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We obtain restrictions on the rational homotopy types of mapping spaces and of classifying spaces of homotopy automorphisms by means of the theory of positive weight decompositions. The theory applies, in particular, to connected components…

The development of algorithmic fractal dimensions in this century has had many fruitful interactions with geometric measure theory, especially fractal geometry in Euclidean spaces. We survey these developments, with emphasis on connections…

We use the method of pseudoanalytic continuation to obtain a characterization of spaces of holomorphic functions with boundary values in Besov spaces in terms of polynomial approximations.

We consider two categories related to symplectic manifolds: 1. Objects are symplectic manifolds and morphisms are symplectic embeddings. 2. Objects are symplectic manifolds endowed with compatible almost complex structure and morphisms are…

We construct holomorphic maps with a Siegel disk whose boundary is not locally connected (and is an indecomposable continuum), yet compactly contained in the domain of definition of the map. Our examples are injective and defined on a…

This article gives an overview, aimed at theoretical particle physicists, of some recent developments in cosmology.

We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e. integrals of motion. The core idea of the…

The concept of synthetic dimensions has emerged as a powerful framework in photonics and atomic physics, enabling the exploration of high-dimensional physics beyond conventional spatial constraints. Originally developed for quantum…

We present a comprehensive survey on removability of compact plane sets with respect to various classes of holomorphic functions. We also discuss some applications and several open questions, some of which are new.

We review recent progress in understanding black hole structure and dynamics via matrix theory.

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.…

A theory of holomorphic extension of eigenfunctions on homogeneous harmonic spaces is developed.

In a previous paper we built a modified Hamiltonian formalism to make possible explicit maps among manifolds. In this paper the modified formalism was generalized. As an application, we have built maps among spaces associated to spinors, as…

The paper is a short survey of recent developments in the area of word maps evaluated on groups and algebras. It is aimed to pose questions relevant to Kac--Moody theory.

We prove a characterization for BLD-mappings between locally complete locally compact path-metric spaces. As a corollary we obtain a sharp limit theorem for BLD-mappings.

In recent years, significant advances have been made in the design and evaluation of balanced (hyper)graph partitioning algorithms. We survey trends of the last decade in practical algorithms for balanced (hyper)graph partitioning together…

We propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original…

In this paper, we study a deformation theory of rigid analytic spaces. We develop a theory of cotangent complexes for rigid geometry which fits in with our deformations. We then use the complexes to give a cohomological description of…

A new approach to the analytic theory of difference equations with rational and elliptic coefficients is proposed. It is based on the construction of canonical meromorphic solutions which are analytical along "thick paths". The concept of…

We develop the theory of $J$-holomorphic discs in Hilbert spaces with almost complex structures. As an aplication, we prove a version of Gromov's symplectic non-squeezing theorem for Hilbert spaces. It can be applied to short-time…