Cannarsa's scientific interests include partial differential equations, control theory, and nonsmooth analysis. His current research is concerned with control of partial differential equations, as well as regularity of viscosity solutions to Hamilton-Jacobi-Bellman equations and Mean Field Games. He authored about 130 papers in international journals and 2 books including "Semiconcave functions, Hamilton-Jacobi equations, and optimal control" (with C. Sinestrari).
Cannarsa has given plenary talks at several international conferences including the SIAM Conference on Control and Its Applications, the Congress of the Italian Mathematical Union, the IFIP TC 7 Conference on Systems Modeling and Optimization, the Congress of the Spanish Society of Applied Mathematics, the French-German-Polish Conference on Optimization, and the Viennese Workshop on Optimal Control and Dynamic Games.
Since June 2018, Cannarsa is the President of the Italian Mathematical Union. Previously, for eight years since June 1999, he was the Vice-President of the Istituto Nazionale di Alta Matematica, a national institution for promotion of mathematical education and research.
Since January 2018, Cannarsa is the Italian coordinator of the LIA COPDESC (Control, Calculus of Variations, Nonlinear PDEs, and Scientific Computing) on Applied Mathematics, an international laboratory issued by CNRS (France), INdAM (Italy) and Max Planck Institutes (Germany). Previously (2010-2017), he coordinated the Italian branch of the European Research Group (GDRE) between France and Italy on the Control of Partial Differential Equations (CONEDP).
Cannarsa is the Editor-in-Chief of the Bollettino dell’Unione Matematica Italiana (Springer) and an editor of several international journals including Evolution Equations and Control Theory (AIMS), Mathematical Control and Related Fields (AIMS), Minimax Theory and its Applications (Heldermann), Nonlinear Analysis: Real World Applications (Elsevier), and Nonlinear Differential Equations and Applications (Birkhäuser).