Workshop

Shape Optimisation and Geometric Spectral Theory

20 - 23 Sep 2022

South Hall Complex. Edinburgh.

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Organiser

Ilaria Fragalà,Politecnico di Milano

Nunzia Gavitone,Università degli Studi di Napoli Federico II

Katie Gittins,Durham University

Asma Hassannezhad,University of Bristol

About

The workshop aimed to bring together both senior leading figures and emerging experts in the fields of shape optimisation, spectral inequalities, Robin and Steklov eigenvalue problems, properties of eigenfunctions and solutions to PDEs.

The main goals were to disseminate and discuss the latest advancements and open problems in these fields and to provide a platform for new collaborations.

Programme

Meet the speakers

Tuesday 20th September

Registration & coffee

Welcome - Introduction

Rafael Benguria

Pontificia Universidad Católica de Chile

A variational formulation for Dirac Operators in bounded domains and applications to spectral geometric inequalities

Talk Slide

Dorin Bucur

Universite de Savoie

Maximization of Neumann eigenvalues

Talk Slide

Michiaki Onodera

Tokyo Institute of Technology

Linear stability analysis of overdetermined problems

Talk Slide

Coffee/Tea

Talk Slide

Michiel van den Berg

University of Bristol

On some variational problems involving capacity, torsional rigidity, perimeter and measure

Abstract

Susanna Terracini

University of Turin

Higher order boundary Harnack principle on nodal domains via degenerate equations

Talk Slide

Laura Monk

University of Bristol

Geometry and spectrum of random hyperbolic surfaces

Abstract

Lunch

Abstract

Pedro Freitas

University of Lisbon (ONLINE)

Extremal values for the spectral determinant of Sturm-Liouville problems

Abstract

Nicola Fusco

Università di Napoli Federico II (ONLINE)

The isoperimetric inequality outside a convex: the case of equality

Talk Slide

Coffee/Tea

Talk Slide

David Jerison

MIT (ONLINE)

Remarks on the geometry of level sets of harmonic functions and eigenfunctions

Talk Slide

Eugenia Malinnikova

Stanford University (ONLINE)

Local version of the Courant nodal domain theorem

Abstract

Public Lecture – Carolyn Gordon at Bayes Centre

Dartmouth College (ONLINE)

Abstract

Wine reception at Bayes

Abstract

Wednesday 21st September

Nikolai Nadirashvili

CNRS

Spectrum of Laplacian with Indefinite Weight

Abstract

Richard Laugesen

University of Illinois Urbana-Champaign

Maximizers beyond the hemisphere for the second Neumann eigenvalue

Talk Slide

Giuseppe Buttazzo

University of Pisa

Upper and lower bounds for some shape functionals

Talk Slide

Coffee/Tea

Talk Slide

Alexandre Girouard

Université Laval

Metric upper bounds for Steklov and Laplace eigenvalues

Talk Slide

Bruno Colbois

University of Neuchâtel

The shape of Riemannian manifolds with large Steklov eigenvalues.

Talk Slide

Mikhail Karpukhin

University College London

Harmonic maps and eigenvalue optimization in higher dimensions

Talk Slide

Lunch

Talk Slide

Aldo Pratelli

University of Pisa

On a quantitative isoperimetric inequality involving the barycentric asymmetry

Abstract

Jimmy Lamboley

Sorbonne université, IMJ-PRG

Regularity in shape optimization under convexity constraint

Talk Slide

Gerasim Kokarev

The University of Leeds

Eigenvalue problems on Cartan-Hadamard manifolds

Talk Slide

Coffee/Tea

Talk Slide

Bozhidar Velichkov

University of Pisa (ONLINE)

On the regularity of the optimal shapes for a class of integral functionals

Abstract

Dario Mazzoleni

University of Pavia (ONLINE)

A variational approach to the Gamow and Hartree atomic models

Abstract

James Kennedy

University of Lisbon (ONLINE)

The behaviour of the spectrum of the Robin Laplacian with a complex boundary parameter

Talk Slide

Drink reception

South Hall

Talk Slide

Thursday 22nd September

Iosif Polterovich

Université de Montréal

Nodal count via topological data analysis

Talk Slide

Antoine Henrot

Institut Élie Cartan de Lorraine

Comparison between Steklov and Neumann eigenvalues

Talk Slide

Carlo Nitsch

University of Naples

Rearranging the gradient

Abstract

Coffee/Tea

Abstract

Alessandro Savo

Universita' di Roma, La Sapienza

Eigenvalue estimates for the Aharonov-Bohm Laplacian in 2D

Talk Slide

Jean Lagacé

King's College London

Spectral Geometry on rough spaces

Abstract

Graziano Crasta

Sapienza University of Rome

Concavity properties of solutions to Robin problems

Talk Slide

Lunch

Talk Slide

Michael Levitin

University of Reading

Pólya’s conjecture for the disk: a computer-assisted proof

Alessandro Giacomini

Università degli Studi di Brescia

On the minimization of the drag force in Stokes fluids: a free discontinuity approach.

Talk Slide

Coffee/Tea

Talk Slide

Francesco Della Pietra

University of Napoli Federico II

On the behaviour of the first eigenvalue of the $p$-Laplacian with Robin boundary conditions as $p$ goes to $1$

Talk Slide

Sabine Bögli

Durham University

On the eigenvalues of the Robin Laplacian with a complex parameter

Abstract

Simon Larson

The University of Gothenburg

An inequality for the normal derivative of the Lane-Emden ground state

Talk Slide

Workshop Dinner at Apiary Restaurant

Add: 33 Newington Road, Newington, Edinburgh EH9 1QR

Talk Slide

Friday 23rd September

Cristina Trombetti

Università degli studi di Napoli

Shape optimization of a thermal insulation problem

Talk Slide

Leonid Parnovski

University College London

Classical wave methods and modern gauge transforms: spectral asymptotics in the one-dimensional case

Talk Slide

Hanne van den Bosch

Universidad de Chile

Poincaré -Sobolev inequalities in domains

Talk Slide

Coffee/Tea

Talk Slide

Paolo Salani

Università di Firenze

Preservation of concavity by the Dirichlet heat flow

Talk Slide

Emily Dryden

Bucknell University

Steklov and mixed eigenvalue bounds on surfaces

Abstract

Bernard Helffer

Nantes Université

Computing nodal deficiency with a refined spectral flow] (after Berkolaiko, Cox, Helffer, Persson-Sundqvist)

Talk Slide

Close of workshop (Lunch provided)

Talk Slide