### Recent Submissions

• #### Right unimodal and bimodal singularities in positive characteristic ﻿

(International Mathematics Research Notices, 2017-08-07)
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. ﻿

(2018-08-15)
A Boltzmann equation, used to describe the Compton scattering in the non-relativistic 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 ﻿

(2018-03-27)
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, 2018-08-29)
We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer bi-Lipschitz transformations (outer bi-Lipschitz homeomorphims of germs in the first case and outer bi-Lipschitz ...
• #### Concurent multi-scale physical parametrization of fire-spotting: A study on the role of macro- and meso-scale 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, 2018-07-30)
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 ...
• #### Surrogate-based global sensitivity analysis for turbulence and fire-spotting effects in regional-scale wildland fire modeling ﻿

(Stochastic Environmental Research and Risk Assessment, 2018-08)
In presence of strong winds, wildfires feature nonlinear behavior, possibly inducing fire-spotting. We present a global sensitivity analysis of a new sub-model for turbulence and fire-spotting included in a wildfire spread ...
• #### On the geometry of strongly flat semigroups and their generalizations ﻿

(2018-09-18)
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 Seiberg-Witten invariant of plumbed 3-manifolds ﻿

(2017-02)
Assume that $M(\mathcal{T})$ is a rational homology sphere plumbed 3--manifold 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 3-manifolds ﻿

(2018-06)
Assume that the link of a complex normal surface singularity is a rational homology sphere. Then its Seiberg-Witten invariant can be computed as the ‘periodic constant’ of the topological multivariable Poincaré series (zeta ...
• #### Némethi’s division algorithm for zeta-functions of plumbed 3-manifolds ﻿

(Bulletin of the London Mathematical Society, 2018-08-27)
A polynomial counterpart of the Seiberg-Witten invariant associated with a negative definite plumbing 3-manifold has been proposed by earlier work of the authors. It is provided by a special decomposition of the zeta-function ...
• #### Some classes of homeomorphisms that preserve multiplicity and tangent cones ﻿

(2018-08-19)
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 ﻿

(2018-06-30)
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 ...
• #### The role of the environment in front propagation ﻿

(Proceedings of the 18th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2018 July 9–14, 2018, 2018-07-09)
In this work we study the role of a complex environment in the propagation of a front with curvature-dependent speed. The motion of the front is split into a drifting part and a fluctuating part. The drifting part is ...
• #### Hölder equivalence of complex analytic curve singularities ﻿

(Bulletin of the London Mathematical Society, 2018-08-06)
We prove that if two germs of irreducible complex analytic curves at $0\in\mathbb{C}^2$ have different sequence of characteristic exponents, then there exists $0<\alpha<1$ such that those germs are not $\alpha$-H\"older ...
• #### The Nash Problem from a Geometric and Topological Perspective ﻿

(2018-04-17)
We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the au- thors influenced it. Later we summarize the main ideas in the higher dimen- ...

(2018-06-18)

(2018-05-08)
• #### Modeling of birth-death and diffusion processes in biological complex environments ﻿

(2018-04-20)
This thesis is centered on the theory of stochastic processes and their applications in biological systems characterized by a complex environment. Three case studies have been modeled by the use of the three fundamental ...