The 2020 edition of the bi-annual congress of the Italian Society of Applied and Industrial Mathematics (SIMAI) will be held in Parma, hosted by the Università di Parma, at the Campus Congress Center “Plesso Aule delle Scienze”, Parco Area delle Scienze, 43124 Parma, from August 30 to September 3, 2021. The aim of the conference is to bring together researchers and professionals from academia and industry who are active in the study of mathematical and numerical models as well as their application to industrial and in general real life problems, to stimulate interdisciplinary research in applied mathematics and to foster interactions of the scientific community with industry. Within this conference, a mini-symposium will be organized whose aim is to cover some of the most critical research areas of the system of CoEs, highlighting topics such as physical-mathematical modelling, numerical algorithms and scintific libraries, mixed-precision arithmetic for scientific computing, data assimilation and uncertainty quantification, pointing out how CoEs activities and applications result in tangible benefits to address scientific, industrial or societal challenges. The mini-symposium is supported by the EU project FocusCoE, an initiative funded to promote the CoEs services and findings to ever more partners from science and industry, with particular focus on small and medium-sized enterprises (SMEs), and thereby reinforce the positive impact of HPC in all of the areas covered by the CoEs.