Departamento de Matemáticas
Szymon Dudek - Introduction to the theory of measures of noncompactness. Examples and counterexamples, fixed-point theorems, and applications
The talk is devoted to theory of measures of noncompactness in Banach spaces and Fréchet spaces. We will present examples and counterexamples of measures of noncompactness in selected Banach and Fréchet spaces that will help to better understand this topic. The next part will cover fixed-point theorems and their applications in studying existence of solutions for certain integral equations.
Fecha: Viernes, 22 de mayo de 2026, 12:30 horas.
Lugar: Aula CI/0001 de la Facultad de Ciencias II.
Szymon Dudek - Quaternions and their applications in computer graphics
The talk is devoted to the quaternion algebra H as a natural generalization of the algebra of complex numbers. We discuss its algebraic structure, including the canonical basis {1, i, j, k}, multiplication relations, conjugation, norm, and the characterization of invertible elements. In the applied part of the presentation, we briefly indicate how these algebraic properties lead to effective computational methods in computer graphics (spatial rotations). The aim of the talk is to emphasize the interplay between abstract algebraic concepts and their concrete geometric and computational realizations.
Fecha: Martes, 19 de mayo de 2026, 11:00 horas.
Lugar: Aula A1/1-50X del Aulario I.
Jónatan Herrera Fernández - Una aproximación sintética al borde causal
Desde su concepción, la relatividad general ha dependido clásicamente de la geometría diferencial, pero el estudio de modelos físicos menos regulares o la necesidad de realizar proximaciones numéricas han motivado nuevos enfoques de baja regularidad. En este contexto, los espacios de longitud lorentizanos, introducidos por Kunzinger y Sämann, surgieron como una alternativa que ha impulsado un amplio desarrollo teórico en los últimos años.
Esta charla tiene tres objetivos: por un lado presentar los espacios métricos lorentzianos, una generalización de los espacios de longitud lorentzianos motivada por la definición de espacio métrico clásico. Por otro, introducir la noción de borde causal, detallando su motivación y propiedades principales. Para finalizar, comentaremos brevemente las líneas de investigación y los posibles desarrollos futuros en esta área.
Fecha: martes, 19 de mayo de 2026, 11:30h.
Lugar: Seminario de matemáticas (0007PB018)
Víctor M. Ortiz Sotomayor - Detrás del “Me gusta”: cómo el álgebra lineal personaliza tu entretenimiento
Los sistemas de recomendación de plataformas como Netflix, Spotify o YouTube se han convertido en una pieza fundamental de nuestra experiencia digital, guiando silenciosamente nuestras lecciones diarias. Detrás de su aparente sencillez se esconde una estructura matemática precisa basada en el filtrado colaborativo. Este seminario propone desvelar los principios algebraicos que los hacen posibles: exploraremos cómo conceptos clásicos como el producto escalar y la noción de espacio vectorial permiten traducir gustos y preferencias en similitudes entre usuarios y productos, descubriendo así la arquitectura matemática que sostiene la personalización del contenido en la era del big data.
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Fecha: martes, 5 de mayo de 2026, a las 13:00 horas.
Lugar: CI/0001 Aula 1 de la Facultad de ciencias
Chenjian Pan - MORE: A Multi-pair Proximal Block Coordinate Descent Algorithm for Multi-block Composite Optimization with Applications in Tensor Decompositions
In this talk, we consider a class of multi-block nonconvex composite optimization problems involving the sum of (p+1) possibly nonsmooth functions and a coupled smooth function depending on all variables. A common approach in the literature for solving such problems is to update the variables sequentially (in Gauss-Seidel order) within each iteration. However, such sequential updating schemes may fail to account for the inherently unequal importance of different variables in real-world applications, where each variable can play a distinct role. To address this limitation, we propose a novel multi-pair proximal block coordinate descent (MORE) algorithm, which efficiently exploits structural imbalance among variables by selecting s pairs (s ≤ p) to update within each iteration, while the remaining variables are updated sequentially. This approach not only enhances flexibility but also exploits the inherent structural imbalance of the problem to accelerate convergence, making it particularly effective for large-scale applications. Theoretically, we establish convergence of the MORE algorithm under the Kurdyka-Lojasiewicz framework. Finally, we demonstrate the practical effectiveness of our method through extensive numerical experiments on tensor decomposition applications.
Fecha: miércoles 29 de abril de 2026 a las 12:30
Lugar: Aulario I, aula A1/1-33P
Simone Verzellesi - Renormalization of contact velocity fields with horizontal Sobolev regularity in Heisenberg groups
The classical Cauchy-Lipschitz theory ensures well-posedness of the flow equation associated with Lipschitz vector fields. A major breakthrough in extending this theory to rough velocity fields was achieved by DiPerna-Lions in the Sobolev setting, and later by Ambrosio in the BV framework. Since then, the theory has been significantly developed under various structural and regularity assumptions, both in Euclidean and metric measure settings.
In this talk, after reviewing the existing theory, we present a new well-posedness result for a class of rough velocity fields in the genuinely sub-Riemannian setting of the Heisenberg group. We describe the main ideas of our approach, and we explain why our result cannot be deduced either from existing Euclidean techniques or from available results in the metric measure framework. Based on a joint work with L. Ambrosio, G. Somma and D. Vittone.
Fecha: martes, 12 de marzo de 2026, de 11h a 12h.
Lugar: Seminario de matemáticas (0007PB018)
Samir Adly - Bridging discrete algorithms and continuous ODEs in accelerated first-order optimization: a historical perspective
This talk explores the historical development of optimization methods, focusing on the deep onnection between discrete algorithms and their associated continuous Ordinary Differential Equations (ODEs). Beginning with Cauchy's foundational work in 1847 on gradient descent, we race the evolution of first-order methods, leading Nesterov's accelerated gradient techniques. The discussion emphasizes how discrete optimization algorithms, such as gradient descent and its accelerated variants, can be understood as numerical discretization of specific ODEs. This continuous-discrete interplay not only provides deeper insights into the structure and performance of modern algorithms but also offers a powerful framework for deriving new methods with improved convergence properties. This talk will explore the key ideas behind optimization acceleration methods, tracing their historical development and grounding them in fundamental mathematical principles. By highlighting the core concepts, the presentation aims to enhance understanding among students and nonspecialist colleagues. Some open questions will be discussed to inspire further research and exploration in this evolving field.
Fecha: 11 de febrero de 2025, 12:00h
Lugar: Seminario de matemáticas
4th International Conference on Variational Analysis and Optimization
En los días del 14 al 17 de Enero de este año se ha celebrado en el Centro de Modelamiento Matemático (CMM) de la Universidad de Chile (Santiago de Chile) el 4th International Conference on Variational Analysis and Optimization (https://eventos.cmm.uchile.cl/lopezcerda2025/).
El evento ha reunido a cerca de cincuenta destacados especialistas en el tema y ha estado dedicado al Profesor Emérito de este departamento Marco López Cerdá, con motivo de su 75 aniversario.
Boureima Sangaré - Some compartmental mathematical models of infectious disease dynamics
In this talk I will present three mathematical models of infectious disease dynamics : malaria and schisto-somiasis. The model of malaria is an autonomous and non-autonomous system, constructed by considering two models: a model of vector population and a model of virus transmission to human. The threshold dynamics of each model is determined and a relation between them established in the case of the au-tonomous system. Furthermore, the Lyapunov principle is applied to study the stability of equilibrium points of the two models. The common basic reproduction number has been determined using the next generation matrix and its implication for malaria management analyzed. In the second part of my talk, I will discuss a non-autonomous and an autonomous model of schistosomiasis transmission with a general incidence function. Firstly, we formulate the non-autonomous model by taking into account the effect of saisonality on the transmission. Secondly, using the average of periodic functions, we further derive the autonomous model associated with the nonautonomous model. Through rigorous analysis via theories and methods of dynamical systems we etablised a number of interestings results on the two systems. Finally, using linear and nonlinear specific incidence function, we perform some numerical simulations to illustrate our theoretical results for the model of schistosomiasis and for the malaria as well.
Fecha: 23 de octubre de 2024, 16:00h
Lugar: Seminario de matemáticas