Universitat Politècnica de Catalunya
Now showing items 1-20 of 33
An algebraic variety defined over a field is said to have Diophantine stability for an extension of this field if the variety does not acquire new points in the extension. Diophantine stability has a growing interest due ...
The Marle-Guillemin-Sternberg (MGS) model is an extremely important tool for the theory of Hamiltonian actions on symplectic manifolds. It has been extensively used to prove many local results both in symplectic geometry ...
Phylogenetics is the study of the evolutionary history and relationships among groups of biological entities (called taxa). The modeling of those evolutionary processes is done by phylogenetic trees whose nodes represent ...
En aquesta tesi interdisciplinar desenvolupem eines algebraiques per a problemes en filogenètica i genòmica. Per estudiar l'evolució molecular de les espècies sovint s'usen models evolutius estocàstics. L'evolució es ...
The main objective of this dissertation is the exploration of certain arithmetic applications of the Euler systems of Beilinson--Flach elements and diagonal cycles. Euler systems have been proved to be a very powerful tool ...
El tratamiento intrínseco de cuestiones relacionadas con la Teoría de Control no lineal a través de la aplicación de técnicas propias de la geometría diferencial ha sido en los últimos años un tema de interés para muy ...
The main aim of this thesis is the study of the Bernstein-Sato polynomial of plane curve singularities. In this context, we prove a conjecture posed by Yano about the generic b-exponents of a plane irreducible curve. In ...
This thesis explores classification and perturbation problems for group actions on a class of Poisson manifolds called $b^m$-Poisson manifolds. $b^m$-Poisson manifolds are manifolds which are symplectic away from a ...
[English] In n-dimensional adaptive applications, conformal simplicial meshes must be lo cally modified. One systematic local modification is to bisect the prescribed simplices while surrounding simplices are bisected ...
Mitjançant tècniques geomètriques, abordem les qüestions següents:<br/><br/>(i) Estudi (caracterització, classificació, famílies diferenciables,...) d'una classe destacada de subespais invariants, els anomenats ...
The traditional way to study algebraic cycles on an algebraic variety uses the Chow groups. However, in the beginnings of the 90's, Blaine Lawson and Eric Friedlander developed a different way to study algebraic cycles on ...
(English) In this thesis we investigate various aspects of the dynamics of Hamiltonian vector fields in singular symplectic manifolds. We concentrate on two questions: first, we investigate a generalization of the Arnold ...
This thesis studies different generalizations of Delaunay triangulations, both from a combinatorial and algorithmic point of view. The Delaunay triangulation of a point set S, denoted DT(S), has vertex set S. An edge uv ...
Many important theories in modern physics can be stated using the tools of differential geometry. It is well known that symplectic geometry is the natural framework to deal with autonomous Hamiltonian mechanics. This admits ...
Geometrical physics is a relatively young branch of applied mathematics that was initiated by the 60's and the 70's when A. Lichnerowicz, W.M. Tulczyjew and J.M. Souriau, among many others, began to study various topics ...
In this thesis, we study the Reeb and Hamiltonian dynamics on singular symplectic and contact manifolds. Those structures are motivated by singularities coming from classical mechanics and fluid dynamics. We start by ...
In this thesis we study the geography of irregular complex projective (or compact Kähler) varieties, paying special attention to the existence of fibrations. The thesis is divided into two parts. In the first one we ...
The study of b-symplectic manifolds was initiated in 2012 by the works of Victor Guillemin, Eva Miranda and Ana Rita Pires (Adv. Math. 264 (2014), 864¿896). These manifolds, which can be understood as symplectic manifolds ...
The main objects of study in this thesis are matroids. In particular we are interested in three particular classes matroids: regular matroids, arithmetic matroids, and internally perfect matroids. Of these families, regular ...
(English) To enhance the simulation accuracy when the solution presents sharp curved features, the community of high-order methods has started to curve not only the boundary but also the interior of unstructured high-order ...
