CIMAT is an interdepartimental center at the University of Catania. It has been devised with the aim to bring together scientists of several applied sciences whose research activity needs the use of advanced Mathematics. The interdisciplinary feature of CIMAT is also a characteristic of the CIMAT DAYS 2021 through which it is intended to foster the exchange of skills between mathematicians and experts of other fields, in particular finance, quantum technology, chemical technology, biomathematics, scientific computing.