Related papers: A view towards mixing in holomorphic correspondenc…
Interactions in complex systems are widely observed across various fields, drawing increased attention from researchers. In mathematics, efforts are made to develop various theories and methods for studying the interactions between spaces.…
We show that in a typical polygon the billiard map as well as its associated subshift obtained by coding orbits by the sequence of sides they visit are topologically weakly mixing.
We study Morse theory on noncompact manifolds equipped with exhaustions by compact pieces, defining the Morse homology of a pair which consists of the manifold and related geometric/homotopy data. We construct a collection of Morse data…
We study the effect of the Howe correspondence on Harish-Chandra series for type I dual pairs over finite fields with odd characteristic. We define a bijection obtained from this correspondence, and enjoying the property of ``having minimal…
A correspondence, by way of Heegaard splittings, between closed oriented 3-manifolds and pairs of surjections from a surface group to a free group has been studied by Stallings, Jaco, and Hempel. This correspondence, by way of trisections,…
We construct a general class of correspondences on hyperelliptic Riemann surfaces of arbitrary genus that combine finitely many Fuchsian genus zero orbifold groups and Blaschke products. As an intermediate step, we first construct analytic…
We describe a part of the recent developments in the theory of separately holomorphic mappings between complex analytic spaces. Our description focuses on works using the technique of holomorphic discs.
We obtain results on approximation of holomorphic maps by algebraic maps, jet transversality theorems for holomorphic and algebraic maps, and the homotopy principle for holomorphic submersions of Stein manifolds to certain algebraic…
Within the context of the mathematical formulation of Merge and the Strong Minimalist Thesis, we present a mathematical model of the morphology-syntax interface. In this setting, morphology has compositional properties responsible for word…
A characterization of relative weak mixing in W*-dynamical systems in terms of a relatively independent joining is proven.
We study the regularity results of holomorphic correspondences. As an application, we combine it with certain recently developed methods to obtain the extension theorem for proper holomorphic mappings between domains with real analytic…
We consider moduli spaces of dynamical systems of correspondences over the projective line as a generalization of moduli spaces of dynamical systems of endomorphisms on the projective line. We obtain the rationality of the moduli spaces.…
The question we deal with here, which was presented to us by Joe Auslander and Anima Nagar, is whether there is a nontrivial cascade (X,T) whose enveloping semigroup, as a dynamical system, is topologically weakly mixing (WM). After an…
In the study of holomorphic maps, the term "rigidity" refers to certain types of results that give us very specific information about a general class of holomorphic maps owing to the geometry of their domains or target spaces. Under this…
The hypothesis of gauge/gravity correspondence (or holographic duality) from string theory has led to unexpected and challenging ways for description of strongly coupled systems. Such descriptions are given in terms of weakly-coupled…
Constructions of spectra from symmetric monoidal categories are typically functorial with respect to strict structure-preserving maps, but often the maps of interest are merely lax monoidal. We describe conditions under which one can…
Weakly orthomodular and dually weakly orthomodular lattices were introduced by the authors in a recent paper. Similarly as for orthomodular lattices we try to introduce an implication in these lattices which can be easily axiomatized and…
Weak almost contact manifolds, i.e., the linear complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor, defined by the author and R. Wolak, allowed us to take a new look at the theory of contact…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
Weak mixing in lattice models is informally the property that ``information does not propagate inside a system''. Strong mixing is the property that ``information does not propagate inside and on the boundary of a system''. In dimension…