Στο πλαίσιο της σειράς σεμιναρίων που διοργανώνεται από το Τμήμα, καλεσμένος μας την Πέμπτη 19 Μαρτίου είναι ο Δρ. Νικόλαος Αθανασίου, μεταδιδακτορικός ερευνητής στο Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης.
Τίτλος: ”The Einstein-Vlasov system in a large data regime”
Ομιλητής: Νικόλαος Αθανασίου
Τοποθεσία: Τμήμα Μαθηματικών, Αίθουσα Β2
Ημέρα: Πέμπτη, 19/03/2026
Ώρα: 12:00
Abstract: In this talk, our object of study is the Einstein-Vlasov system with a massless Vlasov matter field. Our main contribution is the provision of a novel technique for controlling the Vlasov matter in a double null gauge, relying purely on vector field commutation and bypassing the need for introducing Jacobi fields, which has so far been the only existing technique outside of symmetry in this gauge. To obtain it, we have to overcome stringent regularity issues that are existent along this path. Because it relies solely on vector field commutation, our technique is fundamentally simple and flexible enough to be applicable in any data regime. We thus anticipate this to be a helpful tool for many subsequent problems regarding the Einstein-Vlasov system, including, for instance, simplified approaches to the proof of nonlinear stability of Minkowski spacetime with massless Vlasov matter, scattering problems for data close to black holes, approaching cosmic censorship, etc. We further introduce and work in an optimal regularity framework, using this new technique, to obtain a large data semi-global existence theorem and a dynamical trapped surface formation statement for our system. Joint work with P. Mondal and S.T. Yau.