Mathematical Physics (MP)
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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 ... 
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, 20180709)In this work we study the role of a complex environment in the propagation of a front with curvaturedependent 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, 20180806)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
(20180417)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 ... 
Monodromies as têteàtête graphs
(20180508) 
Modeling of birthdeath and diffusion processes in biological complex environments
(20180420)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 ... 
Existence of “$d$wave” Pairs and Density Waves in a Class of Microscopic Models for High Transition Temperature Superconductors
(20180321)Hightemperature superconductors have different properties than conventional superconductors, one of these important properties is nonisotropic symmetry of the order parameter. In this work we present a model that shows ... 
Mixed têteàtête twists as monodromies associated with holomorphic function germs
(20180401)Têteàtête graphs were introduced by N. A’Campo in 2010 with the goal of modeling the monodromy of isolated plane curves. Mixed têteàtête graphs provide a generalization which define mixed têteàtête twists, which ... 
General têteàtête graphs and Seifert manifolds
(20180210)Têteàtête graphs and relative têteàtête graphs were introduced by N. A’Campo in 2010 to model monodromies of isolated plane curves. By recent work of Fdez de Bobadilla, Pe Pereira and the author, they provide a way ... 
Quasiprobability Approach for Modelling Local Extinction and Countergradient in Turbulent Premixed Combustion
(Proceedings/Extended Abstract Book (6 pages) of the XLI Meeting of the Italian Section of the Combustion Institute, 20180523)In opposition to standard probability distributions, quasiprobability distributions can have negative values which highlight nonclassical properties of the corresponding system. In quantum mechanics, such negative values ... 
Effective selfsimilar expansion for the GrossPitaevskii equation
(Physical Review A, 201804)We consider an effective scaling approach for the free expansion of a onedimensional quantum wave packet, consisting in a selfsimilar evolution to be satisfied on average, i.e., by integrating over the coordinates. A ... 
Random diffusivity from stochastic equations: comparison of two models for Brownian yet nonGaussian diffusion
(New Journal of Physics, 201804)A considerable number of systems have recently been reported in which Brownian yet nonGaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the ... 
A proof of the differentiable invariance of the multiplicity using spherical blowingup
(Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 20180421)In this paper we use some properties of spherical blowingup to give an alternative and more geometric proof of GauLipman Theorem about the differentiable invariance of the multiplicity of complex analytic sets. Moreover, ... 
Wildland fire propagation modeling: firespotting parametrisation and energy balance
(Proceedings of the 17th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2017, pp. 805  813, 20170704)Present research concerns the physical background of a wildfire propagation model based on the split of the front motion into two parts  drifting and fluctuating. The drifting part is solved by the level set method and ...