Fondos para apoyar la realizacion de la Fourth Latin American Summer School on Robotics (LACORO 2025). La primera edición se realizó online en octubre de 2020; la segunda fue presencial en enero de 2023; la tercera 2024 en la Universidad de O'Higgins en Rancagua, Chile. La cuarta edición tendrá lugar en diciembre de 2025 en la Universidad de O'Higgins. https://lacoro.org/ Esta Escuela de Verano beneficiará principalmente a Estudiantes y Académicos de las Américas interesados en la Investigación en Inteligencia Artificial aplicada a la Robótica. Nuestro objetivo es fomentar la colaboración nacional y regional en esta área de investigación. Para la primera edición, alcanzamos 241 inscripciones para actividades online de todo el mundo, y la segunda versión tuvo 166 inscripciones para actividades presenciales en enero de 2023, principalmente de Chile, México, Argentina, Brasil y Uruguay.

Fondos para apoyar la realizacion de la Fourth Latin American Summer School on Robotics (LACORO 2025). La primera edición se realizó online en octubre de 2020; la segunda fue presencial en enero de 2023; la tercera 2024 en la Universidad de O'Higgins en Rancagua, Chile. La cuarta edición tendrá lugar en diciembre de 2025 en la Universidad de O'Higgins. https://lacoro.org/ Esta Escuela de Verano beneficiará principalmente a Estudiantes y Académicos de las Américas interesados en la Investigación en Inteligencia Artificial aplicada a la Robótica. Nuestro objetivo es fomentar la colaboración nacional y regional en esta área de investigación. Para la primera edición, alcanzamos 241 inscripciones para actividades online de todo el mundo, y la segunda versión tuvo 166 inscripciones para actividades presenciales en enero de 2023, principalmente de Chile, México, Argentina, Brasil y Uruguay.

This research proposal aims to study the long-term behavior of solutions to partial differential equations arising from dispersive dynamics, kinetic models, and integro-differential dynamics in ecology; and to study extremals of functional inequalities in connection to the ground states of partial differential equations arising from quantum mechanics and diffusion phenomena. Five major topics are proposed: Relativistic quantum mechanics, Dirac operators and functional inequalities; Symmetry breaking in weighted functional inequalities and weighted diffusions; long time dynamics in dispersive PDEs in one space dimension; long-term dynamics in nonlocal models from ecology; and hypocoercivity and decay to equilibrium in kinetic models with heavy tails. The first topic focuses on establishing connections between spectral problems and functional inequalities for Dirac operators. The aim is to analyse the symmetry of optimal spinors in inequalities of Keller-Lieb-Thirring type, and to obtain the solitary waves of Soler-type nonlinear Dirac equations as optimizers of a nonlinear inequality. The second topic aims to characterize a symmetry range in which optimal functions are radially symmetric for weighted logarithmic Sobolev inequalities and a new family of Caffarelli-Kohn-Nirenberg inequalities. A nonlinear carré-du-champ method will be adapted to prove entropy-type estimates. Rigidity, perturbation, and stability issues will be addressed. The third topic seeks to study the asymptotic stability of topological and non-topological solitions for a class of dispersive PDEs in dimension one. A new method is proposed, based on perturbations in weighted spaces with exponential weights, on the so-called virial identities, and on the study of existence of breathers. The fourth topic concerns the description of evolutionary stable strategies of long-term dynamics of integro-differential models that arise in the modeling of structured populations, and to obtain qualitative and quantitative insights on the concentration dynamics. In the fifth topic, the aim is to extend the Dolbeault-Mouhot-Schmeiser method to study the large-time behavior of solutions for a broad family of kinetic equations in which the confinement potential exhibits heavy tails. The goals of this project are multiple: to strengthen and to create new collaborative research networks between France and Chile in the field of nonlinear partial differential equations and applications, to publish co-authored articles in top-tier journals and disseminate the results in international meetings, and to promote the formation of advanced human capital. In order to achieve these goals, yearly workshops will be organized in France and Chile to account for the progress of the investigations as well as to encourage the participation of students and young researchers. International training of doctoral and postdoctoral researchers will be ensured by allocating resources from this project for exchanges. Considering the history of successful collaboration amongst the members of this project, and their expertise in their research fields, we are confident about the successful termination of the project. In particular, we expect to pave the way for new research avenues. The main scientific contribution of this proposal involves adapting state-of-the-art techniques from PDEs and nonlinear analysis to obtain qualitative and quantitative results for variational problems and partial differential equations, in which the setting plays a crucial role: complex-valued matrices (first topic), nonlinear and weighted (second topic), strongly nonlinear and dispersive (third topic), nonlocal (fourth topic), general assumption on the tail of the confining potential (fifth topic). This proposed research will provide insights into spectral theory, stability theory of equilibria of differential equations, optimal rates of convergence to equilibria, and their relation to optimal constants in functional inequalities. The expected results will help improving the understanding of various real-life phenomena, including population-dynamics, relativistic quantum mechanics, and diffussion processes. The viability of the project is sustained on the expertise of the members of the Chilean and French research teams, including experts in partial differential equations, nonlinear analysis, calculus of variations, and mathematical physics. Their successful collaboration record and significant contributions to these fields only strengthen the potential of this proposal. In conclusion, the present research project will not only foster the scientific cooperation between Chile and France but it will also provide meaningful advancements in the aforementioned fields and their application to various physical phenomena.

The school is a crucial socialisation institution that forms young people’s perceptions, attitudes, and beliefs (Gidengil et al., 2016). Moreover, it is the main socialisation space that provides the youth with broader social relationships compared to the intimate social context of the family (Vincent et al., 2018). This Fondecyt project will ethnographically analyse the school’s role in socialising attitudes towards socioeconomic inequality among secondary students in classrooms with a diversified socioeconomic composition. Studying these attitudes is crucial since they might symbolically legitimise or challenge the existing social order (Sandel, 2021) and contribute to the reproduction or transformation of socioeconomic inequalities (Alesina et al., 2012). Since evidence on this issue is key for democratic governments in socioeconomically unequal societies to inform policies for reducing inequality and increasing social cohesion, the project focuses on Chile, a country with extreme levels of socioeconomic inequality (WID, 2022). By identifying opportunities and challenges for schools to promote egalitarian attitudes towards socioeconomic inequality among their socioeconomically diverse students, the project will provide decisive evidence for education policy to improve their support to school communities. The general objective of this project is to analyse how the schools contribute to shaping attitudes towards socioeconomic inequality among secondary students in classrooms that have diversified their socioeconomic composition. The specific objectives are as follows: 1. To characterise the socioeconomic heterogeneity within schools with secondary education in Chile and identify those that have diversified the socioeconomic composition of their students in the last decade. 2. To determine the schools’ pedagogical, organisational and community responses to the increase in their socioeconomic diversity and examine how these responses promote particular attitudes towards socioeconomic inequality. 3. To describe the students' inter-class relationships and identify how these relate to particular attitudes towards socioeconomic inequality, including awareness of inequality, perceptions of the fairness of social inequalities, meritocratic beliefs, and egalitarian preferences. The study will use a sequential mixed methods design, with a first quantitative phase aimed at answering Specific Objective 1 and informing the selection of the sample of schools for the second - ethnographic - phase, which is the predominant one and seeks to answer Specific Objectives 2 and 3: a) Quantitative phase: A Socioeconomic Diversity Index (SDI) will be created using data from the Quality of Education Agency through its SIMCE questionnaire to parents of secondary students for 2014-2024, which asks about the families’ socioeconomic information. Descriptive statistics will be used to describe SDI and its temporal variation by school. b) Ethnographic phase: Ethnographic fieldwork will be deployed in three schools with increased socioeconomic diversity, as measured in the SDI. Fieldwork in each school will last approximately two months, and the following methods will be used: - Interviews with staff members: 10 in each school (30 total), including the Principal, two Deputy Principals, three professionals from a psychosocial support team and four teachers. - Friendship maps and interviews with students: Maps of the students’ social relationships will be built with secondary students, seeking to include the whole class in each school (approximately 100 students in total). Maps will be followed by interviews. - Observations: They will be conducted in classrooms, playgrounds, and school events for approximately 100 hours in each school (approximately 300 hours of observation in total). The expected results include a) a map of all Chilean schools according to their current socioeconomic diversity and its temporal variation; b) in-depth evidence of inter-class relationships between secondary students and how these affect their attitudes towards socioeconomic inequality; and c) a systematisation of the schools’ responses to the students’ socioeconomic heterogeneity, their links to the development of attitudes towards socioeconomic inequality, and their facilitating and hindering elements. These findings will be useful for other schools that are diversifying their student body, wish to do so, or are interested in promoting egalitarian attitudes among their students. Ultimately, the project will provide critical evidence for public policy to promote schools that foster the development of egalitarian attitudes and potentially contribute to reducing social inequalities.

Combinatorial objects frequently appear in various areas of computer science and discrete mathematics. These objects are central to questions in algorithmic design, where we aim to program a computer to efficiently perform tasks involving them. These tasks may include counting objects based on certain parameters, sampling an object uniformly at random, optimizing with respect to an objective function, searching for objects that satisfy specific properties, or generating all objects exactly once. This project focuses on two of these problems: combinatorial generation and the search for highly distinct combinatorial objects. While many of the aforementioned tasks have general-purpose techniques that allow them to tackle multiple problems simultaneously, the situation becomes less clear when dealing with combinatorial generation or the search for distant objects. Much of the effort in these areas has been devoted to developing ad hoc methods. Despite this, these last two problems can be naturally phrased in the language of flip graphs, which encode the similarity between combinatorial objects. In this context, the problem transforms into the traditional graph problems of Hamiltonicity (finding a path that traverses all the vertices exactly once) and diameter (finding two vertices that are farthest apart). Recent research has highlighted the significant value of exploiting polytopal properties and symmetry of flip graphs, leading to unified frameworks that can address many problems simultaneously. The main objective of this project is to contribute to this perspective. Specifically, it aims to enhance our understanding of the polytopal and symmetric properties of flip graphs and use this knowledge to develop efficient algorithms for tackling Hamiltonicity and diameter problems

Beccaria y la escuela clásica pusieron en tela de juicio el sistema de justicia medieval caracterizado por su arbitrariedad y excesiva crueldad. De esta forma, propusieron un conjunto de ideas (p.ej. legalidad, humanidad y proporcionalidad de las penas, debido proceso) para limitar el poder de castigo estatal, racionalizar el uso de la fuerza y disminuir la aplicación de la crueldad, llevando reformar el sistema penal de la época. El pensamiento de otros autores y la emergencia de los derechos humanos permitieron que estas ideas se incorporaran en las actuales democracias liberales comprometidas con el Estado de derecho. Así, en el ámbito penal, a nivel de leyes, constitucional y del derecho internacional, se construyó un sistema de protección del individuo frente al ius puniendi, y que aquí englobamos ampliamente bajo el término “Principios Penales liberales” (en adelante PPL) para referirnos a aquellos principios, sub-principios, ideas, derechos y/o garantías destinadas a limitar y racionalizar el ejercicio de la justicia penal. Aunque estos PPL se encuentran incorporados e institucionalizados, corrientes actuales como el Populismo Penal , la cultura del Control, la punitividad pública, el Derecho Penal del enemigo o los estudios en actitudes punitivas permitirían pensar que los PPL tendrían hoy un bajo respaldo ciudadano. Además, en el actual contexto chileno caracterizado por un incremento en la preocupación por la seguridad, es esperable que la opinión pública vea con reticencia estos PPLL por considerarse que favorecen a los delincuentes y limitan la capacidad estatal para controlar el crimen. Desde el ámbito político, que descansa en buena medida en la opinión pública, algunos actores plantean restablecer la pena de muerte, buscan limitar derecho a defensa gratuito o aumentar desproporcionadamente las penas. También, desde ciertos sectores políticos se ha presionado o cuestionado el actuar de jueces/as y fiscalía sin evaluar las consecuencias de estas acciones para la imparcialidad, en un contexto en el que el término de ‘garantismo jurídico’ parece ser concebido como como una característica negativa del sistema jurídico. Medidas y acciones de este tipo amenazan este conjunto de PPL y la protección del individuo frente al Estado. Dado que, desde el punto de vista politológico, las instituciones requieren de cierto umbral de respaldo subjetivo para su legitimidad social, resulta fundamental estudiar el apoyo ciudadano a los PPL que subyacen al sistema de justicia penal. A pesar, sin embargo, de la relevancia de este tema, la literatura en torno a lo que en adelante llamaremos las ‘Actitudes Ciudadanas hacia los Principios Penales Liberales’ (en adelante APPL) es sumamente escasa. Investigaciones previas solo han abordado el respaldo hacia ciertos principios aislados, hacia un set de PPL , pero no hacia el conjunto completo de PPL subyacentes al sistema de justicia. Sin embargoA pesar de lo anterior, investigación seminal y exploratoria en torno al tema se ha realizado en el contexto chileno identificándose una baja adhesión ciudadana a los PPL y, también,a la vez que, esto se han encontradomantendría un correlatos con el género, la educación y la orientación política de las personas. Por últimoOtro ejemplo de investigación emergente en la temática es, en Reino Unido. En este último páís -con sistema jurídico consuetudinario- se ha validado a nivel confirmatorio una escala (actualmente en revisión) para medir las APPL (en adelante E-APPL). Empero, esta escala no ha sido aplicada aun en otros países, o contextos con sistema de derecho escrito. Adicionalmente, tampoco hay hallazgos sobre los posibles factores explicativos de las APPL y sus consecuencias, relevándose entonces un vacío de conocimiento necesario de abordar. Considerando esto, y mediante una metodología mixta (cuantitativa y cualitativa), nuestra investigación busca estudiar las APPL en población residente en Chile. Específicamente, se busca a) describir los niveles y tipos APPL, b) los posibles factores que explican o dan cuenta de las APPL, y c) las consecuencias de las APPL para la legitimidad y confianza en el sistema de justicia chileno.