Short scientific description

This workshop focuses on some recent research and techniques, mainly of variational type, which have been developed to prove the existence of optimal shapes and to study their properties in the context of spectral geometry. Some celebrated open problems and conjectures will be studied hoping to make a step forward in the direction of solving them, or at least to obtain new partial information.

The event will provide an overview on some recent techniques, which have been developed to prove the existence of optimal shapes and to study their regularity. Indeed, in the last few years, tremendous advances based on free boundary techniques opened the way to attack unsolved problems and to deeply understand fine behaviour of general shape functionals of non-monotonous type.

Precisely,  our activities will concentrate on the following topics:

• Theoretical advances in shape optimization theory: existence of solutions, relaxation phenomena, numerical computations of optimal shapes, calculus of variations techniques, critical shapes, regularity;

• Functional and geometrical inequalities;

• Problems in spectral geometry;

• Optimal shapes and techniques arising from free boundary and free discontinuity problems;

• Advances in the numerical treatment to approximate optimal geometries for spectral problems.

Invited speakers 

Paolo Acampora (Napoli, Italy)

Michiel van den Berg (Bristol, UK)

Giuseppe Buttazzo (Pisa, Italy)

Philippe Charron (London, UK)

Mattia Fogagnolo (Padova, Italy)

Ilaria Fragalà (Milano, Italy)

Pedro Freitas (Lisbon, Portugal)

Katie Gittins (Durham, UK)

Antoine Henrot (Nancy, France)

James Kennedy (Lisbon, Portugal)

David Krejčiřík (Prague, Czech Republic)

Dennis Kriventsov (Rutgers, USA)

Ilaria Lucardesi (Pisa, Italy)

Jimmy Lamboley (Paris, France)

Richard Laugesen (Urbana-Champaign, USA)

Romeo Leylekian (Lisbon, Portugal)

Alba Lia Masiello (Napoli, Italy)

Idriss Mazari (Paris, France)

Mickaël Nahon (Grenoble, France)

Robin Neumayer (Pittsburgh, USA)

Edouard Oudet (Grenoble, France)

Konstantin Pankrashkin (Oldenburg, Germany)

Emanuele Pastorino (Milano, Italy)

Alessandra Pluda (Pisa, Italy)

Alberto Roncoroni (Milano, Italy)

Salvatore Stuvard (Milano, Italy)

Sponsors

This workshop is supported by INdAM Istituto Nazionale di Alta Matematica, the department of Matematica e Applicazioni "R. Caccioppoli" of Università degli Studi di Napoli Federico II and by Laboratoire de Mathématiques UMR 5127 of Université de Savoie.