Related papers: Analytic and pseudo-analytic structures (a survey)
We study scattered piecewise interpretable Hilbert spaces from a model theoretic point of view. We establish strong connections between the Hilbert space structure theorems of [Chevalier Hrushovski 2021] and the model theoretic notions of…
How many are linear connections with prescribed Ricci tensor? How many are statistical structures? The questions are answered in the analytic case by using the Cauchy-Kowalewski theorem.
In this Phd. thesis, a structural analysis of construction schemes is developed. The importance of this study will be justified by constructing several distinct combinatorial objects which have been of great interest in mathematics. We then…
This is a part survey part research paper studying the local topology of complex analytic spaces. We review and strengthen the results of Kapovich--Koll\'ar "Fundamental groups of links of isolated singularities" (1109.4047) and incorporate…
We study the model theoretic strength of various lattices that occur naturally in topology, like closed (semi-linear or semi-algebraic or convex) sets. The method is based on weak monadic second order logic and sharpens previous results by…
In this paper, we study a general Syracuse problem. We give some necessary conditions concerning the existence of eventual non trivial cycles. Some properties based on linear logarithmic forms are established. New general conjectures are…
Talk given at NATO ARW in Kiev (September 2000) "Non-commutative Structures in Mathematics and Physics".
We develop a hierarchical structure (HS) analysis for quantitative description of statistical states of spatially extended systems. Examples discussed here include an experimental reaction-diffusion system with Belousov-Zhabotinsky…
I shall describe a general model-theoretic task to construct expansions of pseudofinite structures and discuss several examples of particular relevance to computational complexity. Then I will present one specific situation where finding a…
Using the Cauchy-Riemann operator, we characterize $Q_K$ spaces, Besov spaces and analytic Morrey spaces in terms of pseudoanalytic extensions of primitive functions. Our results are also true on some classical Banach spaces, such as the…
This is an extended version of notes prepared for the talk at the conference "Rajchman-Zygmund-Marcinkiewicz 2000" based on recent works of the authors.
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
We recall fundamental aspects of the pluriclosed flow equation and survey various existence and convergence results, and the various analytic techniques used to establish them. Building on this, we formulate a precise conjectural…
We show that a real analytic restricted log-exp-analytic function has a holomorphic extension which is again restricted log-exp-analytic. We also establish a parametric version of this result.
These notes grew out of a mini-course given from May 13th to May 17th at UQAM in Montreal during a workshop on Diophantine Approximation and Value Distribution Theory. We start with an overview of Lang-Vojta's conjectures on…
We study the problem of holomorphic extension of a smooth CR mapping from a real analytic hypersurface to a real algebraic set in complex spaces of different dimensions.
In this paper, we prove a general theorem concerning the analyticity of the closure of a subspace defined by a family of variations of mixed Hodge structures, which includes the analyticity of the zero loci of degenerating normal functions.…
Following G. Mints(Kluwer 2000 and draft 2013), we present terminating and bicomplete proof searches in multi-succedent sequent calculi for intuitionistic propositional logic, fragments of intuitionistic predicate logic and full…
We investigate the isomorphism types of combinatorial geometries arising from Hrushovski's flat strongly minimal structures and answer some questions from Hrushovski's original paper.
In this paper we present a proof of Hartogs' extension theorem, following T. Sobieszek's paper from 2003. Hartogs' theorem provides a large class of domains where holomorphic functions have analytic continuation to larger domains, and is "a…