Lumer Lectures

This series of lectures is named after Gunter Lumer, a great mathematician with extensive achievements and a deep curiosity for applied functional analysis and operator theory, and is a joint scientific activity of all Action's Working Groups. The lectures will be delivered by carefully selected distinguished scientists whose research interests are related to our Action.

Gunter Lumer was born in Frankfurt, Germany in 1929. With Nazism on the rise, the Lumer family left Germany in 1933 and settled in France, and then in Uruguay. Gunter graduated in 1957 with a degree in electrical engineering from the University of Montevideo, he then received a Guggenheim fellowship to study at the University of Chicago. There he received his Ph.D. in Mathematics in 1959. Although Gunter Lumer's professional focus was on functional analysis, partial differential equations, and evolution equations, he nourished a broad interest for almost all areas of mathematics and for science in general. He published more than one hundred papers and edited many books. Probably his best known result is the celebrated Lumer-Phillips theorem, which gives necessary and sufficient conditions on an operator to generate a strongly continuous semigroup of contractions on a general Banach space. This result, published in the Pacific Journal of Mathematics in 1961, is a key contribution to the theory of operator semigroups. The research areas of our Action are closely related to some of Gunter's research activities in the 80's, and also brings together many of his collaborators and students. In a sense he is at the origin of the topics developed in this Action.

More details about Gunter Lumer's life and activities can be found on the following link.

 

Marcel Filoche (École Polytechnique): The landscape of wave localization in complex or disordered systems

Wednesday, 26 May 2021, 16:30 (CET)

Youtube link where the direct streaming of the talk will happen

Marcel Filoche received his Ph.D. in 1991 from the Université Paris-Sud Orsay. He then worked for the France Telecom R&D center, before joining the CNRS in 1997. Since 2008 he is CNRS Research Director at the Condensed Matter Physics lab at École Polytechnique. Since 2018 he is also among the PIs of a research collaboration on Localization of Waves, sponsored by the Simons Foundations. He is the author of over 180 articles on biophysics, condensed matter, and wave phenomena in mathematics and theoretical physics.

Abstract: In disordered systems or complex geometry, standing waves can undergo a strange phenomenon that has puzzled physicists and mathematicians for over 60 years, called “wave localization”. This localization, which consists of a concentration (or a focusing) of the energy of the waves in a very restricted sub-region of the whole domain, has been demonstrated experimentally in mechanics, acoustics and quantum physics. During this talk, we will present a new theory which brings out an underlying and universal structure, the localization landscape, solution of a Dirichlet problem associated with the wave equation [1]. In quantum systems, this landscape also allows us to define an “effective localization potential” which predicts the localization regions, the energies of the localized modes, the density of states, as well as the long-range decay of the wave functions. This theory holds in any dimension, for continuous or discrete systems. We will present the major mathematical properties of this landscape. Finally, we will review applications of this theory in mechanics, semiconductor physics, as well as molecular and cold atom systems.
[1] M. Filoche & S. Mayboroda, Proc. Natl Acad. Sci. (2012) 109:14761-14766.

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