Zero-Sum Ramsey Theory: Graphs, Sequences and More (19w5132)


(Universidad Nacional Autónoma de México)

Yair Caro (University of Haifa-Oranim)

(Universidad Nacional Autónoma de México)


The Casa Matemática Oaxaca (CMO) will host the "Zero-Sum Ramsey Theory: Graphs, Sequences and More" workshop in Oaxaca, from November 10, 2019 to November 15, 2019.

Zero-sum Ramsey theory (also Zero-sum theory) is a very rich branch in Combinatorics which combines tools from Number theory, Algebra, Linear algebra, Graph theory, Discrete analysis and other branches in Mathematics. It deals with problems of the following kind: given a combinatorial structure whose elements are assigned different weights (usually elements from an Abelian group $A$), one seeks for conditions that guarantee the existence of certain substructure whose weights of its elements sum up to zero (in $A$). Since the beginning of the 60's, where the first result of this kind by Erd\H{o}s, Gizburg and Ziv was published, the study of such kind of problems has received growing interest among Mathematicians. However, the topic gets usually absorbed by the large amount of related research in Combinatorics and it usually does not stand out as an individual branch in the different conferences from the area.

With this workshop, we aim to give Zero-sum Ramsey theory more visibility and gather different mathematicians with a mutual interest in the subject in order to foster the exchange of ideas and recent advances as well as to encourage young researchers to get involved. Moreover, we would like to make awareness of the inter-disciplinary aspect of the topic and establish new directions of future research.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT