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 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 $K_t$. Very small values can be calculated but already $r(5,5)$ is beyond our computational power to determine exactly. Therefore Ramsey theorists have focused mainly on asymptotics. Erdős and his collaborators drove the subject forward in the 1940s, establishing bounds and posing beautiful open problems, many of which are known to be notoriously hard and have remained stubborn to this day. ...continue reading.

Santander Workshop on Geometric and Algebraic Combinatorics

The Santander Workshop on Geometric and Algebraic Combinatorics will take place at Universidad de Cantabria in Santander (Spain), in January 15-19, 2024, with its format consisting of two mini courses, eight invited talks, plus short talks and posters contributed from participants. ...continue reading.

Kick-off meeting

The kick-off meeting took place on 12/04/2023. It was held online.