### Recent Submissions

• #### Wildfire Spreading: a new application of the Beta distribution ﻿

(2022)
This dissertation is in the mathematical physics area, more specifically, applications in the statistics field. The thesis, under the supervision of Dr. Gianni Pagnini, was carried out at the BCAM - Basque Centre for ...
• #### Beta Distribution in Wildfire Spreading ﻿

(2022)
This paper is the result of research work carried out in collaboration with the Statistical Physics team of the Basque Center for Applied Mathematics in Bilbao, supervised by Dr. Gianni Pagnini. Main subject is PROPAGATOR, ...
• #### Statistical Characterization of Wildfire Dynamics: Studying the Relation Between Burned Area and Head of the Fire ﻿

(2022-06-06)
We show that the probability density function (PDF) of an area enclosed by a random perimeter is driven by the PDF of the integration bounds and the mean value of the perimeter function. With reference to wildfires, if the ...
• #### Uniform Lech's inequality ﻿

(2022)
Let (R,m) be a Noetherian local ring, and let M be a finitely generated R-module of dimension d. We prove that the set [Formula presented] is bounded below by 1/d!e(R‾) where R‾=R/Ann(M). Moreover, when Mˆ is equidimensional, ...
• #### A b-symplectic slice theorem ﻿

(2022-01-01)
In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of b -symplectic manifolds started in Guillemin, Miranda, and Pires Adv. Math. 264 (2014), 864–896, we ...
• #### COHOMOLOGY OF CONTACT LOCI ﻿

(2022-01-01)
We construct a spectral sequence converging to the cohomology with compact support of the m-th contact locus of a complex polynomial. The first page is explicitly described in terms of a log resolution and coincides with ...
• #### Classical dynamics from self-consistency equations in quantum mechanics ﻿

(2022-05-09)
During the last three decades, P. Bóna has developed a non-linear generalization of quantum mechanics, based on symplectic structures for normal states and offering a general setting which is convenient to study the emergence ...
• #### Time Dynamics in Quantum Field Theory Systems ﻿

(2022-12-23)
In this doctoral thesis, we develop and investigate new mathematical tools that are intended to allow for a rigorous description of non–perturbative quantum field theory (QFT) dynamics. Here, the term QFT is to be understood ...
• #### Implementing Bogoliubov Transformations Beyond the Shale-Stinespring Condition ﻿

(2022-04-28)
We provide two extensions of a dense subspace of Fock space, such that Bogoliubov transformations become implementable on them, even though they violate the Shale-Stinespring condition, so they are not implementable on ...
• #### Extended State Space for Describing Renormalized Fock Spaces in QFT ﻿

(2022-06-04)
In quantum field theory (QFT) models, it often seems natural to use, instead of wave functions from Fock space, wave functions that are not square-integrable and have prefactors involving divergent integrals (known as ...
• #### Lower bounds on Hilbert-Kunz multiplicities and maximal F-signature ﻿

(2022)
ABSTRACT. Hilbert–Kunz multiplicity and F-signature are numerical invariants of commutative rings in positive characteristic that measure severity of singularities: for a regular ring both invariants are equal to one and ...
• #### Uniform Lech's inequality ﻿

(2022)
Let (R,m) be a Noetherian local ring of dimension d ≥ 2. We prove that if e(R􏰊red) > 1, then the classical Lech’s inequality can be improved uniformly for all m-primary ideals, that is, there exists ε > 0 such that e(I) ...
• #### Moderately Discontinuous Homology ﻿

(2021-01-01)
We introduce a new metric homology theory, which we call Moderately Discontinuous Homology, designed to capture Lipschitz properties of metric singular subanalytic germs. The main novelty of our approach is to allow ...
• #### Entanglement of classical and quantum short-range dynamics in mean-field systems ﻿

(2021-11-01)
The relationship between classical and quantum mechanics is usually understood via the limit ħ→0. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity ...
• #### Linearization of holomorphic families of algebraic automor- phisms of the affine plane ﻿

(2022-01-03)
Let $G$ be a reductive group. We prove that a family of polynomial actions of $G$ on $\mathbb{C}^2$, holomorphically parametrized by an open Riemann surface, is linearizable. As an application, we show that a particular ...
• #### The Abel map for surface singularities III: Elliptic germs ﻿

(2021-01-01)
The present note is part of a series of articles targeting the theory of Abel maps associated with complex normal surface singularities with rational homology sphere links (Nagy and Némethi in Math Annal 375(3):1427–1487, ...
• #### Delta invariant of curves on rational surfaces I. An analytic approach ﻿

(2021-01-01)
We prove that if (C, 0) is a reduced curve germ on a rational surface singularity (X, 0) then its delta invariant can be recovered by a concrete expression associated with the embedded topological type of the pair C X. ...
• #### High temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graph ﻿

(2021-08-01)
The Kubo-Martin-Schwinger (KMS) condition is a widely studied fundamental property in quantum statistical mechanics which characterizes the thermal equilibrium states of quantum systems. In the seventies, Gallavotti and ...
• #### Parametrization simple irreducible plane curve singularities in arbitrary characteristic ﻿

(2020-01-01)
We study the classification of plane curve singularities in arbitrary characteristic. We first give a bound for the determinacy of a plane curve singularity with respect to pararametrization equivalence in terms of its ...
• #### Classification of Lipschitz simple function germs ﻿

(2020-07-01)
It was shown by Henry and Parusiński in 2003 that the bi-Lipschitz right equivalence of function germs admits moduli. In this article, we introduce the notion of Lipschitz simple function germ and present the complete ...