Francesco Serra Cassano

• Laurea in Mathematics at the University of Pisa in october 1986 .
• Scholarship from " Istituto Nazionale di Alta Matematica "Francesco Severi" (Rome, Italy), from november 1 1987 to october 31 1988.
• PhD student at the Department of Mathematics of University of Pisa, from november 1 1988 to october 31 1991.
• Scholarship of University of Pisa for attending the courses of the "D.E.A." in Mathematics of the University of Paris VI at the " Laboratoire d'Analyse Numerique", from january 1 to june 15 1991.

• Assistant Professor of Mathematical Analysis at the Faculty of Sciences of the University of Bologna from november 1 1991 to october 31 1993.
• Associate Professor of Mathematical Analysis at the Faculty of Science of University of Trento, from november 1 1993 to october 31 2001. 
• Professor of Mathematical Analysis: at the Faculty of Sciences-University of Trento, from november 1 2001 to october 29 2012; at the  Department of Mathematics- University of Trento, from october 29 2012-september 30 2024.
• Coordinator of the Graduate School in Mathematics of the University of Trento: from november 1 2002 to october 31 2005; from december 6,  2012 to january 14, 2016.
• Deputy Head of the Department of Mathematics- University of Trento from december 4 2012-present
• Recent positions as visiting professor: University of Jyvaskyla, Finland (March-June 2001, October 2014); University of Bern, Switzerland (april 2001, may 2010, november 2014); University of Oxford, United Kingdom (june 2006); University of Helsinki; Finland (april 2008); Academia Sinica of Taipei, Taiwan (december 2010); University of Granada, Spain (june 2012); Institut Henri Poincaré, Paris (september-october 2014).

N THE PAST:
G- convergence for degenerate elliptic and parabolic operators, $Gamma$- convergence of degenerate integral functionals. Relaxation of degenerate integral functionals and density of regular functions in weighted Sobolev spaces and/or Sobolev spaces with respect to vector fields. Regularity of solutions for linear degenerate elliptic equations and regularity of minima for degenerate integral functionals.

MORE RECENTLY:
calculus of variations and geometric measure theory in sub- Riemannian ( or Carnot- Carathéodory) metric structures.

More precisely:

• sets of finite perimeter, regular and Lipschitz surfaces, graphs and rectifiability in intrinsic sense in Carnot groups ;
• area formula and currents in the Heisenberg group;
• measures concentrated on hypersurfaces in sub- Riemannian structures and applications to the two-transition phases;
• Bernstein problem for intrinsic graphs in the Heisenberg group;
• regularity of minimal boundaries in the Heisenberg group;
• variational convergences for functionals and PDEs depending on vector fields;
• flows of non Lipschitz vector fields and applications to solutions of continuity and transport equations.

• Organizer, with L. Ambrosio, B. Franchi, I. Markina and R. Serapioni,of the schools “Analysis and Geometry on Metric Spaces” held in Trento and Levico Terme (may 1999, june 2001,may 2003, may 2005, june 2007, june 2009, june 2011, june 2013, june 2015, june 2017, june 2019).
• Organizer  with L. Ambrosio, G. Dal Maso, P. Marcellini and R. Serapioni,  since 2001 to 2018, and with L. Ambrosio, G. Dal Maso, N. Gigli and R. Serapioni, since 2019 to present, of the  annual Italian Meeting of Calculus of Variations, held in Levico Terme (Italy).
• Member of the editorial board of Analysis and Geometry in Metric Spaces (http://versita.com/agms/).

MAIN   INVITED LECTURES:

• AMS meeting, session on “Analysis and Geometry in Carnot- Carathéodory spaces”, Notre Dame, Indiana-Usa (4/8-9/2000);
• University of Jyvaskila- Finland (Spring 2001);
• Worhshop on “Geometric Analysis”, Bern-Switzerland (12/11-12/2001);
• Workshop “Calculus of Variations”, Oberwalfach- Germany (6/30-7/7/2002);
• Workshop “Second Order Subelliptic Equations and Applications”, Cortona (AR)-Italy (6/15-21/2003);
• Conference “Analysis on Metric Measure Spaces”, Banach Center, Bedlewo- Poland (7/15-23/2004);
• AMS meeting, session on “Analysis and Geometry in Carnot- Carathéodory spaces”, Albuquerque, New Mexico-USA (10/16-17/2004);
• University of Oxford- UK (June 2006);
• School on Neuromathematics of Vision, Centro De Giorgi, Pisa (9/4-9/2006)
• Fourth Pacific Rim Conference on Mathematics, Hong Kong (12/7-11/2007)
• University of Helsinki- Finland (4/7-11/2008)
• Workshop "Remembering Riccardo", Napoli (10/22/2009)
• Workshop "New Trends in Sub-Riemannian Geometry", Nice (France) (3/30-4/2/2010)
• Workshop on "Non-Riemannian Mapping Theory and Geometry" , Bern (Switzerland) (5/12-15/2010)
• Workshop on "Mean Curvature Equation in Heisenberg Geometry" , Taipei (Taiwan) (12/18-19/2010)
• Workshop on "Geometric Analysis on sub-Riemannian and Metric Spaces" , Pisa (10/10-14/2011)
• Workshop on "Geometric and Singular Analysis", Potsdam (Germany) (3/11-16/2012)
• School "Geometric Variational Problems", Granada (Spain) (6/18-20/2012)
• 10th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, Madrid (Spain) (7/7-11/2014)
• Course of Geometric Measure Theory ( in collaboration with L. Ambrosio) within the trimester "Geometry, Analysis and Dynamics on Sub-Riemannian Manifolds" (Paris, 9/8-14/2014)
• Workshop "Geometric Analysis on sub-Riemannian Manifolds" (Paris, 9/29-10/3/2014)
• Workshop "MAnET on Sub-Riemannian Analysis,PDE and Applications" (Bern, 1/26-30/2015)
• Workshop "Singular Phenomena and Singular Geometries" (Pisa, 6/20-23/2016)
• Workshop "New Trends in PDEs" (Catania, 5/29-30/2018)
• UMI-SIMAI-PTM-Joint Meeting (Wroclaw,Poland, 9/17-20/2018)
• Workshop "Classical and new methodos in Calculus of Variations and PDEs" (Salerno, 1/9-10/2019)
• Conference "Sub-Riemmannian Geometry and beyond, II" (Jyvaskyla, Finland, 2/18-22/2019)
• Conference "Some Topics of Geometric Analysis and Geometric Measure Theory" (Pisa, Centro De Giorgi, 4/16-17/2019)
• Workshop "Dissipitave and Subelliptic Equations" (Pisa, Centro De Giorgi, 2/10-12/2020)
• AMS Spring Eastern Virtual Sectional Meeting-Special Session on Geometric and Functional Inequalities and Nonlinear PDE (formerly at the Brown University, 3/20-21/2021)
• Recent Progress in Geometric Analysis and PDEs (Bologna, Dipartimento di Matematica, 9/16-18/2021)
• Conference “Calculus of variations and geometric measure theory” (Pisa, Polo Fibonacci,6/12-16/2023

• Advisor of the following PHD students of the Graduate School in Mathematics : F. Bigolin (Trento, 2009), F. Corni (Bologna, 2021, co-supervision with B. Franchi), F. Essebei (Trento, 2022, co-supervision with A. Pinamonti), Maione (Trento, 2020, co-supervision with A. Pinamonti), R. Monti (Trento, 2001), S. Nicolussi Golo (Trento, 2017, co- supervision with E. Le Donne, University of Jyvaskyla, Finland), F. Paronetto (Trento, 1998), A. Pinamonti (Trento,2011), M. Vedovato (Trento, 2022), K. Zambanini (Trento,co-supervision with A. Pinamonti, current PhD student).
• Supervisor of the following post-doc students of the Department of Mathematics of the University of Trento: C. Afeltra, F. Bigolin, G. Giovannardi,F. Montefalcone, F. Paronetto,A. Pinamonti,  N. Scherbakova,D. Vittone.
• Coordinaror of the local research group "Geometric measure theory and variational problems in Riemannian and Sub- Riemannian metric structures" within the national project (PRIN) "Variational methods in optimal mass transportation and in geometric measure theory" (coordinator L. Ambrosio, Scuola Normale Superiore, Pisa).
• Coordinator of the section "Calculus of Variations and Optimal Control Theory"  at  the "XIX Congresso Unione Matematica Italiana", held in Bologna from September 12 to 17, 2011.