Facultat de Matemàtiques i Estadística
Recent Submissions
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p-adic L-functions, p-adic Gross-Zagier formulas and plectic points
(Universitat Politècnica de Catalunya, 2022-04-19)
Doctoral thesis
Open AccessIn this work we generalize the construction of p-adic anticyclotomic L-functions associated to an elliptic curve E/F and a quadratic extension K/F, by defining a measure µ_f^p attached to K/F and an automorphic form. In ... -
Probabilistic and extremal studies in additive combinatorics
(Universitat Politècnica de Catalunya, 2022-01-26)
Doctoral thesis
Open AccessThe results in this thesis concern extremal and probabilistic topics in number theoretic settings. We prove sufficient conditions on when certain types of integer solutions to linear systems of equations in binomial ... -
Geometrical aspects of contact mechanical systems and field theories
(Universitat Politècnica de Catalunya, 2021-12-17)
Doctoral thesis
Open AccessMany 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 ... -
Threshold phenomena involving the connected components of random graphs and digraphs
(Universitat Politècnica de Catalunya, 2021-12-13)
Doctoral thesis
Open AccessWe consider some models of random graphs and directed graphs and investigate their behavior near thresholds for the appearance of certain types of connected components. Firstly, we look at the critical window for the ... -
A census for curves and surfaces with diophantine stability over finite fields
(Universitat Politècnica de Catalunya, 2021-10-29)
Doctoral thesis
Open AccessAn 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 ... -
Genomics tools in the cloud: the new frontier in omics data analysis
(Universitat Politècnica de Catalunya, 2021-10-19)
Doctoral thesis
Open AccessSubstantial technological advancements in next generation sequencing (NGS) have revolutionized the genomic field. Over the last years, the speed and throughput of NGS technologies have increased while their costs have ... -
A study on structure recovery and the broadcasting problem
(Universitat Politècnica de Catalunya, 2021-09-17)
Doctoral thesis
Open AccessThe thesis contains a study of two problems of combinatorial statistics. The first one is structure learning for partial correlation graphs and the second one is the broadcasting problem on certain families of random ... -
Ejection-collision orbits in the restricted three-body problem
(Universitat Politècnica de Catalunya, 2021-07-06)
Doctoral thesis
Open AccessThe main objective of this dissertation is the study of the ejection-collision (EC) orbits in the circular and planar Restricted Three Body Problem (RTBP from now on). In particular, we will focus on the analytical and ... -
An effective method to study the Hopf-Galois module structure of certain extensions of fields
(Universitat Politècnica de Catalunya, 2021-07-02)
Doctoral thesis
Open AccessWe develop a method to compute a basis of the associated order in a Hopf Galois structure H of the ring of integers O_L of an extension of number or p-adic fields L/K. We state and prove a necessary and sufficient condition ... -
Algebraic and semi-algebraic phylogenetic reconstruction
(Universitat Politècnica de Catalunya, 2021-07-22)
Doctoral thesis
Open AccessPhylogenetics 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 ... -
Qualitative properties of solutions to integro-differential elliptic problems
(Universitat Politècnica de Catalunya, 2021-07-14)
Doctoral thesis
Open AccessThe thesis is devoted to the analysis of elliptic PDEs and related problems. It is mainly focused on the study of qualitative and regularity properties of solutions to integro-differential equations. The study of such ... -
The geometry and topology of steady Euler flows, integrability and singular geometric structures
(Universitat Politècnica de Catalunya, 2021-05-26)
Doctoral thesis
Open AccessIn 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 ...
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