### Recent Submissions

• #### The abel map for surface singularities II. Generic analytic structure ﻿

We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure ...
• #### Reflection maps ﻿

(Mathematische Annalen, 2020)
Given a reflection group G acting on a complex vector space V , a reflection map is the composition of an embedding X → V with the quotient map V → Cp of G. We show how these maps, which can highly singular, may be studied ...
• #### Decomposition theorem and torus actions of complexity one ﻿

(European Journal of Mathematics, 2020)
We algorithmically compute the intersection cohomology Betti numbers of any complete normal algebraic variety with a torus action of complexity one.
• #### The random diffusivity approach for diffusion in heterogeneous systems ﻿

(2020-12-16)
The two hallmark features of Brownian motion are the linear growth $\langle x^2(t) \rangle = 2 D d t$ of the mean squared displacement (MSD) with diffusion coefficient $D$ in $d$ spatial dimensions, and the Gaussian ...
• #### Gut microbiota ecology: Biodiversity estimated from hybrid neutral-niche model increases with health status and aging ﻿

(Plos One, 2020-10-30)
In this work we propose an index to estimate the gut microbiota biodiversity using a modeling approach with the aim of describing its relationship with health and aging. The gut microbiota, a complex ecosystem that links ...
• #### Local Topological Obstruction For Divisors ﻿

(Revista Matematica Complutense, 2020)
Given a smooth, projective variety $X$ and an effective divisor $D\,\subseteq\, X$, it is well-known that the (topological) obstruction to the deformation of the fundamental class of $D$ as a Hodge class, lies in ...
• #### Universal spectral features of different classes of random diffusivity processes ﻿

(New Journal of Physics, 2020-06-26)
Stochastic models based on random diffusivities, such as the diffusing- diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically ...
• #### Kato-matsumoto-type results for disentanglements ﻿

(Cambridge University Press, 2020)
We consider the possible disentanglements of holomorphic map germs f : (Cn, 0) → (CN , 0), 0 < n < N, with nonisolated locus of instability Inst(f). The aim is to achieve lower bounds for their (homological) connectiv- ity ...
• #### On a conjecture of harris ﻿

(World Scientific, 2019)
For d ≥ 4, the Noether-Lefschetz locus NLd parametrizes smooth, degree d sur- faces in P3 with Picard number at least 2. A conjecture of Harris states that there are only finitely many irreducible components of the ...
• #### On the length of perverse sheaves on hyperplane arrangements ﻿

(european Journal of Mathematics, 2019)
Abstract. In this article we address the length of perverse sheaves arising as direct images of rank one local systems on complements of hyperplane arrangements. In the case of a cone over an essential line arrangement ...
• #### The Abel map for surface singularities I. Generalities and examples ﻿

(Mathematische Annalen, 2019)
Abstract. Let (X, o) be a complex normal surface singularity. We fix one of its good resolutions X → X, an effective cycle Z supported on the reduced exceptional curve, and any possible (first Chern) class l′ ∈ H 2 (X , ...
• #### Classical dynamics generated by long-range interactions for lattice fermions and quantum spins ﻿

(J. Math. Anal. Appl., 2021)
We study the macroscopic dynamical properties of fermion and quantum-spin systems with long-range, or mean-field, interactions. The results obtained are far beyond previous ones and require the development of a mathematical ...
• #### Macroscopic Dynamics of the Strong-Coupling BCS-Hubbard Model, ﻿

(Physics of Particles and Nuclei, 2020)
The aim of the current paper is to illustrate, in a simple example, our recent, very general, rigorous results on the dynamical properties of fermions and quantum-spin systems with long-range, or meanfield, interactions, ...
• #### Lieb–Robinson Bounds for Multi–Commutators and Applications to Response Theory ﻿

(Springer Briefs in Math. Phys., 2017)
We generalize to multi-commutators the usual Lieb–Robinson bounds for commutators. In the spirit of constructive QFT, this is done so as to allow the use of combinatorics of minimally connected graphs (tree expansions) in ...
• #### Quantum Dynamics Generated by Long-Range Interactions for Lattice Fermion and Quantum Spins ﻿

(J. Math. Anal. Appl., 2021)
We study the macroscopic dynamics of fermion and quantum-spin systems with long-range, or mean-field, interactions, which turns out to be equivalent to an intricate combination of classical and short-range quantum dynamics. ...
• #### A generalized Stefan model accounting for system memory and non-locality ﻿

(International Communications in Heat and Mass Transfer, 2020-05)
The Stefan problem, involving the tracking of an evolving phase-change front, is the prototypical example of a moving boundary problem. In basic one- dimensional problems it is well known that the front advances as the ...
• #### Some classes of homeomorphisms that preserve multiplicity and tangent cones ﻿

(AMERICAN MATHEMATICAL SOCIETY, 2020-01-01)
In this paper we present some applications of A’Campo-Lˆe’s Theorem and we study some relations between Zariski’s Questions A and B. It is presented some classes of homeomorphisms that preserve multiplicity and tangent ...
• #### The Nash Problem from Geometric and Topological Perspective ﻿

(WORLD SCIENTIFIC (EUROPE), 2020-03-01)
We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the authors influenced it. Later, we summarize the main ideas in the higher dimensional ...
• #### A hypothesis about parallelism vs. seriality in dreams ﻿

(Front. Psychol., 2019-10-10)
The current article discusses the hypothesis about parallelism vs. Seriality in dreams. The process of dream building implies the construction of a complex network of closely interrelated sources. On the other hand, the ...
• #### Equivariant motivic integration and proof of the integral identity conjecture for regular functions ﻿

(Mathematische Annalen, 2019-12-02)
We develop Denef-Loeser’s motivic integration to an equivariant version and use it to prove the full integral identity conjecture for regular functions. In comparison with Hartmann’s work, the equivariant Grothendieck ...