Related papers: A characterization of quasi-rational polygons
This introductory survey deals with mathematical and physical properties of discrete structures such as point sets and tilings. The emphasis is on proper generalizations of concepts and ideas from classical crystallography. In particular,…
The purpose of this chapter is to provide an overview of the exciting field of black hole quasi-normal modes and its capabilities to test general relativity in the 21st century. After motivating this line of research, we provide a…
We study equivariant geometry and rationality of moduli spaces of points on the projective line, for twists associated with permutations of the points.
This paper is a sequel to my paper "Introducing the Plaid Model". In this paper it is shown that the plaid model has unbounded polygonal paths for every irrational parameter. This result parallels my result that outer billiards on kites has…
We study long-term evolution of radiating quasi-Q-balls in 1+1 dimensional models without mass threshold. Two different models are considered, the model with a rational modification of the usual Q-ball sextic potential and the model of a…
We study the deep interplay between geometry of quadrics in d-dimensional space and the dynamics of related integrable billiard systems. Various generalizations of Poncelet theorem are reviewed. The corresponding analytic conditions of…
Parametric Cartan theory of exterior differential systems, and explicit cohomology of projective manifolds reveal united rationality features of differential algebraic geometry.
The goal of this note is to show how recent results on the theory of quasi-stationary distributions allow to deduce effortlessly general criteria for the geometric convergence of normalized unbounded semigroups.
In this short note we consider the finite-dimensional distributions of sets of states generated by dispersing billiards with a random initial condition. We establish a functional correlation bound on the distance between the…
This survey paper was primarily written as as the support for a course pesented at the JNCF2025: it aims to present some material that illustrates the kind of estimates one can obtain in effective algebraic geometry, for affine polynomial…
Two polygons $P,Q$ are code equivalent if there are billiard orbits $u,v$ which hit the same sequence of sides and such that the projections of the orbits are dense in the boundaries $\partial P, \partial Q$. Our main results show when code…
The billiard problem of statistical physics is considered in a new geometric approach with a symmetric phase space. The structure and topological features of typical billiard phase portrait are defined. The connection between geometric,…
We provide explicit equations and parameterizations of some new rational Gushel-Mukai fourfolds of special type.
This article presents a new method to calculate eigenvalues of right triangle billiards. Its efficiency is comparable to the boundary integral method and more recently developed variants. Its simplicity and explicitness however allow new…
In this paper, we define what is called a quasi-Reinhardt domain and study biholomorphisms between such domains. We show that all biholomorphisms between two bounded quasi-Reinhardt domains fixing the origin are polynomial mappings, and we…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
We study sufficient conditions on weight functions under which norm approximations by analytic polynomials are possible. The weights we study include radial, non-radial, and angular weights.
We review the papers [1-3]. We discuss possibilities of studying the quasi-normal modes of black holes that are not known in an analytical form. Such black holes appear as solutions in various theoretical models and real astrophysical…
A polynomial ring with rational coefficients is an irreducible representation of Lie algebras of endomorphisms of exterior powers of a infinite countable dimensional $\mathbb{Q}$-vector space. We give an explicit description of it, using…
We consider nearly-perfect cuboids (NPC), where the only irrational is one of the face diagonals. Obtained are three rational parametrizations for NPC with one parameter.