Care tutte e cari tutti,
segnalo, anche da parte di Mario, il seminario "Transport of Gaussian measures under the flow of Hamiltonian PDEs: quasi-invariance and singularity" che sarà tenuto da Leonardo Tolomeo (Univ. of Edinburgh) martedì prossimo 20 Febbraio alle ore 14 in Aula Seminari. Il seminario è tra le attività SPASS, ma credo possa interessare anche gli analisti.
Il link dell'evento è il seguente: https://www.dm.unipi.it/en/seminar/?id=65ccf769e7bee0277813b9eb Riporto per comodità anche l'abstract qui in basso.
Luigi
-------- Speaker: Leonardo Tolomeo (University of Edinburgh)
Title: Transport of Gaussian measures under the flow of Hamiltonian PDEs: quasi-invariance and singularity
Abstract: In this talk, we consider the Cauchy problem for the fractional NLS with cubic nonlinearity (FNLS), posed on the one-dimensional torus T, subject to initial data distributed according to a family of Gaussian measures. We first discuss how the flow of Hamiltonian equations transports these Gaussian measures. When the transported measure is absolutely continuous with respect to the initial measure, we say that the initial measure is quasi-invariant. In the high-dispersion regime, we exploit quasi-invariance to build a (unique) global flow for initial data with negative regularity, in a regime that cannot be replicated by the deterministic (pathwise) theory. In the 0-dispersion regime, we discuss the limits of this approach, and exhibit a sharp transition from quasi-invariance to singularity, depending on the regularity of the initial measure.
This is based on joint works with J. Forlano (UCLA/University of Edinburgh) and with J. Coe (University of Edinburgh).