Seminars appear in decreasing order in relation to date. To find an activity of your interest just go down on the list. Normally seminars are given in english. If not, they will be marked as **Spanish Only.**

## Combinatorial Contracts.

Abstract: An emerging frontier in Algorithmic Game Theory is Algorithmic Contract Theory, which studies the classic hidden-action principal-agent problem of contract theory through the computational lens. In this talk, I will present three basic ways in which the problem can be combinatorial and survey both hardness and poly-time (approximation) results. The analysis will uncover some surprising connections (but also fundamental differences) to combinatorial auctions.

## Turbulent steady states in the nonlinear Schrodinger equation.

Abstract: The nonlinear Schrodinger (NLS) equation, also known as the Gross-Pitaevskii equation, is one of the most common equations in physics. Its applications go from the propagation of light in nonlinear media to the description of gravity waves and Bose-Einstein condensates. In general, the NLS equation describes the evolution of nonlinear waves. Such waves interact and transfer energy and other invariants along scales in a cascade process. This phenomenon is known as wave turbulence and is described by the (weak) wave turbulence theory...

## Evaluación del coeficiente de atenuación difusa de la radiación fotosintéticamente activa en el lago Villarrica.

Resumen: “El coeficiente de atenuación difusa de la radiación fotosintéticamente activa es una propiedad óptica inherente importante del campo de luz subacuático. Este parámetro, como medida de la transparencia del medio, es un buen indicador de la calidad del agua. En este estudio, se utilizaron imágenes Landsat 8 OLI y Sentinel-2A/B MSI basadas en algoritmos para estimar el coeficiente de atenuación difusa de la radiación fotosintéticamente activa en un lago en el centro-sur de Chile. Los datos estimados de los algoritmos del módulo ACOLITE...

## Group actions with discrete spectrum and their amorphic complexity.

Abstract: Amorphic complexity, originally introduced for integer actions, is a topological invariant which measures the complexity of dynamical systems in the regime of zero entropy. We will introduce its definition for actions by locally compact sigma-compact amenable groups on compact metric spaces. Further, we will illustrate some of its basic properties and show why it is tailor-made to study strictly ergodic group actions with discrete spectrum and continuous eigenfunctions. This class of actions includes, in particular, Delone...

## Dirichlet-to-Neumann and Calderon operator via deep learning techniques.

Abstract: In this talk we consider the Dirichlet-to-Neumann operator and the Calderón mapping appearing in Calderon’s inverse problem. Using deep learning techniques, we prove that these maps are rigorously approximated by infinite-dimensional neural networks.

## Long time asymptotics of large data in the Kadomtsev-Petviashvili models and geometrical aspects of its dynamics.

Abstract: In this talk we consider the Kadomtsev-Petviashvili equations posed on R2. For both models, we provide sequential in time asymptotic descriptions of solutions obtained from arbitrarily large initial data, inside and far regions of the plane not containing lumps or line solitons, and under minimal regularity assumptions. A geometrical description of the dynamics will be given in terms of parabolic regions.

## Determinación de erosión costera con imágenes satelitales Sentinel-2 entre 2015 – 2022. Caso de estudio Bahía de Algarrobo, Chile Central

Resumen: En los últimos años, la erosión costera ha aumentado a nivel mundial por la frecuencia e intensidad de eventos de tormentas, convirtiéndose en una de las principales amenazas que afectan a la zona costera a diferentes escalas. En la Bahía de Algarrobo los eventos de marejadas frecuentes e intensas en las temporadas primavera-verano y las intervenciones antrópicas en humedales costeros, sobre la playa y las dunas han intensificado los procesos erosivos. El objetivo del trabajo es determinar las tasas de erosión costera a partir del...

## Simplified Kalman filtering for non-linear models.

Abstract: We will discuss the problem of approximate statistical inference in the hidden Markov models where the observation equations are non-linear. We propose a Bayesian approach based on a Gaussian approximation as well as its versions suitable for “large” problems. The proposed approach may be seen as an approximate Kalman filter which is generic in the sense that it can be used for any non-linear relationship between the hidden state and the outcome. We show how the proposed simplified Kalman filter can be used in the...

## On traveling waves for the Gross-Pitaevskii equations.

Abstract: In this talk, we will discuss some properties of traveling waves solutions for some variants of the classical Gross-Pitaevskii equation in the whole space, in order to include new physical models in Bose-Einstein condensates and nonlinear optics. We are interested in the existence of finite energy localized traveling waves solutions with nonvanishing conditions at infinity, i.e. dark solitons. After a review of the state of the art in the classical case, we will show some results for a family of Gross-Pitaevskii equations with...

## Conjugacy classes of germs near a hyperbolic fixed point in dimension 1.

RESUMEN: A famous linearization theorem of Sternberg claims that, in dimension 1, near a hyperbolic fixed point (i.e. a fixed point where the derivative differs from 1), a germ of C^r diffeomorphism is C^r conjugate to its linear part when r is greater than or equal to 2. This result fails to be true in lower regularity, even for C^1 diffeomorphisms with absolutely continuous derivative. We will explain how to construct whole continuous families of such germs with the same derivative at a common fixed point but which are not pairwise...