相关论文: Zilber's notion of logically perfect structure: Un…
We give an algebraic description of the structure of the analytic universal cover of a complex abelian variety which suffices to determine the structure up to isomorphism. More generally, we classify the models of theories of "universal…
Finite covers are a technique for building new structures from simpler ones. The original motivation to study finite covers is in the Ladder theorem of Zilber which describes how totally categorical structures are built from strictly…
We study the model theory of covers of groups definable in o-minimal structures. This includes the case of covers of compact real Lie groups. In particular we study categoricity questions, pointing out some notable differences with the case…
We use tools of mathematical logic to analyse the notion of a path on an complex algebraic variety, and are led to formulate a "rigidity" property of fundamental groups specific to algebraic varieties, as well as to define a bona fide…
We study rack and quandle coverings from a universal algebraic viewpoint and we show how they can be understood using the notion of strongly abelian congruences. We provide an abstract characterization of several particular types of…
We find a natural $L_{\omega_1,\omega}$-axiomatisation $\Sigma$ of a structure on the upper half-plane $\mathbb{H}$ as the covering space of modular curves. The main theorem states that $\Sigma$ has a unique model in every uncountable…
A notion known as smooth envelope, or superposition closure, appears naturally in several approaches to generalized smooth manifolds which were proposed in the last decades. Such an operation is indispensable in order to perform…
This paper develops a categorical framework to clarify the relationship between the completeness and compactness theorems in classical first-order logic. Rather than claiming that different model constructions yield naturally isomorphic…
We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively…
There are theories of coverings of $C^*$-algebras which can be included into a following list: coverings of commutative $C^*$-algebras, coverings of $C^*$-algebras of groupoids and foliations, coverings of noncommutative tori, the double…
We suggest to compactify the universal covering of the moduli space of complex structures by non-commutative spaces. The latter are described by certain categories of sheaves with connections which are flat along foliations. In the case of…
Canonical models are of central importance in modal logic, in particular as they witness strong completeness and hence compactness. While the canonical model construction is well understood for Kripke semantics, non-normal modal logics…
Beyond the crucial role they play in the foundations of the theory of overconvergent modular forms, canonical subgroups have found new applications to analytic continuation of overconvergent modular forms. For such applications, it is…
Observables in a quantum system, represented by a Hilbert space, are given by the orthogonal bases of the aforementioned Hilbert space. Categorical Quantum Mechanics provides further abstraction of such observables, allowing for a…
These lecture notes survey the emerging area of Universal Proof Theory, which investigates general questions about the existence, equivalence, and characterization of good proof systems for broad classes of logics. In particular, the notes…
We suggest to look at formal sentences describing complex algebraic varieties together with their universal covers as topological invariants. We prove that for abelian varieties and Shimura varieties this is indeed a complete invariant,…
Central to the theory of special cube complexes is Haglund and Wise's construction of the canonical completion and retraction, which enables one to build finite covers of special cube complexes in a highly controlled manner. In this paper…
In the long paper "Family Blowup formula, Admissible Graphs and the Enumeration of Singular Curves (I)" (appearing in JDG), the author solved the enumeration problem of nodal (or general singular) curve counting on algebraic surfaces by…
Necessary and sufficient conditions are presented for the (first-order) theory of a universal class of algebraic structures (algebras) to admit a model completion, extending a characterization provided by Wheeler. For varieties of algebras…
We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…