Scientific Organisers
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Ilaria Fragalà, Politecnico di Milano
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Nunzia Gavitone, Università degli Studi di Napoli Federico II
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Katie Gittins, Durham University
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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
| 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 | |
| Dorin Bucur, Universite de Savoie | Maximization of Neumann eigenvalues | |
| Michiaki Onodera, Tokyo Institute of Technology | Linear stability analysis of overdetermined problems | |
| Coffee/Tea | ||
| Michiel van den Berg, University of Bristol | On some variational problems involving capacity, torsional rigidity, perimeter and measure | |
| Susanna Terracini, University of Turin | Higher order boundary Harnack principle on nodal domains via degenerate equations | |
| Laura Monk, University of Bristol | Geometry and spectrum of random hyperbolic surfaces | |
| Lunch | ||
| Pedro Freitas, University of Lisbon (ONLINE) | Extremal values for the spectral determinant of Sturm-Liouville problems | |
| Nicola Fusco, Università di Napoli Federico II (ONLINE) | The isoperimetric inequality outside a convex: the case of equality | |
| Coffee/Tea | ||
| David Jerison, MIT (ONLINE) | Remarks on the geometry of level sets of harmonic functions and eigenfunctions | |
| Eugenia Malinnikova, Stanford University (ONLINE) | Local version of the Courant nodal domain theorem | |
| Public Lecture – Carolyn Gordon at Bayes Centre, Dartmouth College (ONLINE) | ||
| Wine reception at Bayes | ||
| Wednesday 21st September | ||
| Nikolai Nadirashvili, CNRS | Spectrum of Laplacian with Indefinite Weight | |
| Richard Laugesen, University of Illinois Urbana-Champaign | Maximizers beyond the hemisphere for the second Neumann eigenvalue | |
| Giuseppe Buttazzo, University of Pisa | Upper and lower bounds for some shape functionals | |
| Coffee/Tea | ||
| Alexandre Girouard, Université Laval | Metric upper bounds for Steklov and Laplace eigenvalues | |
| Bruno Colbois, University of Neuchâtel | The shape of Riemannian manifolds with large Steklov eigenvalues. | |
| Mikhail Karpukhin, University College London | Harmonic maps and eigenvalue optimization in higher dimensions | |
| Lunch | ||
| Aldo Pratelli, University of Pisa | On a quantitative isoperimetric inequality involving the barycentric asymmetry | |
| Jimmy Lamboley, Sorbonne université, IMJ-PRG | Regularity in shape optimization under convexity constraint | |
| Gerasim Kokarev, The University of Leeds | Eigenvalue problems on Cartan-Hadamard manifolds | |
| Coffee/Tea | ||
| Bozhidar Velichkov, University of Pisa (ONLINE) | On the regularity of the optimal shapes for a class of integral functionals | |
| Dario Mazzoleni , University of Pavia (ONLINE) | A variational approach to the Gamow and Hartree atomic models | |
| James Kennedy , University of Lisbon (ONLINE) | The behaviour of the spectrum of the Robin Laplacian with a complex boundary parameter | |
| Drink reception | South Hall | |
| Thursday 22nd September | ||
| Iosif Polterovich, Université de Montréal | Nodal count via topological data analysis | |
| Antoine Henrot, Institut Élie Cartan de Lorraine | Comparison between Steklov and Neumann eigenvalues | |
| Carlo Nitsch, University of Naples | Rearranging the gradient | |
| Coffee/Tea | ||
| Alessandro Savo, Universita' di Roma, La Sapienza | Eigenvalue estimates for the Aharonov-Bohm Laplacian in 2D | |
| Jean Lagacé, King's College London | Spectral Geometry on rough spaces | |
| Graziano Crasta, Sapienza University of Rome | Concavity properties of solutions to Robin problems | |
| Lunch | ||
| Michael Levitin, University of Reading | Pólya’s conjecture for the disk: a computer-assisted proof |
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| Alessandro Giacomini, Università degli Studi di Brescia | On the minimization of the drag force in Stokes fluids: a free discontinuity approach. | |
| Coffee/Tea | ||
| 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 $1$ | |
| Sabine Bögli, Durham University | On the eigenvalues of the Robin Laplacian with a complex parameter | |
| Simon Larson, The University of Gothenburg | An inequality for the normal derivative of the Lane-Emden ground state | |
| Workshop Dinner at Apiary Restaurant | Add: 33 Newington Road, Newington, Edinburgh EH9 1QR | |
| Friday 23rd September | ||
| Cristina Trombetti, Università degli studi di Napoli | Shape optimization of a thermal insulation problem | |
| Leonid Parnovski, University College London | Classical wave methods and modern gauge transforms: spectral asymptotics in the one-dimensional case | |
| Hanne van den Bosch, Universidad de Chile | Poincaré -Sobolev inequalities in domains | |
| Coffee/Tea | ||
| Paolo Salani, Università di Firenze | Preservation of concavity by the Dirichlet heat flow | |
| Emily Dryden, Bucknell University | Steklov and mixed eigenvalue bounds on surfaces | |
| Bernard Helffer, Nantes Université | Computing nodal deficiency with a refined spectral flow] (after Berkolaiko, Cox, Helffer, Persson-Sundqvist) | |
| Close of workshop (Lunch provided) |
Sponsors and Funders:
Funding for the workshop comes from ICMS, Clay Mathematics Institute, Foundation Compositio Mathematica, and Heilbronn Institute for Mathematical Research. It is organised in partnership with the Clay Mathematics Institute.
