Analysis section
Invited speakers:
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Contributed talks:
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Programme:
Mon 30th March, 2026
| 3:00pm – 3:30pm | Jeff Galkowski (UCL) |
| 3:30pm – 4:00pm | Matteo Capoferri (Heriot Watt and Università di Milano) |
| “Anderson localization in high-contrast random media” (abstract) | |
| 4:00pm – 4:30pm | Coffee break |
| 4:30pm – 5:00pm | Apala Majumdar (Manchester) |
| “Free boundary-value problems in the Landau-de Gennes theory for nematic liquid crystals - spindles, tactoids and bacterial biofilms” (abstract) | |
| 5:00pm – 5:30pm | Ian Wood (Kent) |
| 5:30pm – 6:00pm | Sukrid Petpradittha (Durham) |
| “Lieb–Thirring type inequalities for non-self-adjoint Schrödinger operators” (abstract) |
Tue 31st March, 2026
| 3:00pm – 3:30pm | Veronique Fischer (Bath) |
| 3:30pm – 4:00pm | Misha Karpukhin (UCL) |
| “Eigenvalue optimisation in geometric analysis” (abstract) | |
| 4:00pm – 4:30pm | Coffee break |
| 4:30pm – 5:00pm | Christiane Tretter (Bern) |
| 5:00pm – 5:30pm | Jean-Claude Cuenin (Loughborough) |
| 5:30pm – 6:00pm | Yulin Gong (Bristol) |
| “Observability and semiclassical control for Schrödinger equations on non-compact hyperbolic surfaces” (abstract) |
Wed 1st April, 2026
| 3:00pm – 3:30pm | Samuel Kittle (UCL) |
| 3:30pm – 4:00pm | Lauritz Streck (Edinburgh) |
| 4:00pm – 4:30pm | Coffee break |
| 4:30pm – 5:00pm | Benjamin Eichinger (Lancaster) |
| 5:00pm – 5:30pm | Itamar Oliveira (Birmingham) |
| “Multiple convolutions and multilinear fractal Fourier extension” (abstract) | |
| 5:30pm – 6:00pm | Sugata Mondal (Reading) |
| “Small eigenvalues and their stability under finite coverings” (abstract) |
Analysis section organisers:
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Abstracts:
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Matteo Capoferri (Heriot Watt and Università di Milano): Anderson localization in high-contrast random media
Consider a two-phase composite material with highly contrasting constituents, comprised of soft spherical inclusions with random radii dispersed in a stiff matrix. The modelling of such media has recently attracted significant interest from the research community, including in the context of stochastic homogenization. In particular, it has been proved that the spectrum of the operator describing them may feature a band-gap structure in the regime where heterogeneities take place on a sufficiently small scale. However, the nature of the limiting (as the small scale tends to zero) spectrum in the above setting is non-classical and not completely understood. In my talk I will discuss the occurrence of Anderson localization near spectral band edges, thus shedding some light on the limiting behaviour of the spectrum. The results rely on recent nontrivial advancements in quantitative unique continuation for PDEs. This is joint work with Matthias Täufer.
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Yulin Gong (Bristol): Observability and semiclassical control for Schrödinger equations on non-compact hyperbolic surfaces
In this talk, we study the observability of the Schrödinger equation on \(X\), a non-compact covering space of a compact hyperbolic surface \(M\). Using a generalized Bloch theory, wave functions on \(X\) are identified as sections of a unitary flat Hilbert bundle over \(M\). We extend the semiclassical analysis to unitary flat Hilbert bundles and generalize Dyatlov and Jin’s semiclassical control to all flat unitary Hilbert bundles over \(M\), with uniform constants independent of the choice of bundle. Furthermore, if the Riemannian cover \(X \rightarrow M\) is a normal cover with a virtually Abelian deck transform group \(\Gamma\), we apply the generalized Bloch theorem to derive the observability from all \(\Gamma\)-periodic open subsets of \(X\). We will also discuss the application of uniform semiclassical control in spectral geometry. This is joint work with Xin Fu (Westlake University) and Yunlei Wang (Louisiana State University).
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Misha Karpukhin (UCL): Eigenvalue optimisation in geometric analysis
The study of sharp upper bounds for Laplacian eigenvalues under area constraints is a classical topic in spectral geometry. A key source of interest lies in the remarkable fact that metrics achieving equality in such bounds correspond to metrics induced by minimal surfaces in spheres. Even more strikingly, analogous connections between eigenvalues and natural geometric structures continue to emerge across diverse settings. In this talk, I will highlight notable examples of these correspondences and discuss their implications for both spectral estimates and geometric analysis.
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Apala Majumdar (Manchester): Free boundary-value problems in the Landau-de Gennes theory for nematic liquid crystals - spindles, tactoids and bacterial biofilms
We introduce a diffuse-interface Landau-de Gennes free energy for nematic liquid crystals (NLC) systems, with free boundaries, in three dimensions submerged in isotropic liquid, and a phase field is introduced to model the deformable interface. The energy consists of the original Landau-de Gennes free energy, three penalty terms and a volume constraint.
We prove the existence and regularity of minimizers for the diffuse-interface energy functional. We also prove a uniform maximum principle of the minimizer under appropriate assumptions, together with a uniqueness result for small domains. Then, we establish a sharp-interface limit where minimizers of the diffuse-interface energy converge to a minimizer of a sharp-interface energy using methods from \(\Gamma\)-convergence. We conclude the talk with numerical experiments on the different energy minimizing shapes, e.g., spherical shapes, tactoids, spindles etc., many of which are also naturally observed in suspensions of viruses and bacteria and can have implications for drug delivery and therapeutics.
This is joint work with Dawei Wu, Yucen Han, Pingwen Zhang, Baoming Shi and Lei Shang.
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Sugata Mondal (Reading): Small eigenvalues and their stability under finite coverings
Small eigenvalues of hyperbolic surfaces gained renewed interests in the recent years, in connection with random spectral-gap questions. In this talk, I will explain some old and recent results on this topic. The talk will be based on results obtained with Werner Ballmann, Henrik Matthiesen and Panagiotis Polymerakis.
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Itamar Oliveira (Birmingham): Multiple convolutions and multilinear fractal Fourier extension
The classical Stein-Tomas theorem extends from the theory of linear Fourier restriction estimates for smooth manifolds to the one of fractal measures exhibiting Fourier decay. In the multilinear ‘smooth’ setting, transversality allows for estimates beyond those implied by the linear theory. The goal of this talk is to investigate the question ‘how does transversality manifest itself in the fractal world?’ We will show, for instance, that it could be through integrability properties of the multiple convolution of the measures involved, but that is just the beginning of the story. In the special case of Cantor-type fractals, we will construct multilinear Knapp examples through certain co-Sidon sets which, in some cases, will give more restrictive necessary conditions for a multilinear theorem to hold than those currently available in the literature. This is joint work with Ana de Orellana (University of St. Andrews, Scotland).
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Sukrid Petpradittha (Durham): Lieb–Thirring type inequalities for non-self-adjoint Schrödinger operators
The purpose of this talk is to present recent developments on Lieb–Thirring (LT) type inequalities for Schrödinger operators with complex potentials. We first discuss an open problem concerning a possible generalisation of the LT inequality, posed by Demuth, Hansmann, and Katriel (DHK) in 2013. In view of joint work with S. Bögli and F. Štampach, we show that the proposed DHK bound is false. Next we present the LT type estimates proved by Bögli (2023), which concern eigenvalue power sums with an exponent \(\gamma \geq 1\). In recent joint work with S. Bögli, we extend such estimates to the range \(\gamma < 1\) by means of a new eigenvalue counting estimate for non-self-adjoint operators. Lastly, we prove that our generalised LT bounds are optimal.
Contact:
All further questions and inquiries can be addressed to Marco Marletta at:
- MarlettaM at cardiff dot ac dot uk