The Department is currently seat of:

• A local unit of the PRIN 2020 project “Advanced polyhedral discretisation of heterogeneous PDEs for multiphysics problems” (responsible: A. Russo).
• A local unit of the PRIN 2022 project "Singular Interactions and Effective Models in Mathematical Physics" (responsible and national PI: D. Noja).
• A local unit of the PRIN 2022 project “Advanced Space-TIme disCrEtization methods: theory, solvers and applications (ASTICE)” (responsible: L. Mascotto).
• A local unit of the PRIN 2022 project “Geometry of Random FIelds and Applications” (GRAFIA) (responsible: M. Rossi).
• A local unit of the PRIN 2022 project “Evolutionary Poisson Games: Theory and Applications” (responsible: M. Pireddu).
• A local unit of the PRIN 2022 project “FREYA - Fault REactivation: a hYbrid numerical Approach” (responsible: F. Dassi).
• A local unit of the PRIN 2022 project “Group theory and its applications” (responsible: P. Spiga).
• A local unit of the PRIN 2022 project “Modeling, Control and Games through Partial Differential Equations” (responsible: M. Garavello).
• A local unit of the PRIN 2022 project “Pattern formation in nonlinear phenomena” (responsible: V. Felli).
• A local unit of the PRIN 2022 project “Effective quantum gravity” (responsible: A. Tomasiello).
• A local unit of the PRIN 2022 project “The fascination of integrability: from non-linear waves to aleatory matrices” (responsible: G. Falqui).
• A local unit of the PRIN 2022 project “Interactions between geometric structures and theories of functions” (responsible: S. Mongodi).

It was also the coordinating institute of the H2020-MSCA-RISE 2017 project IPaDEGAN ("Integrable Partial Differential Equations: Geometry, Asymptotics, and Numerics", coordinator G. Falqui), approved by the EU in 2017 for a duration of 4 years starting in January 2018.

Among the projects that have been based in the Department, we also mention the ERC-2015-CoG CAVE project ("Challenges and Advancements in Virtual Elements", P.I. L. Beirão da Veiga), started in 2016 with a 5-year duration and the local units of a PRIN 2017 project (responsible L. Beirão da Veiga) and 5 PRIN 2015 projects in various fields of mathematics (responsible: F. Caravenna, G. Guerra, S. Meda, G. Tessitore, T. Weigel). Four members of the Department were members of a further PRIN 2015 project, for which V. Felli is responsible.