Particles in Interaction and Wave Turbulence

  • Speaker
  • Isabelle Gallagher, Ph.D.Professor, Professor of Mathematics, École Normale Supérieure de Paris (ENS)
    Director, Foundation Sciences Mathématiques de Paris
Date & Time

About Simons Foundation Lectures

Simons Foundation Lectures are free public colloquia related to basic science and mathematics. These high-level talks are intended for professors, students, postdocs and business professionals, but interested people from the metropolitan area are welcome as well.
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A huge system of equations describes the interactions of waves, such as those found in fluid dynamics and quantum mechanics. The theory of wave turbulence is designed to extract from those equations a ‘master equation’ that retains the physical system’s essential features. The interest of such a procedure is to drastically decrease the complexity of the system while exhibiting some universal behavior despite the underlying complexity of the interactions. This theory is yet to be set on rigorous foundations. In this talk, Isabelle Gallagher will focus on the more tractable case where the interactions are between particles (like atoms in a gas) instead of waves. She will show that the ‘master equation’ turns out to be Boltzmann’s famous equation, which he formally derived in 1872.

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About the Speaker

Gallagher is a professor at École Normale Supérieure in Paris and the Université de Paris, and member of the CNRS laboratory DMA (Département de Mathématiques et Applications). She is a former student of the École Polytechnique, holder of a Ph.D. from Sorbonne Université (formerly UPMC), and a former CNRS research fellow at the Université Paris Sud and the Ecole Polytechnique.

Gallagher is a specialist in non-linear partial differential equations, particularly mechanics equations. She and her collaborators have made good progress on Hilbert’s sixth problem, seeking to reconcile microscopic and macroscopic descriptions of fluids. Her work has been awarded many times. In particular, she received the 2008 Paul Doistau-Émile Blutet Prize and the 2018 Sophie Germain Prize from the Académie des Sciences and the CNRS silver medal in 2016.

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