Seminari de doctorandsLebesgue's decomposition theorem without tears
Resum: Lebesgue's decomposition theorem is an important result in measure theory which says that for any given two measures, one can be decomposed as a sum of two measures which are respectively diffuse and concentrated with respect to the other. We will introduce the setting of the theorem without requiring any background in measure theory, and we will give a short, easy and self-contained proof of a generalization of this theorem. I found such a beautiful proof in [1], which we will follow.
Segon Seminari de Teoria de Categories
Resum: Lecture seminar on anem seguint el llibre "Categories for the Working Mathematician". Cada setmana el conferenciant és un dels participants al seminari, en el format \emph{working seminar} o \emph{lecture seminar}.
The naming of the Vandermonde determinant
Resum: We will study what is arguably the most famous case of mathematical epynomy: The Vandermonde determinant. Following [1], we will discuss Vandermonde's contribution to the development of the determinant, his involvement in the French revolution and the concerns regarding his authorship on the nowadays called Vandermonde determinant. Did he ever consider such an object? And, if not, why do we call it Vandermonde's determinant?
EstadísticaEstimation of life expectancy for time-varying factors and the importance of different causes of death: the Life Years Lost method, developed R functions, and example on mental disorders
Resum: The life expectancy at birth is a summary measure of life table mortality rates, which is frequently used in demography. It is estimated as the area under the survival curve corresponding to the mortality rates and represents the expected lifetime in a population for which the age-specific mortality rates apply now and in the future. Along those lines, the number of Life Years Lost is used to measure the reduction in life expectancy for a specific group of persons, for example those diagnosed with a specific disease; however, its calculation is not straightforward. In this session, I will introduce a new method to estimate Life Years Lost among persons with a specific disease, including its decomposition according to different causes of death using a competing risks framework. In addition, I will present results on Life Years Lost associated with mental disorders based on population-based registers from Denmark including 7.4 million persons
GeometriaMin-max width and volume of Riemannian three-dimensional spheres
Resum: By the work of Simon and Smith, every Riemannian three-dimensional sphere contains an embedded minimal two-dimensional sphere. Their method of construction is a min-max method for the area functional and the area of this minimal sphere is bounded from above by a number depending only on the ambient geometry, known as the width. In this talk, we will discuss upper bounds for the width among certain classes of metrics with the same volume. This is joint work with Rafael Montezuma (UMass-Amhrest).
Topological rigidity and finiteness for non-geometric 3-manifolds
Resum: The Riemannian geometry of non-geometric 3-manifolds (that is, those which do not admit any of the eight complete maximal homogeneous 3-dimensional geometries) deserved considerably less attention than their geometric counterparts, with a few remarkable exceptions. In this seminar, we will explain some peculiar topological rigidity and finiteness properties of the class of non-geometric Riemannian 3-manifolds with bounded entropy and diameter, with respect to the Gromov-Hausdorff distance. The talk is based on the papers https://arxiv.org/abs/1705.06213 and https://arxiv.org/abs/1711.06210 in collaboration with F. Cerocchi"
Entropia de volum i longituds de corbas homotòpicament independents
Resum: Presentaré una desigualtat per les varietats riemannianes tancades que impliqua l'entropía del volum i el conjunt de longituds de qualsevol família de corbes homotòpicament independents basats en un mateix punt. Aquesta desigualitat implica un teorema del collaret universal, és a dir sense restricció de curvatura. És un treball en col.laboració amb el Louis Merlin.
Rational parallelisms and generalized Cartan geometries on complex manifolds
Resum: This talk deals with (generalized) holomorphic Cartan geometries on compact complex manifols. The concept of holomorphic Cartan geometry encapsulates many interesting geometric structures including holomorphic parallelisms, holomorphic Riemannian metrics, holomorphic conformal structures, holomorphic affine connections or holomorphic projective connections. A more flexible notion is that of a generalized Cartan geometry which allows some degeneracy of the geometric structure. This encapsulates for example some interesting rational parallelisms.
Sistemes DinàmicsChaos: why, where and how much
Resum: We consider the chaos which appears in real problems assuming:1) determinism; 2) a mathematical model; 3) good agreement between physical experiments and predictions coming from the model.
On the secant map as a plane dynamical system
Resum: The plane dynamical system generated by the secant method applied to real polynomials ia a particular example to a large family of differentiable plane dynamical systems given by rational components. In this seminar we will present some results we have found about the shape and distribution of the atrracting basins, as well as other considerations. This is a joint work with Antonio Garijo.
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