Shape Optimisation and Spectral Geometry

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Shape Optimisation and Spectral Geometry

 29 Jun - 03 Jul 2015

ICMS, 15 South College Street Edinburgh

  • Dorin Bucur, Université de Savoie
  • Guiseppe Buttazzo, University of Pisa
  • Aldo Pratelli, Friedrich-Alexander-Universität
  • Michiel van den Berg, University of Bristol

About:

The main purpose of this workshop was to bring together experts working on various topics involving partial differential equations, with particular attention to the dependence of the solutions of the state equations on the geometry of their domain of definition. Participants included specialists on shape optimization, spectral geometry, isoperimetric inequalities and other inequalities.

Group photographs of workshop participants can be found on the ICMS Flickr account.  

Speakers

  • Mark Ashbaugh, University of Missouri - A Sharp Lower Bound for the First Eigenvalue of the Vibrating Clamped Plate Under Compression

  • Ilaria Fragalà, Politecnico di Milano - Mahler Inequality for the First Eigenvalue of the Dirichlet Laplacia

  • Bruno Colbois, University of Neuchâtel - The Shape of Riemannian Manifolds and Submanifolds with Large Eigenvalues

  • Guido De Philippis, ENS - Regularity of Free Boundaries in Anisotropic Capillarity Problems and the Validity of Young's lLaw

  • Pedro Freitas, University of Lisbon - Optimal Laplace Determinants

  • Peter Gilkey, University of Oregon - Heat Content Asymptotics 

  • Bozhidar Velichkov, Université Joseph Fourier

  • Almut Burchard, University of Toronto

  • Iosif Polterovich, Université de Montréal - Spectral Geometry for the Steklov Problem

  • Leonid Parnovski, University College London - Asymptotic Behaviour of the Local

  • Carlo Nitsch, University of Naples - On the Elastic Energy of Planar Curves 

  • Susanna Terracini, University of Torino - Existence and Regularity of Solutions to Optimal Partition Problems Involving Laplacian Eigenvalues  

  • Rafael Benguria, Pontificia Universidad Católica - The Brezis-Nirenberg Problem on Mathbb{S}^n, in Spaces of Fractional Dimension

  • Richard Laugesen, University of Illinois - Steklov Spectral Inequalities Through Quasiconformal Mapping 

  • Evans Harrell, Georgia Institute of Technology - Semiclassically Sharp Bounds for Sums of Eigenvalues and Heat Traces 

  • Antoine Henrot, Université de Lorraine - Towards the Sharp Constant in the Quantitative Isoperimetric Inequality in the Plane

  • Dario Mazzoleni, University of Torino - A Surgery Result for the Spectrum of the Dirichlet Laplacian

  • Cristina Trombetti, University of Naples - Best Constants in Some Sobolev Poincaré Trace Inequalities

  • Alexandre Girouard, Université Laval - The Spectral Gap of Graphs and Steklov Eigenvalues on Surfaces

  • Jimmy Lamboley, University Paris-Dauphine - Optimal Compliance Problem

  • Nicola Fusco, University of Naples - Stability and Minimality for a Nonlocal Variational Problem

  • James Kennedy, University of Stuttgart - Eigenvalue Estimates for Quantum Graphs

  • Bernd Kawohl, University of Cologne - On Buttons and Balls that Cannot Run Away

  • Lorenzo Brasco, Aix-Marseille Université - An Improved Energy Bound for Schrödinger Operators 

  • Nicolai Nadirashvili, CNRS - Extremals of Conformal Spectrum of the Laplacian

  • Emily Dryden, Bucknell University - Can You Hear the Metric on a Sphere?

  • Michel Pierre, ENS and IRMAR - Estimates of Shape Deriatives Around Nonsmooth Domain

  • Bernard Helffer, Université Paris-Sud - On Noal and Minimal K-Partitions

  • Virgininie Bonnaillie-Noel, CNRS, ENS Paris - Minimal Spectral Partitions

  • Julie Rowlett, Chalmers University - When Can One Hear the Shape of a Drum?

  • Friedmann Brock, Leipzig University - Isoperimetric Inequalities with Power Weights

Sponsors and Funders:

This workshop was supported by the EPSRC, Foundaton Compositio and the ERC grant 258685.