Different interplays between different fields of Mathematics and different domains of Social Sciences The need for quantitative predictions in Social Sciences has very much increased in the last decades. In this development, mathematics plays a special role by bringing to a field generally considered as included in "humanities" a new paradigm of rigor and precision. Conversely, social sciences have long continued to provide mathematicians with a fruitful and inexhaustible source of inspiration. From the study/observation of various collective movements (for example, vehicular or pedestrian flow) to the problem of cultural heritage, important sections of new mathematics have emerged. This short  conference aims to update a number of reciprocal links between Social Sciences and Mathematics around four emblematic themes of this relationship: the dynamics of opinions (and economy,  and networks), traffic, sociology and cultural heritage.