Mathematical Physics (MP)
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A jacobian module for disentanglements and applications to Mond's conjecture
(Revista Matemática Complutense, 2019)Let $f:(\mathbb C^n,S)\to (\mathbb C^{n+1},0)$ be a germ whose image is given by $g=0$. We define an $\mathcal O_{n+1}$module $M(g)$ with the property that $\mathscr A_e$$\operatorname{codim}(f)\le \dim_\mathbb C M(g)$, ... 
RandomFront 2.3 A physical parametrisation of firespotting for operational fire spread models: Implementation in WRFSfire and response analysis with LSFire+
(Geoscientific Model Development, 201812)Firespotting is often responsible for a dangerous flare up in the wildfire and causes secondary ignitions isolated from the primary fire zone leading to perilous situations. The main aim of the present research to provide ... 
On Zariski’s multiplicity problem at infinity
(Proceedings of the American Mathematical Society, 20180814)We address a metric version of Zariski's multiplicity conjecture at infinity that says that two complex algebraic affine sets which are biLipschitz homeomorphic at infinity must have the same degree. More specifically, ... 
Measurevalued weak solutions to some kinetic equations with singular kernels for quantum particles
(20181219)In this thesis, we present a mathematical study of three problems arising in the kinetic theory of quantum gases. In the first part, we consider a Boltzmann equation that is used to describe the time evolution of the ... 
Singularities in Geometry and Topology
(20180618)This thesis consists of two different topics that are not related. The thesis has two different and independent parts that can be read in any order. The purpose of this work is to study two topics in singularity theory: ... 
Crossover from anomalous to normal diffusion: truncated powerlaw noise correlations and applications to dynamics in lipid bilayers
(New Journal of Physics, 20181018)The emerging diffusive dynamics in many complex systems shows a characteristic crossover behaviour from anomalous to normal diffusion which is otherwise fitted by two independent powerlaws. A prominent example for a ... 
Right unimodal and bimodal singularities in positive characteristic
(International Mathematics Research Notices, 20170807)The problem of classification of real and complex singularities was initiated by Arnol'd in the sixties who classified simple, unimodal and bimodal singularities w.r.t. right equivalence. The classification of simple ... 
On a Boltzmann equation for Compton scattering, from non relativistic electrons at low density.
(20180815)A Boltzmann equation, used to describe the Compton scattering in the nonrelativistic limit is considered. A truncation of the very singular redistribution function is introduced and justified. The existence of weak solutions ... 
On a system of equations for the normal fluid  condensate interaction in a Bose gas
(20180327)The existence of global solutions for a system of differential equations is proved, and some of their properties are described. The system involves a kinetic equation for quantum particles. It is a simplified version of ... 
Multiplicity and degree as bi‐Lipschitz invariants for complex sets
(Journal of Topology, 20180829)We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer biLipschitz transformations (outer biLipschitz homeomorphims of germs in the first case and outer biLipschitz ... 
Concurent multiscale physical parametrization of firespotting: A study on the role of macro and mesoscale characteristics of the system
(Advances in Forest Fire Research, 2018)The strong impact of wildfires in terms of lives and homes lost and of damage to ecosystems, calls for an urgent improvement in the risk management. The aim of the present research is the improvement of these software ... 
Wildfire propagation modelling
(Geophysical Research Abstracts Vol. 20, 2018)Wildfires are a concrete problem with a strong impact on human life, property and the environment, because they cause disruption and are an important source of pollutants. Climate change and ... 
Langevin equation in complex media and anomalous diffusion
(Journal of the Royal Society Interface, 20180730)The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modelling approaches for the description of anomalous diffusion in biological systems, such ... 
Surrogatebased global sensitivity analysis for turbulence and firespotting effects in regionalscale wildland fire modeling
(Stochastic Environmental Research and Risk Assessment, 201808)In presence of strong winds, wildfires feature nonlinear behavior, possibly inducing firespotting. We present a global sensitivity analysis of a new submodel for turbulence and firespotting included in a wildfire spread ... 
On the geometry of strongly flat semigroups and their generalizations
(20180918)Our goal is to convince the readers that the theory of complex normal surface singularities can be a powerful tool in the study of numerical semigroups, and, in the same time, a very rich source of interesting affine and ... 
Surgery formulae for the SeibergWitten invariant of plumbed 3manifolds
(201702)Assume that $M(\mathcal{T})$ is a rational homology sphere plumbed 3manifold associated with a connected negative definite graph $\mathcal{T}$. We consider the combinatorial multivariable Poincar\'e series associated ... 
Combinatorial duality for Poincaré series, polytopes and invariants of plumbed 3manifolds
(201806)Assume that the link of a complex normal surface singularity is a rational homology sphere. Then its SeibergWitten invariant can be computed as the ‘periodic constant’ of the topological multivariable Poincaré series (zeta ... 
Némethi’s division algorithm for zetafunctions of plumbed 3manifolds
(Bulletin of the London Mathematical Society, 20180827)A polynomial counterpart of the SeibergWitten invariant associated with a negative definite plumbing 3manifold has been proposed by earlier work of the authors. It is provided by a special decomposition of the zetafunction ... 
Some classes of homeomorphisms that preserve multiplicity and tangent cones
(20180819)In this paper it is presented some classes of homeomorphisms that preserve multiplicity and tangent cones of complex analytic sets. Moreover, we present a class of homeomorphisms that has the multiplicity as an invariant ... 
Semialgebraic CMC surfaces in $\mathbb{R}^3$ with singularities
(20180630)In this paper we present a classification of a class of semialgebraic CMC surfaces in $\mathbb{R}^3$ that generalizes the recent classification made by Barbosa and do Carmo in 2016 (complete reference is in the paper), we ...