Planas Bahí, Arnau (Date of defense: 2020-09-30)
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 ...
Cardona Aguilar, Robert (Date of defense: 2021-05-26)
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 ...
Oms, Cédric (Date of defense: 2020-10-02)
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 ...
Braddell, Róisín (Date of defense: 2021-02-17)
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 ...
Vrioni, Brikena (Date of defense: 2021-10-29)
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 ...
Garrote López, Marina (Date of defense: 2021-07-22)
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 ...
Cano Vila, María del Pilar (Date of defense: 2020-06-25)
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 ...
Rivero Salgado, Óscar (Date of defense: 2021-02-12)
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 ...
Blanco Fernández, Guillem (Date of defense: 2020-04-16)
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 ...
Rivas Guijarro, Xavier (Date of defense: 2021-12-17)
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 ...