seminar

Ponente: Arnold de la Peña Cuao (Departamento de Estadística e I.O. Universidad de Granada).

Título: Modelización y análisis de variables de tipo económico mediante procesos de difusión. El caso de Colombia.

Abstract: El modelado de variables económicas dinámicas es un área de investigación en constante evolución que abarca diversos temas económicos. Este estudio modela el índice de consumo (IPC) básico en Colombia utilizando el proceso de difusión log-normal no homogéneo con factores exógenos lineales. La metodología combina un procedimiento bayesiano para la selección de factores exógenos que identificó cinco variables clave, con la estimación por máxima verosimilitud de los parámetros del modelo que permiten la obtención de expresionesanalíticas para las características principales del proceso y lafunción de densidad de probabilidad del estimador de la mediacondicional. Los resultados muestran que el modelo supera lasproyecciones del Banco Central en múltiples horizontes temporales,capturando el repunte inflacionario post-pandemia y post-invasión aUcrania de 2022. El análisis de escenarios revela que las tasas deinterés y la política monetaria son los principales factores queinfluyen en el IPC, seguidos por el sector externo y el mercado laboral.Este enfoque representa un avance significativo para economíasemergentes susceptibles a choques internos y externos, proporcionandoherramientas analíticas robustas para la toma de decisiones de política monetaria.

Ponente: Sabina Musto (Departamento de Matemáticas, Università degli Studi di Salerno).

Título: From Growth to Collapse: Modeling Population Dynamics via Lognormal diffusions processes with random catastrophes.

Fecha y hora: 22 de mayo de 2026, 11:30.

Abstract: Stochastic growth models and sigmoidal dynamics are essentialtools for describing patterns that frequently arise in natural systems. They are widely used in biology and ecology to represent mechanisms suchas population development, disease spread, and adaptive responses toenvironmental fluctuations. In this work, we investigate a lognormaldiffusion process subject to random catastrophic events, modeled assudden jumps that reset the system to a new random state. The novelty ofthe model lies in the assumption that the post-catastrophe restart levelfollows a binomial distribution. As a consequence, after eachcatastrophic event the population does not simply revert to its initialsize, but instead to a random level reflecting the survival probabilityof individual members. We apply this framework to the dynamics of a wolf population exposed to external disturbances. The findings show that themodel can realistically reproduce complex population trajectories, displaying periods of gradual growth interspersed with sudden declines triggered by unpredictable external shocks.

abstract

martes 4 de mayo — 10:00

Aula A16, Facultad de Ciencias

Conferenciante: Stéphane Mischler (Université Paris-Dauphine)

Título: Longtime behavior for evolution PDEs - An overview of semigroup techniques

Resumen: I will present an overview of semigroup techniques that make possible for many evolution PDEs: (1) to obtain the convergence to the equilibrium or more generally to the remarkable solution, sometimes with optimal or at least constructive rate, for linear problems; (2) to establish the existence of global solutions in a perturbative regime around the equilibrium for nonlinear problems.

Resumen: Two- or higher dimensional approximations are useful for
employing numerical methods such as quadrature rules or solving
partial differential equations in physics. Kernels methods are known
to be extremely versatile with respect to dimension and which
approximands are required. At the same time we must choose the right
distance functions or approaches to approximations when modelling data
even in simple instances like two dimensions. We shall show some
methods beginning with least-squares approximations on circles and
spheres to illustrate these points before we proceed to the general
and new cases of many types of kernel functions in any dimensions.

The least squares approximations on circles and spheres are chosen as
examples in order to honour Carl Friedrich Gauß from Göttingen whose
250th birthday is soon and who used least squares approximations on
circles and ellipses to approximate the positions of the planetoid
Ceres to extreme accuracy without employing a computer.

martes 28 de abril — 11:00

Aula A16, Facultad de Ciencias

Conferenciante 1: Simone Mauro (Università della Calabria)

Título: Least Energy Solutions for Cooperative and Competitive
Schrödinger Systems with Neumann Boundary Conditions

Resumen: Link

Conferenciante 2: Alessandro Goffi (Università degli Studi di Firenze)

Título: Global geometric estimates for the heat equation via duality
methods

Resumen: I discuss first-order and second-order regularization effectsfor solutions to the classical heat equation. In particular I propose aglobal approach to study smoothing effects of Hamilton-Li-Yau type: suchapproach is nonlinear in spirit and it is based on the Bernstein method and
duality techniques à la Evans. In a similar way, I also deal with the of geometric properties for the heat flow as initiated by Brascamp-Lieb. In contrast to maximum principle methods based on sup-norm procedures, the integral method I describe relies on contractivity properties for advection-diffusion equations and it applies to problems with homogeneous Neumann conditions posed equally on bounded and unbounded convex domains under suitable assumptions on their geometry. This is based on the paper https://arxiv.org/abs/2409.15456 obtained in collaboration with G. Tralli.

📅 martes 21 de abril — 11:00

📍 Aula A16, Facultad de Ciencias

👤 Conferenciante: Tomás Sanz-Perela (Universitat de Barcelona)

📖 Título: A shape optimization problem for quantum dot Dirac operators

📄 Resumen: In this talk, I will present a shape optimization problem for a Dirac operator and a strategy to approach it. In particular, I will describe the connections between this problem and related shape optimization questions for the Dirichlet Laplacian, a complex version of the Robin Laplacian, and the embedding of a Hardy space into a Bergman space. The talk is based on a joint work with A. Arrizabalaga, A. Mas, and L. Vega (2023), as well as two recent works: one by J. Duran (2026), and another in collaboration with J. Duran and A. Mas (2026).

Abstract: Guiding Vector Fields (GVFs) are a powerful tool for path following in robotic systems, but their extension to rotational motion on SO(3) is nontrivial. In this seminar, I will first discuss the challenges associated with attitude representations and introduce the basic notions of geometric control on SO(3). I will then present my current work on GVF-based path following defined directly on SO(3), leading to a singularity-free formulation suitable for aerobatic flight. The seminar will conclude with several simulation examples, along with practical tips for implementing Lie group operations, not only in high-level simulations but also in real-time autopilot systems.

Título: Isometric immersions into three-dimensional metric Lie groups

Conferenciante: José M. Manzano Universidad de Jaén

Abstract: In this talk, we study isometric immersions of surfaces into simply connected three-dimensional unimodular Lie groups endowed with left-invariant metrics, both in the Riemannian and Lorentzian settings (assuming in the latter case that Milnor’s operator is diagonalizable). We present global coordinate models for these metric Lie groups, depending analytically on their structure constants, and discuss several fundamental results that characterize such immersions. In particular, we investigate to what extent an immersion can be reconstructed from natural geometric data, including (a) the tangent projections of a left-invariant frame, (b) the left-invariant Gauss map, and (c) the shape operator. As a main result, we show that an isometric immersion is essentially determined by its left-invariant Gauss map, up to certain well-controlled angular companions, which are characterized in terms of a PDE.

This is a joint work with I. Castro and J. S. Santiago available at https://urldefense.com/v3/__https://arxiv.org/abs/2507.16728__;!!D9dNQwwGXtA!VHgqqWNqm-z6EOA44sIrlEZtm7ox7qR4pwq34_VctkMdc8rmLNQuqlBM7m8XxpxcHT3pn7w4iuX_lQE22Y1xsvQ$ .

📅 martes 14 de abril — 11:00

📍 Aula A13, Facultad de Ciencias

👤Conferenciante: Joan Mateu (Universitat Autònoma de Barcelona)

📖 Título: Minimisers for anisotropic Riesz energies.

📄 Resumen: We will characterize energy minimisers for a class of nonlocal interaction energies where the attraction is quadratic, and the repulsion is Riesz-like and anisotropic. We will show that, if the Fourier transform of the repulsive potential is positive, the minimiser is supported on a fully-dimensional ellipsoid, and its density is given by a Barenblatt-type profile.