has led to significant advances in solving inverse problems, particularly through the optimal selection of parameters or observation strategies. A rigorous and systematic approach to tackle such problems is provided by bilevel optimization, where the lower-level problem corresponds to a model-based inverse problem—often governed by a partial differential equation (PDE)—and the upper-level objective encodes a data-driven loss functional, typically defined over a training set. Unlike classical variational models, the presence of PDE constraints introduces substantial analytical and computational challenges. In this talk, I will present a bilevel optimization framework for PDE-constrained inverse problems, and discuss recent results on the existence of optimal parameters. Furthermore, I will explore the possibility of reformulating the bilevel problem as a single-level optimization problem under suitable assumptions. Finally, I will derive and discuss first-order optimality conditions for the resulting problem, highlighting key mathematical difficulties and future directions.

Speaker: Juan Carlos De Los Reyes (Centro de Modelización Matemática MODEMAT y Escuela Politécnica Nacional, Quito).

The link to join the seminar is:
https://uchile.zoom.us/j/98721784149?pwd=df7YyCDGwMXlNuDX0kwKvob08edgk7.1

Los invitamos a participar en el webinar del Plan Nacional Sumo Primero: “Estudio de la Geometría en Sumo Primero”, junto al profesor Masami Isoda, académico de la Universidad de Tsukuba (Japón) y autor de la colección de textos Sumo Primero.

Durante este encuentro profundizaremos en la propuesta para la enseñanza de la geometría presente en la colección, revisando la progresión de los aprendizajes y orientaciones para su implementación en el aula.

Inscríbete aquí: https://uchile.zoom.us/webinar/register/WN_Sun7Pe5wT8mMediwUAjOww#/registration

Speaker: Mathieu Dedenon, University of Geneva, Swizerland

RESUMEN: Los flujos y homeomorfismos expansivos en espacios métricos compactos han sido extensamente estudiados debido a sus propiedades ergódicas. Recientemente, se ha trabajado en extender estos resultados a sistemas no invertibles, esto es, endomorfismos y semiflujos.

En esta charla contrastaremos dos formas que han surgido para abordar este problema, la expansividad positiva y los límites inversos. Repasaremos los resultados de Jaque y Herrero, que muestran ciertas limitaciones impuestas por la propiedad de expansividad positiva. Tras esto, veremos como los límites inversos nos permiten trabajar con un mayor conjunto de sistemas dinámicos y construiremos ejemplos no triviales de sistemas no invertibles con propiedades expansivas.

EXPOSITOR: Juan Peña (Universidad de Chile)

Abstract: Diego Ferruzzo is director of Brazil Flying Labs, an initiative dedicated to promoting the use of geospatial technologies, drones, and innovation to address social, environmental, and humanitarian challenges in Latin America. This webinar will discuss how satellite imagery from the Copernicus program’s Sentinel-2 constellation has helped develop a solution that provides free, up-to-date, and accurate information on the extent and severity of damage caused by wildfires.

Speaker: Diego Ferruzzo, director of Brazil Flying Labs

Live stream on YouTube: https://www.youtube.com/watch?v=tvgOGA89CZs

Abstract:
The wave kinetic equation (WKE) is a fundamental effective equation in wave turbulence theory that describes the evolution of the energy spectrum in a weakly interacting nonlinear wave system, with important applications in fields such as oceanography, plasma physics and nonlinear optics. Recent breakthrough results by Deng and Hani established the first full-range mathematical derivation of the 4-wave (or cubic) WKE from the (dispersive, reversible) nonlinear Schrödinger equation under suitable scaling limits.

Abstract: 

Quasinormality is a classical constraint qualification originally introduced by Hestenes in 1975 and subsequently extensively studied in nonlinear programming and in problems with abstract constraints. In this talk, we extend this concept to the setting of nonlinear semidefinite programming (NSDP). We show that the proposed condition is strictly weaker than Robinson’s constraint qualification, while still guaranteeing the existence of exact penalty functions, local error bounds, and boundedness of dual sequences generated by augmented Lagrangian methods.

As a consequence, convergence to Karush–Kuhn–Tucker points can be established for a broader class of NSDPs under mild regularity assumptions. In addition, a pseudonormality condition is introduced and explored.

Speaker: Daiana Oliveira dos Santos (Federal University of São Paulo)
When:  Miércoles 10 de junio de 2026, a las 16.15 horas
Venue: John von Neumann Seminar Room, Center for Mathematical Modeling (Beauchef 851, North Building, 7th Floor)

Programa
11:00 – 11:50: Recepción de asistentes y cóctel de bienvenida
11:50 – 12:00: Ingreso a la Sala Maryam Mirzakhani
12:00 – 12:05: Bienvenida, a cargo de Florencio Utreras, director de CopernicusLAC Chile
12:05 – 12:25: Redes Ópticas: Conectividad Avanzada para Educación, Investigación e IA, presentada por Gustavo Wymerszberg, Account Manager de Ciena
12:25 – 12:45: Modernización de la Conectividad de CopernicusLAC: Implementación de Infraestructura DWDM de Alta Capacidad entre CMM y REUNA, presentada por Rubén García, gerente TI de CopernicusLAC Chile
12:45 – 12:55: Espacio de preguntas y conversación con los expositores
12:55 – 13:00: Cierre de la actividad

Les invitamos a inscribirse en el siguiente enlace: https://go.cmm.uchile.cl/cienaday