Related papers: Gromatics illustrations from newly discovered pave…
In the eighth century BC something peculiar seems to happen on Sicily. The archaeological record starts to show the arrival of Greek material culture. By the fifth century BC the island is effectively 'Hellenised' and ancient historians…
Two mappings in a finite field, the Frobenius mapping and the cyclic shift mapping, are applied on lines in PG($n,p$) or codes in the Grassmannian, to form automorphisms groups in the Grassmanian and in its codes. These automorphisms are…
The goal of this article is to motivate and describe how Gromov-Witten theory can and has provided tools to understand the moduli space of curves. For example, ideas and methods from Gromov-Witten theory have led to both conjectures and…
This work is a collection of old and new aplications of Galois cohomology to the clasification of algebraic and arithmetical objects.
We investigate two-dimensional, periodic ornaments of the Late Hellenistic (some centuries before the Common Era, the Classical Period) and Early Roman (Common Era) classical periods found at different locations in Asia Minor in Turkey and…
We propose the use of image processing to enhance the Google Maps of some archaeological areas of Egypt. In particular we analyse that place which is considered the cradle of pyramids, where it was announced the discovery of a new pyramid…
Finding Hemisystems is a challenging problem and just few examples arising from the Hermitian surface are known. A recent method to obtain Hemisystems is based on using maximal curves. Along this side of research, we provide new examples of…
In this note we present House of Graphs (http://hog.grinvin.org) which is a new database of graphs. The key principle is to have a searchable database and offer -- next to complete lists of some graph classes -- also a list of special…
In 1738, the King of Naples and future King of Spain, Carlos III, commissioned the Spanish military engineer Roque Joaqu\'in de Alcubierre to begin the excavations of the ruins of the ancient Roman city of Pompeii and its surroundings,…
In this paper, we analyze the stochastic properties of some large size (area) polyominoe's perimeter such that the directed column-convex polyomino, the column-convex polyomino, the directed diagonally-convex polyomino, the staircase (or…
The structure of topological spaces is analysed here through the lenses of fibrous preorders. Each topological space has an associated fibrous preorder and those fibrous preorders which return a topological space are called spacial. A…
A new generalisation of the notion of space, called "vectoid", is suggested in this work. Basic definitions, examples and properties are presented, as well as a construction of direct product of vectoids. Proofs of more complicated…
These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The…
We show how the birth of perspective painting in the Italian Renaissance led to a new way of interpreting space that resulted in the creation of projective geometry. Unlike other works on this subject, we explicitly show how the craft of…
In this note we present a computational approach to the construction of ovoids of the Hermitian surface and show some related experimental results.
The study of arboreal Galois representations (that is, Galois groups arising from iteration of polynomial and rational functions) originated with work of Odoni in the 1980s. Beginning in the early 2000s it underwent a period of renewed…
In this paper we introduce, for each closed orientable surface, an analogue of Tits buildings adjusted to investigation of the Torelli group of this surface. It is a simplicial complex with some additional structure. We call this complex…
Pyramids introduced by Gromov are generalized objects of metric spaces with Borel probability measures. We study non-trivial pyramids, where non-trivial means that they are not represented as metric measure spaces. In this paper, we…
In this expository paper, we provide an intuition and illustration-driven overview of two recent results that tie the dynamics of certain homeomorphisms of infinite-type surfaces, called end-periodic homeomorphisms, to the geometry of their…
The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov-Witten classes, and a…