On the coexistence of competing languages

18 pages, 12 figures, 47 references. To appear in EPJ BInternational audienceWe investigate the evolution of competing languages, a subject where much previous literature suggests that the outcome is always the domination of one language over all the others. Since coexistence of languages is observed in reality, we here revisit the question of language competition, with an emphasis on uncovering the ways in which coexistence might emerge. We find that this emergence is related to symmetry breaking, and explore two particular scenarios -- the first relating to an imbalance in the population dynamics of language speakers in a single geographical area, and the second to do with spatial heterogeneity, where language preferences are specific to different geographical regions. For each of these, the investigation of paradigmatic situations leads us to a quantitative understanding of the conditions leading to language coexistence. We also obtain predictions of the number of surviving languages as a function of various model parameters