Care tutte e cari tutti,

vi ricordiamo che il prossimo Colloquium di dipartimento si svolgerà domani alle ore 16 in Aula Magna, con oratrice Gigliola Staffilani (Massachusetts Institute of Technology (MIT)). Trovate qui sotto tutti i dettagli. Speriamo di vedervi numerosi!

Un caro saluto,
Chiara, Davide e Ilaria


Care tutte e cari tutti,

Siamo lieti di invitarvi al prossimo Colloquium di Dipartimento, che si terrà mercoledì 10 giugno alle ore 16:00 in Aula Magna. In questa occasione, Gigliola Staffilani (Massachusetts Institute of Technology (MIT)) terrà un seminario dal titolo

"The Study of Wave Turbulence: A Breeding Ground for Mathematical Techniques" 

L'abstract dell'intervento è riportato in fondo a questa email.

La ricerca di Gigliola Staffilani si situa nell'ambito delle equazioni differenziali alle derivate parziali e analisi armonica, in particolare PDE nonlineari dispersive. La professoressa Staffilani ha ricevuto numerosi riconoscimenti internazionali, è titolare della cattedra Abby Rockefeller Mauzé di Matematica al MIT, ed è membro della National Academy of Sciences e della American Academy of Arts and Sciences. 

L'incontro è aperto a tutti gli interessati, anche non specialisti.

Il colloquio sarà seguito da un rinfresco con la relatrice.

Speriamo di vedervi numerosi!

Un caro saluto,
Chiara, Davide e Ilaria

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Dear all,

We are pleased to invite you to the next Department Colloquium, which will take place on Wednesday 10 June at 4:00 pm in the Aula Magna. On this occasion, Gigliola Staffilani (Massachusetts Institute of Technology (MIT)) will give a talk with title


"The Study of Wave Turbulence: A Breeding Ground for Mathematical Techniques" 

The abstract of the talk is included at the end of this email.

Gigliola Staffilani’s research focuses on partial differential equations and harmonic analysis, specifically on non-linear dispersive PDEs. Professor Staffilani has received numerous international awards, she holds the Abby Rockefeller Mauzé Professorship in Mathematics at MIT, and she is an elected member of both the National Academy of Sciences and the American Academy of Arts and Sciences.

The event is open to all interested participants, including non-specialists.

The colloquium will be followed by refreshments with the speaker.

We hope to see many of you there!

Best regards,
Chiara, Davide and Ilaria

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Speaker: Gigliola Staffilani, Massachusetts Institute of Technology (MIT)

Title: The Study of Wave Turbulence: A Breeding Ground for Mathematical Techniques

Abstract: Wave turbulence theory provides a unifying framework for analyzing the nonlinear interactions of dispersive waves across diverse physical regimes. These interactions manifest over an extensive range of scales and media, encompassing phenomena such as gravitational waves in astrophysical contexts, surface waves in fluid dynamics, coherent structures in quantum systems, and even pattern formation in everyday fluid flows.

Despite their widespread occurrence, the mathematical analysis of such systems remains exceptionally challenging due to the interplay between nonlinearity, dispersion, and randomness. These difficulties have catalyzed the development of sophisticated analytical and probabilistic tools, drawing from partial differential equations, statistical mechanics, and dynamical systems theory.

In this lecture, I will present a short survey of recent advances in the rigorous treatment of wave turbulence, emphasizing key techniques, foundational results, and open problems. Some attention will be given to the derivation of kinetic equations, and the role of resonant interactions in the long-time dynamics of weakly nonlinear wave systems.