Multiplier ideals in two-dimensional local rings with rational singularities 

    Dachs Cadefau, Ferran (Date of defense: 2016-06-13)

    The aim of this memoir is to study multiplier ideals in two-dimensional local rings having at worst rational singularities. We also want to extend this study to the case of mixed multiplier ideals. The main achievements ...

    On the fractional Yamabe problem with isolated singularities and related issues 

    Torre Pedraza, Azahara de la (Date of defense: 2016-12-19)

    My research is based on non-local elliptic semilinear equations in conformal geometry. The fractional curvature is defined from the conformal fractional Laplacian and it is a non-local version of some of the classical local ...

    Rheological models for tissue relaxation and fluidisation 

    Asadipour, Nina (Date of defense: 2016-03-04)

    We present a cell-centred model for the simulation of multicellular soft tissues that takes into account the underlying active process at the cytoskeletal level, and allows for active and passive cell-cell reorganisation ...

    Stark-Heegner points and p-adic L-functions 

    Casazza, Daniele (Date of defense: 2016-10-28)

    Let K|Q be a number field and let Z(K,s) be its associated complex L-function. The analytic class number formula relates special values of Z(K,s) with algebraic invariants of the field K itself. It admits a Galois equivariant ...

    The embedding problem for Markov matrices 

    Roca Lacostena, Jordi (Date of defense: 2021-05-18)

    The goal of this thesis is to solve the embedding problem for Markov matrices, posed by Gustav Elfving in1937. A Markov matrix is non-negative square matrix whose rows sum to 1. We say that such a matrix M is embeddable ...

    The variational approach to brittle fracture in materials with anisotropic surface energy and in thin sheets 

    Li, Bin (Date of defense: 2016-03-08)

    Fracture mechanics of brittle materials has focused on bulk materials with isotropic surface energy. In this situation different physical principles for crack path selection are very similar or even equivalent. The situation ...