Scientific Organisers
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Sabine Boegli , Durham University
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Matteo Capoferri , Heriot-Watt University
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Jean-Claude Cuenin , Loughborough University
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Katie Gittins , Durham University
About:
Spectral Theory in the UK has a longstanding history, encompassing the influential works of scientists such as Titchmarsh, Born and Dirac. It naturally sits at the crossroads of numerous branches of mathematics, from the very pure to the more applied side of the subject, including but not limited to operator theory, analysis of PDEs, harmonic analysis, differential geometry, numerical analysis, number theory and mathematical physics.
Research in Spectral Theory is currently expanding rapidly on multiple fronts and experiencing worldwide growth. By bringing together leading experts in the field from all around the world, this workshop provided an effective environment for exchanging ideas, developing new collaborations, and inspiring future generations in the field, building upon the rich and diverse research landscape in Spectral Theory in the UK.
This workshop was one of the central activities of the UK Spectral Theory Network, supported by the Isaac Newton Institute. As such, it featured several contributed talks by Early Career Researchers and had a strong commitment to promoting diversity in Mathematics.
This workshop was organised in partnership with the Clay Mathematics Institute.
Dmitri Vassiliev (UCL) delivered the public lecture titled Spectral Theory: what's it all about and what is it's use.
Programme
| MONDAY 09 SEPTEMBER 2024 | ||
| Registration and Refreshments | ||
| Welcome and Housekeeping | ||
| Wilhelm Schlag, Yale University | The distorted Fourier transform and some applications | |
| Refreshments | ||
| Tanya Christiansen, Missouri | Eigenvalues and resonances of Schr\"{o}dinger operators near zero in dimension two | |
| Lunch | ||
| Michael Magee, Durham University | Optimal spectral gaps | |
| Jade Brisson, Université de Neuchâtel | Upper bounds, spectral ratios and spectral gaps for Steklov eigenvalues of warped products | |
| Refreshments | ||
| Gianpaolo Piscitelli, Università degli studi di Napoli Federico II | The first Robin-Neumann eigenvalue: isoperimetric and quantitative inequalities | |
| George Coote, University of Cambridge | Thresholds of Spectral Computations: Exploring Provability and Phase Transitions in the Solvability Complexity Index | |
| Welcome reception | ||
| TUESDAY 10 SEPTEMBER 2024 | ||
| Fioralba Cakoni, Rutgers University | Transmission Eigenvalues and Non-scattering: Spectral Theory Meets Free Boundary Regularity | |
| Refreshments | ||
| Christopher Judge, Indiana University Bloomington | Recent progress on the hot spots conjecture | |
| Lawford Hatcher, Indiana University Bloomington | The hot spots conjecture with mixed boundary conditions | |
| Lunch | ||
| Simon Chandler-Wilde, University of Reading | Computing the Essential Spectrum of the Neumann–Poincaré Operator on Highly Oscillatory Boundaries | |
| Iveta Semorádová, Czech Technical University and Cardiff University | Pt -symmetric oscillators with one-center point interactions | |
| Refreshments | ||
| Sukrid Petpradittha, Durham University | Lieb-thirring type inequalities for multidimensional schrodinger operators with complex-valued potentials | |
| Ghada Jameel, Cardiff University | Eigenvalue Bounds for Perturbed Periodic Dirac Operators | |
| Public Lecture - Dmitri Vassiliev, University College London | Spectral theory: what’s it all about and what is its use | |
| WEDNESDAY 11 SEPTEMBER 2024 | ||
| Alberto Enciso, ICMAT | An “almost Schiffer” problem on Neumann eigenfunctions of planar domains | |
| Refreshments | ||
| Cristina Trombetti, University of Naples | Talenti type comparison result for the Neumann boundary value problem | |
| Martijn Kluitenberg, University of Groningen | Cheeger's inequality in sub-Riemannian geometry | |
| Lunch and Free Afternoon | ||
| THURSDAY 12 SEPTEMBER 2024 | ||
| Maciej Zworski, UC Berkeley | Classical/quantum correspondence in Lindblad evolution | |
| Refreshments | ||
| Marcello Seri, University of Groningen | A panorama of singular sub-Laplacians and their spectra | |
| Marcello Malagutti, University College London | Asymptotic Properties for the Spectrum of Semiregular Global Systems | |
| Lunch | ||
| Emily Dryden, Bucknell University | Steklov spectral finiteness for convex polygonal domains | |
| Giorgio Saracco, Università di Firenze | Existence of minimizers of Cheeger's functional among convex sets | |
| Refreshments | ||
| Jan Dereziński, University of Warsaw | Point-splitting and dimensional regularization in quantum mechanics | |
| Matthias Langer, University of Strathclyde | Eigenvalues of canonical systems | |
| Workshop Dinner, hosted at Apex Hotel | ||
| FRIDAY 13 SEPTEMBER 2024 | ||
| Asma Hassannezhad, University of Bristol | Low Steklov eigenvalue of finite volume hyperbolic surfaces | |
| Refreshments | ||
| Siavash Sadeghi, University of Reading | Wavenumber-explicit bounds for first kind integral equations in wave scattering. | |
| Lyonell Boulton, Heriot-Watt University | Weak revivals in time-evolution models, a spectral theory point of view | |
| Lunch and End of Workshop |
