Care tutte, cari tutti, per il prossimo evento del ciclo dei Seminari di Analisi, martedì 11 giugno alle ore 17, in Aula Riunioni, avremo il piacere di ascoltare Federica Dragoni (University of Cardiff), che terrà un seminario <https://www.dm.unipi.it/en/seminar/?id=663cbf185b29178e24cd9c85> dal titolo "Semiconcavity of the square distance in Carnot groups". Trovate l'abstract qui sotto. Il seminario sarà preceduto da una merenda alle 16:45 nella stessa aula. A presto, Ilaria Lucardesi e Luigi Forcella --------------------------------------------- Dear all, on Tuesday 11th June at 5PM, in "Aula Riunioni", for the Mathematical Analysis Seminar, we will have the pleasure of listening to Federica Dragoni (University of Cardiff). The title of the talk<https://www.dm.unipi.it/en/seminar/?id=663cbf185b29178e24cd9c85> is "Semiconcavity of the square distance in Carnot groups". Please find the abstract below. The seminar will be preceded by a snack in the same room, starting at 4:45 PM. See you soon, Ilaria Lucardesi and Luigi Forcella --------------------------------------------- Speaker: Federica Dragoni (University of Cardiff) Title: Semiconcavity of the square distance in Carnot groups Abstract: Semiconcavity and semiconvexity are key regularity properties for functions with many applications in a broad range of mathematical subjects. The notions of semiconcavity and semiconvexity have been adapted to different geometrical contexts, in particular in sub-Riemannian structures such as Carnot groups, where they turn out to be extremely useful for the study of solutions of degenerate PDEs. In this talk I will show that, for a suitable class of Carnot groups, the Carnot-Carathéodory distance is semiconcave, in the sense of the group, in the whole space. I will also give some applications to solutions of non-coercive Hamilton-Jacobi equations. Joint work with Qing Liu and Ye Zhang from OIST (Okinawa, Japan).