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.
Limiting distributions of Spherical and Spin O(N) models: Appearance of GFF.
Resumen: Spherical model is a mathematical model of a ferromagnet introduced by Berlin and Kac in 1952 as a rough but analytically convenient modification of the Ising model. Since its inception it has enjoyed considerable popularity among the mathematicians and physicists as an exactly soluble model exhibiting a phase transition. In this talk we will explain its relation to the Gaussian free field in the infinite volume limit and to the spin O(N) model in the infinite spin-dimensionality limit of the latter.
Aplicaciones Racionales Degeneradas.
RESUMEN: El espacio de parámetros de aplicaciones racionales, de un grado dado, es una variedad compleja no-compacta. El objetivo de la charla es examinar la dinámica de funciones racionales que están cerca de infinito en el espacio de parámetros, es decir, cuando degeneran. Haré un resumen de resultados y técnicas conocidas. El énfasis estará en la relación entre la medida de máxima entropía y el comportamiento de la aplicación que envía un mapa f a su n-ésimo iterado. Este es un trabajo conjunto, en progreso, con...
Contour methods for -dimensional Long-Range Ising Model.
Resumen: On the -dimensional lattice with , the phase transition of the nearest-neighbor ferromagnetic Ising model can be proved by using Peierls argument, that requires a notion of contours, geometric curves on the dual of the lattice to study the spontaneous symmetry breaking. It is known that the one-dimensional nearest-neighbor ferromagnetic Ising model does not undergo a phase transition at any temperature. On the other hand, if we add a polynomially decaying long-range interaction given by for , the works by Dyson and...
Mapas no-uniformemente hiperbólicos en T2.
RESUMEN Un mapa f se considera no-uniformemente hiperbólico (NUH) si sus exponentes de Lyapunov son distintos de cero en casi todas partes. El primer ejemplo de un mapa NUH que no es Anosov fue presentado por A. Katok en 1977. Además, se ha demostrado que cualquier superficie admite difeomorfismos que satisfacen esta propiedad. Sin embargo, estos difeomorfismos suelen ser frágiles en ciertos aspectos: si f no es Anosov, cualquier difeomorfismo NUH conservativo puede ser aproximado en la topología C1 por un difeomorfismo cuyos exponentes de...
New developments in the study of the elasticity equation for the analysis of inverse problems applied in Geoscience.
Abstract: This talk presents the analysis of an elasticity equation with interface conditions as a way to understand the formation of subduction earthquakes and how it is possible to determine geophysical characteristics of some tectonic plates from surface measurements. First, two different numerical methods based on finite elements are analyzed to solve the forward problem by comparing their algorithmic complexity and some properties necessary to solve an inverse problem. Then, the inverse problem of recovering the coseismic slip (one of...
Effective Mass of the Fröhlich Polaron: Recent Progress and Open Question.
Resumen: Landau and Pekar (in 1948) and Spohn (in 1987) conjectured that the effective mass $m(\alpha)$ of the Fröhlich Polaron at coupling parameter $\alpha$ grows as $\alpha^4$ as $\alpha\to\infty$ with an explicit pre-factor. In a recent joint work with C. Mukherjee, M. Sellke, and S. R. S. Varadhan, we prove the lower bound $m(\alpha) \geq C \alpha^4$, which matches (up to a constant) the corresponding sharp upper bound shown recently by combining the results from Brooks and Seiringer (2022) and Polzer (2023).
All convex bodies in the subdifferential of a locally Lipschitz function.
Abstract: We construct a differentiable locally Lipschitz function f in R^d with the following property: for every convex body K of R^d, there exists x in R^d such that the subdifferential of f at x coincides with K (in the sense of limiting or Clarke). We show that our technique can be further refined to recover all compact connected subsets with nonempty interior in the image of the limiting subdifferential of a locally Lipschitz function. We end this talk with a brief discussion about how large the set of functions with the aforementioned...
A Statistical framework for the modeling of continuous phenotypical progression in Alzheimer’s Disease.
Abstract: Throughout an organism’s life, many biological systems transition through complex biophysical processes. These processes serve as indicators of the underlying biological states. Inferring these latent unobserved states is a key problem in modern biology and neuroscience. Unfortunately, in many experimental setups, we can, at best, obtain snapshots of the system at different times for different individuals, and one major challenge is reconciling those measurements. This formalism is particularly relevant in the study of Alzheimer’s...
Rigidez suave para difeomorfismos de Anosov en R3
RESUMEN Una clase interesante de sistemas dinámicos a estudiar es la de los difeomorfismos de Anosov. Esta clase presenta un comportamiento complejo en cuanto a sus órbitas. Es sabido que estos son estructuralmente estables, es decir, si perturbamos suavemente el sistema original esta nueva dinámica es Anosov y conjugada bajo un homeomorfismo bi-Hölder. En esta charla vamos a discutir que condiciones uno precisa para que dos difeomorfismos de Anosov conjugados bajo un homeomorfismo sean efectivamente conjugados suavemente, es decir, que...
