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The first algorithm for sampling the space of thick equilateral knots, as a function of thickness, will be described. This algorithm is based on previous algorithms of applying random reflections. To prove the existence of the algorithm, we…
In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
The purpose of this short note was to outline the current status, then in 2011, of some research programs aiming at a categorification of parts of A.Connes' non-commutative geometry and to provide an outlook on some possible subsequent…
In many real world datasets arising from social networks, there are hidden higher order relations among data points which cannot be captured using graph modeling. It is natural to use a more general notion of hypergraphs to model such…
We generalize generating functions for hypergeometric orthogonal polynomials, namely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These generalizations of generating functions are accomplished through series rearrangement using…
Exact solutions construction in scalar fields cosmology is of growing interest. In this work we review the results which obtained with the help of one of the most effective method. Namely, the method of generating functions for exact…
In this paper we study plus-one generated arrangements of conics and lines in the complex projective plane with simple singularities. We provide several degree-wise classification results that allow us to construct explicit examples of such…
We present a variation of quasi-isometry to approach the problem of defining a geometric notion equivalent to commensurability. In short, this variation can be summarized as "quasi-isometry with uniform parameters for a large enough family…
In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization…
These short (personal) notes appeared as the result of my attempt to address the question raised in the title.
Hypergeometric motives are family of motives associated to hypergeometric local systems. Their special features, in particular their rigidity, makes them more tractable than general motives. In the present article we prove most of the…
In this short note is on the equivalence between non-Newtonian metric (particularly multiplicative metric) and metric. We present a different proof the fact that the notion of a non-Newtonian metric space is not more general than that of a…
The aim of this paper is to study co-prolongations of central extensions. We construct the obstruction theory for co-prolongations and classify the equivalence classes of these by kernels of a homomorphisms between 2-dimensional cohomology…
Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other…
Almost contact manifolds with B-metric are considered. A special linear connection is introduced, which preserves the almost contact B-metric structure on these manifolds. This connection is investigated on some classes of the considered…
Hypergeometric solutions to the q-Painlev\'e equations are constructed by direct linearization of disrcrete Riccati equations. The decoupling factors are explicitly determined so that the linear systems give rise to q-hypergeometric…
We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie with a certain radius. From a modelling…
Building on recent work of Robertson and Steger, we associate a C*-algebra to a combinatorial object which may be thought of as a higher rank graph. This C*-algebra is shown to be isomorphic to that of the associated path groupoid.…
This work is a continuation of [1]. As in the previous article, here we will describe some interesting ideas and a lot of new theorems in plane geometry related to them.