Francesco Serra Cassano

Francesco Serra Cassano is a Full Professor at the Department of Mathematics, University of Trento, Italy. His research focuses on Calculus of Variations and Geometric Measure Theory in sub-Riemannian (Carnot/Heisenberg) metric structures.

• Laurea in Mathematics, University of Pisa (1986)
• PhD studies, University of Pisa (1988-1991)
• Scholarship at Université Paris VI (1991)

His research explores intrinsic geometric objects in Carnot groups, including finite perimeter sets, Lipschitz surfaces, area formulas, and minimal surfaces. Recent work addresses Bernstein problems and regularity of solutions to vector field-dependent PDEs.

Key trends in his 15 most recent publications include:

• Advances in intrinsic graph theory and minimal surfaces in Heisenberg groups
• Gamma-convergence of functionals depending on vector fields
• Poincaré-type inequalities in sub-Riemannian settings
• Approximation theorems for weighted Sobolev spaces
• Applications to two-phase transition models

He has organized major schools/conferences including:

• Analysis and Geometry on Metric Spaces (Trento-Levico Terme, 1999-2019)
• Italian Meeting of Calculus of Variations (Levico Terme, 2001-2018)
• Sub-Riemannian Geometry and Beyond (Jyvaskyla, 2019)

As an advisor, he has supervised 10 PhD students and 8 postdocs, including collaborations with international institutions like the University of Jyvaskila (Finland) and Scuola Normale Superiore (Pisa). He currently coordinates the local research group "Geometric measure theory and variational problems in Riemannian and Sub-Riemannian metric structures" under the national PRIN project.