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The Quantum Harmonic Oscillator as a Zariski Geometry
Annals of Pure and Applied Logic. 2014. Vol. 165. No. 6. P. 1149–1168.
Sustretov D., Zilber B., Solanki V.
We carry out a model-theoretic analysis of the Heisenberg algebra. To this end, a geometric structure is associated to the Heisenberg algebra and is shown to be a Zariski geometry. Furthermore, this Zariski geometry is shown to be non-classical, in the sense that it is not interpretable in an algebraically closed field. On assuming self-adjointness of the position and momentum operators, one obtains a discrete substructure of which the original Zariski geometry is seen as the complexification.
Keywords: model theory
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
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Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
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Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
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Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
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Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
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Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
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Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
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Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
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Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
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Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
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Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Gaianov N., Parusnikova A., / Cornell University. Серия math "arxiv.org". 2025.
An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation ...
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Popov V., / Series arXiv "math". 2025. No. 2502.01539.
We prove that the variety of flexes of algebraic curves
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Gnetov F., Konakov V., / Series arXiv "math". 2025. No. 2512.04667.
We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural
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Kazakov A., Koryakin V., Safonov K. et al., / Series arXiv "math". 2025.
The Lorenz attractor is the first example of a robustly chaotic non-hyperbolic attractor. Each orbit of such an attractor has a positive top Lyapunov exponent, and this property persists under small perturbations despite possible bifurcations of the attractor. In this paper, we study the boundary of the Lorenz attractor existence region in the Shimizu-Morioka model. ...
Added: December 4, 2025
., 2025.
The 17th International Summer School-Conference “Problems Allied to Model Theory and Universal Algebra” was held on 19–26 of June 2025 at Sobolev Institute of Mathematics, Novosibirsk State Technical University NETI and at the Camping Center “Erlagol” in Altai mauntains. The School was organized by Algebra and Mathematical Logic Department of Novosibirsk State Technical University (NSTU ...
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Novosibirsk: ., 2023.
The 15th International Summer School-Conference “Problems Allied to
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“Erlagol” in Altai mountains. The School was organized by Algebra and
Mathematical Logic Department of Novosibirsk State Technical University
(NSTU NETI) and Sobolev Institute of Mathematics of Siberian Branch ...
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Gavrilovich M., Communications in Algebra 2020 Vol. 48 No. 4 P. 1548–1566
We formulate two conjectures about étale cohomology and fundamental groups motivated by categoricity conjectures in model theory. One conjecture says that there is a unique ZZ-form of the étale cohomology of complex algebraic varieties, up to Aut(C)Aut(C)-action on the source category; put differently, each comparison isomorphism between Betti and étale cohomology comes from a choice of a ...
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Rodin A., , in: Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts.: Springer, 2019. Ch. 9 P. 191–219.
Homotopy Type theory and its Model theory provide a novel formal
semantic framework for representing scientific theories. This framework
supports a constructive view of theories according to which a theory
is essentially characterised by its methods. The constructive view of
theories was earlier defended by Ernest Nagel and a number of other
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Sustretov D., Journal of Symbolic Logic 2016 Vol. 81 No. 3 P. 917–935
The objective of this article is to characterise elimination of finite generalised imaginaries (as defined by Hrushovski) in terms of group cohomology. As an application, I consider series of Zariski geometries constructed by Hrushovski and Zilber, and indicate how their non-definability in algebraically closed fields and other theories is connected to eliminability of certain generalised ...
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Zolin E., Logic Journal of the IGPL 2015 Vol. 23 No. 6 P. 861–880
The celebrated theorem proved by Goldblatt and Thomason in 1974 gives necessary and sufficient conditions for an elementary class of Kripke frames to be modally definable. Here we obtain a local analogue of this result, which deals with modal definability of classes of pointed frames. Furthermore, we generalize it to the case of n-frames, which ...
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