Noticias en español
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 aspects for two commonly used treatments,...
Read MoreA 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 the system and the stability of equilibriums. We...
Read MoreAsymptotic 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 solution is controlled by checking explicitly a...
Read MoreMultiple 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 play a central role in the polynomial Szemerédi...
Read MoreFrom 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 the interaction between ocean eddy processes and...
Read MoreUniquely ergodic subshifts over compactifications of the naturals
RESUMEN: In this talk, we will discuss one-dimensional substitution subshifts over (infinite) compact alphabets and their dynamical properties. As a motivating class, we will focus on shifts generated by a parametrised family of substitutions on certain compactifications of the natural numbers. We will provide a general checkable condition for unique ergodicity that relies on compactness properties of the substitution operator, which the analogue of the substitution matrix for infinite alphabets.
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