Discrete and Algorithmic Mathematics Red de Matemática Discreta y Algorítmica

Discrete and algorithmic mathematics is an area that studies combinatorial and discrete structures, in particular graphs and networks, finite geometries, discrete geometric structures and combinatorial aspects in algebra and number theory. It includes their computational and algorithmic aspects arising from the particularly natural connection of discrete mathematics with computer science. With tools coming from analysis, topology, algebra, geometry and probability and a wide range of applications in computer science, information theory, coding theory, statistics, physics, biology and social sciences, discrete mathematics is a genuine interdisciplinary area both within mathematics and in connection with science and technology as a whole.

The main goal of this Network is to foster cooperation among the existing groups in the area in Spain, reinforcing their scientific collaboration, coordinating scientific activities and training of young researchers and increase the international visibility of the Spanish research in Discrete Mathematics. It will reinforce the participation of female researchers and promote outreach activities for the social awareness of science and technology with particular focus on Discrete Mathematics.

Recent trends V: The Weighted Region Problem

Shortest path problems, where the goal is to find an optimal path between two points in the plane, are among the fundamental problems in computational geometry. These problems are crucial for a variety of applications, GPS navigation is perhaps the best-known application. However, there are numerous daily-life problems that can be solved using shortest path algorithms. ...continue reading.

Recent trends IV: From a naive question to a long-standing conjecture

My aim is to talk about a question on numerical semigroups posed by Herbert Wilf (Wilf 1978) in the late seventies. This question deserves to be included in the gallery of easy-to-state but dangerous problems. That it is easy to state will soon become apparent. ...continue reading.

Recent trends III: Subsets of the integers without three term arithmetic progressions

Let $A\subset \lbrace 1,\ldots, N\rbrace $ be a subset without non-trivial 3-term arithmetic progressions (APs), i.e., such that the equation $a+b=2c$ only has solutions for $a,b,c\in A$ if $a=b=c$. What is the maximum size $r_3(N):=\max_{A\subset \lbrace 1,\ldots,N\rbrace \text{ without 3 APs}}(|A|)$ that we can have? This question and many similar ones have driven the development of an important part of additive combinatorics during the last century ...continue reading.

Recent trends II: Codes, finite fields and skew polynomials

Polynomials are used in virtually every area of Mathematics, and Coding Theory is not an exception. One of the most used error-correcting codes in practice are Reed-Solomon codes, which are defined as subspaces whose vectors are evaluations of polynomials (over a finite field $\mathbb{F}_q$) up to a certain degree ...continue reading.

Recent trends I: Geometry, randomness and Ramsey theory

Since its inception in the early 1900s, Ramsey theory has flourished and become a cornerstone of modern discrete mathematics (and beyond). The central question asks to determine $r(s,t)$; the minimum integer $n\in \mathbb{N}$ such that any red/blue-colouring of the edges of the complete graph $K_n$ results in either a red $K_s$ or a blue $K_t$ ...continue reading.