Prossimi notiziari settimanali
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Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 13-05-2024 al 19-05-2024
Mercoledì 15 maggio 2024
Ore 16:00, Aula M3, Dipartimento di Matematica e Fisica, Università Roma Tre
Junior seminar di Geometria Algebrica
Zakaria Brahimi (Università degli studi Roma Tre)
Cubic fourfolds: some rational examples
Projective spaces are the most basic algebraic varieties that we know and rational varieties are those that are the closest possible to being projective spaces. The question of rationality of algebraic varieties has led to the development of a rich and beautiful theory and many questions are still open. Historically, the rationality problem for quadric and cubic surfaces was settled classically over one hundred years ago. In this seminar, we will talk about some rational cubic fourfolds that are known. We look for them inside Hassett Divisors; These divisors are codimension one varieties in the Moduli space of cubic fourfolds. Maggiori informazioni sul sito: https://ricerca.mat.uniroma3.it/seminari/junior_seminars.html
Mercoledì 15 maggio 2024
Ore 16:15, sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Raffaele Scandone (Università di Napoli)
Growth of Sobolev norms for a quantum fluid system
I will discuss the existence of turbulent solutions to a quantum hydrodynamic (QHD) system, with periodic boundary conditions. A suitable nonlinear change of variables (the Madelung transform) formally connects the QHD system to a non-linear Schrödinger (NLS) equation, for which we can construct smooth solutions displaying arbitrarily large growth of Sobolev norms above the energy regularity level. This amounts to a cascade in time of the energy to higher Fourier modes. In addition, these solutions can be designed to be small amplitude perturbations of stationary states, which implies in particular absence of quantum vortices. This allows to exploit an equivalence between high regularity QHD- and NLS- norms, which eventually yields the existence of smooth, turbulent solutions to the quantum hydrodynamic system. Based on joint work with F. Giuliani
Per informazioni, rivolgersi a: basile@mat.uniroma1.it, domenico.monaco@uniroma1.it
Giovedì 16 maggio 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
P(n)/N(p): Problemi differenziali nonlineari/Nonlinear differential problems
Luigi Muglia (Università della Calabria)
OPTIMAL SECOND ORDER BOUNDARY REGULARITY FOR SOLUTIONS TO p-LAPLACE EQUATIONS
Solutions to \(p\)-Laplace equations are not, in general, of class\( C^2\). The study of Sobolev regularity of the second derivatives is, therefore, a crucial issue. An important contribution by Cianchi and Maz’ya shows that, if the source term is in \(L^2\), then the field \(|\nabla u|^{p−2}\nabla u\) is in \(W^{1,2}\). The \(L^2\)-regularity of the source term is also a necessary condition. During the talk, following a paper in collaboration with Luigi Montoro and Berardino Sciunzi, we will obtain under suitable assumptions, sharp second order estimates, thus proving the optimal regularity of the vector field \(|\nabla u|^{p−2}\nabla u\), up to the boundary.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it
Le comunicazioni relative a seminari da includere in questo notiziario devono pervenire esclusivamente
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