Noticias en español
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.
Una versión abstracta de la desigualdad de Gronwall.
RESUMEN: ¿Es posible considerar el lema de Gronwall como un principio del máximo? En esta charla elemental presentaremos una versión abstracta del lema, en términos de la cota espectral de un operador definido en un látice de Banach. Como consecuencia, deduciremos versiones generalizadas del lema, así como aplicaciones a sistemas discretos y resultados de unicidad para problemas semilineales.
From non-local to local Navier-Stokes equations
Resumen: Inspired by some experimental (numerical) works on fractional diffusion PDEs, we develop a rigorous framework to prove that solutions to the fractional Navier-Stokes equations, which involve the fractional Laplacian operator, converge to a solution of the classical case. Precisely, in the setting of mild solutions, we prove uniform convergence in both the time and spatial variables and derive a precise convergence rate, revealing some phenomenological effects.
Caminos de Santiago: small separating path systems for complete graphs.
Summary: In a communication network of n nodes, each linked to every other, a single link fails. How can we discover which link is broken without going through the burdensome process of examining separately all \(\Theta(n^2)\) of them? A quick way to determine the faulty link would be to propagate messages through a designated set of paths S, such that for every two links there exists a path in S that contains exactly one of them. We say that such a set S (weakly) separates the network. It is known that a separating path system for a network...
Dominios de Baker hiperbólicos y formalismo termodinámico.
RESUMEN: Aplicamos técnicas de formalismo termodinámico a una familia de funciones enteras que tiene dominios de Baker de tipo hiperbólico probando la existencia de medidas conformes y obteniendo una fórmula de tipo Bowen para la dimensión de Hausdorff de un subconjunto “dinámicamente bueno” del conjunto de Julia. (Este es un trabajo conjunto con I. Inoquio).
Computational methods for cardiac catheter ablation procedures.
Abstract: Cardiac ablation treatments are essential procedures for the treatment of severe cases of cardiac arrhythmias. Using a catheter, these minimally invasive treatments introduce scarring in the cardiac tissue, insulating arrhythmogenic areas and restoring the normal sinus rhythm of the heart. The creation of digital twins and personalized models can aid in therapy planning and improvement of the efficacy and safety of interventional procedures. In this talk we will delve into the multiscale and multiphysics mathematical modelling...
Asymptotic stability of small solitary waves for the one-dimensional cubic-quintic Schrödinger equation.
Abstract: I will present two results on the asymptotic stability of small solitary waves for the one-dimensional cubic-quintic Schrödinger equation. The first result concerns the focusing-defocusing double power nonlinearity, for which the linearized operator around the small solitary waves has no internal mode. The second result concerns the more delicate case of the focusing-focusing double power nonlinearity, for which the linearized operator around the small solitary waves actually has an internal mode. The internal mode component of the...
Multiple ergodic averages along polynomials for systems of commuting transformations.
RESUMEN: The last 50 years have seen tremendous activity at the interface between ergodic theory, combinatorics and number theory that started with Furstenberg’s dynamical proof of the Szemerédi theorem from the 1970s. The goal of this line of research has been to prove new multiple recurrence results and then deduce combinatorial corollaries. To achieve this, one wants to understand the limiting behaviour of relevant multiple ergodic averages. Of particular interest are averages of commuting transformations with polynomial iterates: they...
A qualitative analysis of an Aβ-monomer model with inflammation processes for Alzheimer’s disease.
Abstract: We introduce and study a new model for the progression of Alzheimer’s disease incorporating the interactions of A_beta-monomers, oligomers, microglial cells and interleukins with neurons through different mechanisms such as protein polymerization, inflammation processes and neural stress reactions. In order to understand the complete interactions between these elements, we study a spatially-homogeneous simplified model that allows to determine the effect of key parameters such as degradation rates in the asymptotic behavior of...
From turbulence to climate: pathways and ecology of upper ocean nutrient flux
Summary: Ocean currents shape the distribution and magnitude of microbial populations with cascading influences on the global carbon cycle. In this talk, I will derive a parameterization for the turbulent flux of biological tracers and highlight the role of biological timescales. This parameterization reveals a growth-transport feedback that can generate diversity in phytoplankton community structure at fine scales (1-10 km) and higher net productivity in the presence of community diversity. I will then use ship-board observations to examine...
