Herglotz-Nevanlinna Functions and their Applications

Accueil › Animation Scientifique › Herglotz-Nevanlinna Functions and their Applications

Hybrid Conference "Herglotz-Nevanlinna Functions and their Applications to Dispersive Systems and Composite Materials", from 23 to 27 May 2022, in Marseille CIRM, Luminy Campus.

Description :
Herglotz-Nevanlinna functions are analytic functions with a nonnegative imaginary part in a given tubulardomain (such as the upper-half plane of the complex plane). Discovered in the 1920s, these functions have a long history in analysis (spectral theory, moment problem...) and appear more recently as a key tool inapplied sciences to study the dispersion in electromagnetic systems such as metamaterials, in the analysis of effective tensors of composite materials and in the study of the Dirichlet-to-Neumann (DtN) map in inverse problems. Indeed, the mathematical properties of Herglotz-Nevanlinna functions (integral representations, sum rules, continued fraction expansions...) are extremely useful to derive fundamental limits and quantitative bounds on a physical property with respect to the frequency (for dispersive systems) or with the respectto the geometry (for composite materials). Knowing the sharpness of these bounds in a class of materials generates a lot of applications in electromagnetism and composites design. Finally, a recent breakthrough appears in inverse problems and imaging in composite media where a deep connection was made between the DtN map and these functions. However, nowadays, most of the topical issues necessitate a deep understanding of Herglotz-Nevanlinna’s functions depending not only of one variable but also of several variables (as for composites composed of at least three phases or spatially dispersive media whose permittivity depends both on the wave number and the frequency). Another challenge which appears to be crucial for some applications (e.g. the DtN map in composite media) is to deal with Herglotz-Nevanlinna operator valued functions. Thus, the aim of this conference is to gather several communities : pure mathematicians, applied mathematicians, physicists and engineers around Herglotz-Nevanlinna functions and their connections with physics and engineering. Its main focus is communicating the needs of people on the applied side and the tools of those on the more theoretical side and thus laying the foundations for future interactions.

Scientific Committee :
 Elena Cherkaev, University of Utah
 Patrick Joly, Poems team, CNRS, INRIA, ENSTA Paris
 Mihai Putinar, University of California at Santa Barbara
 Mario Silveirinha, University of Lisbon
 Christiane Tretter, University of Bern

Organizing Committee
 Anne-Sophie Bonnet-Ben Dhia, Poems team, CNRS, INRIA, ENSTA Paris
 Maxence Cassier, CNRS, Institut Fresnel, Aix Marseille Université, Centrale Marseille
 Boris Gralak, CNRS, Institut Fresnel, Aix Marseille Université,Centrale Marseille
 Annemarie Luger, Stockholm University
 Graeme Milton, University of Utah

 Free Access to video conferences with the CIRM Audiovisual Mathematics Library

Speakers : Andrea Alu (Cuny University), Christian Berg (University of Copenhagen), Anne-Sophie Bonnet-Ben Dhia (Poems team, CNRS, INRIA, ENSTA Paris), Camille Carvalho (INSA Lyon, Institut Camille Jordan), Elena Cherkaev (University of Utah), Guillaume Démesy (Institut Fresnel, Aix-Marseille Université, Centrale Marseille), Kenneth Golden (University of Utah), Yury Grabovsky (Temple University), Sébastien Guenneau (CNRS, UMI Abraham De Moivre, Imperial College), Fernando Guevara Vasquez (University of Utah), Mats Gustafsson (Lund University), Christophe Hazard (Poems team, CNRS, INRIA, ENSTA Paris), Patrick Joly (Poems team, CNRS, INRIA, ENSTA Paris), Lars Jonsson (Royal Institute of Technology of Stockholm), Maryna Kachanovska (Poems team, CNRS, INRIA, ENSTA Paris), Pavel Kurasov (University of Stockholm), Simon Lemaire (Université de Lille), Robert Lipton (Louisiana State University), Annemarie Luger (Stockholm University), Ornella Mattei (San Francisco State University), Owen Miller (Yale University), Graeme Milton (University of Utah), Florian Monteghetti (ISAE-SUPAERO, Université de Toulouse), Mitja Nedic (University of Ljubljana), Miao-jung Yvonne Ou (University of Delawaere), Konstantin Pankrashkin (University of Oldenburg), Henrik Laurberg Pedersen (University of Copenhagen), Mihai Putinar (University of California at Santa Barbara), Mahran Rihani (Poems team, CNRS, INRIA, ENSTA Paris), Mário Silveirinha (University of Lisbon), Aaron Welters (Florida Institute of Technology), Ian Wood (University of Kent)

More Information on https://conferences.cirm-math.fr/2225.html