Universitat Politècnica de Catalunya
Now showing items 1-20 of 20
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 ...
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 ...
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 ...
Mitjançant tècniques geomètriques, abordem les qüestions següents:<br/><br/>(i) Estudi (caracterització, classificació, famílies diferenciables,...) d'una classe destacada de subespais invariants, els anomenats ...
(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 ...
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 ...
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 ...
(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 ...
En primer lloc, s'evidencia que el disseny que involucra grafisme es pot analitzar com articulat en dos nivells o etapes, un de concepció, intel·lectual, i un altre d'execució, manual o físic, ambdós sempre en interrelació ...
The theories of gravity are one of the most important topics in theoretical physics and mathematical physics nowadays. The classical formulation of gravity uses the Hilbert-Einstein Lagrangian, which is a singular ...
In this thesis, we study the application of symplectic geometry, regular and singular, to symplectic dynamical systems.We start with a motivating case: the relation between symplectic foliations and global transverse ...
(English) To simulate unsteady phenomena on complex moving geometry, computational scientists and engineers have been interested in unstructured space-time discretizations. These space-time discretizations aim to overcome ...
In this work we present the study we did in Graph Theory. In the firsts chapteres of the tesis we study the pieces of information that can be obtained from a graph: the spectrum of the adjacency matrix, the preintersection ...
(English) In this thesis, we study Poisson Structures on Moduli Spaces and Group actions. In particular, we focus on b^m-symplectic structures that can be seen both as symplectic structures with singularities and a particular ...
In this thesis, we make a deep investigation of the geometry and dynamics of several objects (singular or not) appearing in nature. The main goal is to study rigidity versus flexibility dynamical behavior of the objects ...
