• Uniform Lech's inequality 

  Ma, L.; Smirnov, I. (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 

  Braddell, R.; Kiesenhofer, A.; Miranda, E. (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 

  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 ...

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