• COHOMOLOGY OF CONTACT LOCI 

  Budur, N.; Fernández de Bobadilla, J.; Le, Q.; Nguyen, D. (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 

  Bru, J.-B.; de Siqueira Pedra, W. (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 

  LIll, S. (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 

  LIll, S. (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 

  LIll, S. (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 

  Jeffries, J.; Nakajima, Y.; Smirnov, I.; Watanabe, K.; Yoshida, K. (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 

  Ma, L.; Smirnov, I. (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 

  Fernández de Bobadilla, J.; Heinze, S.; Sampaio, J.E. (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 

  Bru, J. B.; de Siqueira Pedra, W. (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 

  Kuroda, S.; Kutzschebauch, F.; Pelka, T.R. (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 

  Nagy, J.; Némethi, A. (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 

  Cogolludo-Agustín, J.I.; László, T.; Martín-Morales, J.; Némethi, A. (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 

  Zied, A.; Ratsimanetrimanana, A. (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 

  Duc, N.H. (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 

  Nguyen, N.; Ruas, M.; Trivedi, S. (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 

  LIll, S.; Tumulka, R. (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 

  Sposini, V.; Vitali, S.; Paradisi, P.; Pagnini, G. (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 

  Bazzani, A.; Vitali, S.; Montanari, C.; Monti, M.; Rambaldi, S.; Castellani, G. (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 

  Pallarés Torres, I.; Peñafort Sanchis, Guillermo (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 

  Pełka, T.; Raźny, P. (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 ...

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