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Now showing items 1-10 of 129

#### 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 ...

#### Globally subanalytic CMC surfaces in $\mathbb{R}^3$ with singularities

(Proceedings A of the Royal Society of Edinburgh, 2020-03-02)

In this paper we present a classification of a class of globally subanalytic CMC surfaces in $\mathbb{R}^3$ that generalizes the recent classification made by Barbosa and do Carmo in 2016. We show that a globally subanalytic ...

#### 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 ...

#### Multiplicity, regularity and blow-spherical equivalence of complex analytic sets

(The Asian Journal of Mathematics, 2020-01-29)

This paper is devoted to study multiplicity and regularity of complex analytic sets. We present an equivalence for complex analytical sets, named blow-spherical equivalence and we obtain several applications with this new ...

#### Multiplicity of singularities is not a bi-Lipschitz invariant

(Mathematische Annalen, 2020-01-17)

It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity.

#### 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 ...

#### 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 ...

#### Neron models of intermediate Jacobians associated to moduli spaces

(Revista Matemática Complutense, 2019-12-01)

Let $\pi_1:\mathcal{X} \to \Delta$ be a flat family of smooth, projective curves of genus $g \ge 2$, degenerating to an irreducible nodal curve $X_0$ with exactly one node. Fix an invertible sheaf $\mathcal{L}$ on $\mathcal{X}$ ...

#### Moderately Discontinuous Algebraic Topology for Metric Subanalytic Germs

(2019-10-31)

We have developed both a homology theory and a homotopy theory in the context of metric subanalytic germs (see Definition 2.1). The former is called MD homology and is covered in Chapter 2, which contains a paper that is ...

#### Equilibrium and Transport Properties of Quantum Many-Body Systems

(2019-10-30)

This thesis is a study of equilibrium and dynamical properties of macroscopic quantum many-body problems. An important part of the manuscript concerns the study of heat and charge transport properties of fermions on the ...