We present the theory of nonlocal minimal surfaces, with special attention to regularity, sheeting, maximum principle, and stickiness. We also link this theory to the study of long-range phase transition and to the analysis of its symmetry properties.

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The course presents the theory of nonlocal minimal surfaces, with special attention to regularity, sheeting, maximum principle, and stickiness. Guest lecturers: - Serena Dipierro (Full Professor at University of Western Australia): She is a Professor (Level E) at the University of Western Australia and a Senate member since 2023. She has held prestigious roles, including DECRA Fellow (2018–2022), Fulbright Research Scholar at Columbia University (2019), and Humboldt Research Fellow in Germany (2015–2017). Her research focuses on Nonlinear Analysis, Variational Methods, Nonlocal Operators, and related topics. With a Ph.D. in Mathematical Analysis from SISSA, Trieste (2012), she has published extensively and contributed to global research. Active in academic leadership, she is a member of the Academic Board at UWA and the doctoral board at the University of Calabria. She also serves as Secretary of the Women in Mathematics Special Interest Group (WIMSIG). - Enrico Valdinoci: (Full Professor at University of Western Australia): He is a Full Professor at the University of Western Australia, specializing in Nonlinear Partial Differential Equations and Nonlocal Problems. He earned his Ph.D. in Mathematics from the University of Texas at Austin in 2002 and has held prominent academic positions, including professorships at the University of Melbourne and the University of Milan, as well as a leadership role at the Weierstraß-Institut in Berlin. A dedicated educator, Valdinoci has taught advanced courses at institutions worldwide, such as Columbia University and Universidad Autónoma de Madrid. His research focuses on variational problems, fractional Laplacians, and the interplay between analysis and geometry.

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Presentazione orale

P.D.2-2 - Maggio

May