### Recent Submissions

• #### 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 ...
• #### Another Proof of Born's Rule on Arbitrary Cauchy Surfaces ﻿

(2021-10-14)
In 2017, Lienert and Tumulka proved Born's rule on arbitrary Cauchy surfaces in Minkowski space-time assuming Born's rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well ...
• #### Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk ﻿

(2021-07-24)
In this contribution we show that fractional diffusion emerges from a simple Markovian Gaussian random walk when the medium displays a power-law heterogeneity. Within the framework of the continuous time random walk, the ...
• #### Stochastic Properties of Colliding Hard Spheres in a Non-equilibrium Thermal Bath ﻿

(2021-07-24)
We consider the problem of describing the dynamics of a test particle moving in a thermal bath using the stochastic differential equations. We briefly recall the stochastic approach to the Brownian based on the statistical ...
• #### Image Milnor Number Formulas for Weighted-Homogeneous Map-Germs ﻿

(2021-07-05)
We give formulas for the image Milnor number of a weighted-homogeneous map-germ $(\mathbb{C}^n,0)\to(\mathbb{C}^{n+1},0)$, for $n=4$ and $5$, in terms of weights and degrees. Our expressions are obtained by a purely ...
• #### Classification of smooth factorial affine surfaces of Kodaira dimension zero with trivial units ﻿

(2021-07-31)
We give a corrected statement of (Gurjar and Miyanishi 1988, Theorem 2), which classifies smooth affine surfaces of Kodaira dimension zero, whose coordinate ring is factorial and has trivial units. Denote the class of such ...
• #### Some contributions to the theory of singularities and their characteristic classes ﻿

(2021-06-02)
In this Ph.D. thesis, we give some contributions to the theory of singularities, as well as to the theory of characteristic classes of singular spaces. The first part of this thesis is devoted to the theory of singularities ...
• #### Stochastic resetting by a random amplitude ﻿

(2021-05-18)
Stochastic resetting, a diffusive process whose amplitude is reset to the origin at random times, is a vividly studied strategy to optimize encounter dynamics, e.g., in chemical reactions. Here we generalize the resetting ...