Analysis section
Invited speakers:
|
|
Contributed talks:
|
Programme (all talks are in Abacws/2.26):
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) |
| “Spectrum of the Maxwell equations for a flat interface between non-homogeneous dispersive media” (abstract) | |
| 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 | Véronique Fischer (Bath) |
| “High-frequency analysis for subelliptic operators” (abstract) | |
| 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) |
| “Essential numerical ranges” (abstract) | |
| 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) |
| “A geometric approach to counting rationals near curves” (abstract) | |
| 4:00pm – 4:30pm | Coffee break |
| 4:30pm – 5:00pm | Benjamin Eichinger (Lancaster) |
| “Necessary and sufficient conditions for universality limits” (abstract) | |
| 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:
|
Abstracts:
-
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.
-
Benjamin Eichinger (Lancaster): Necessary and sufficient conditions for universality limits
This talk is concerned with the local asymptotic behavior of zeros of orthogonal polynomials associated with a real measure as the degree tends to infinity. This is a topic of classical interest going back to results of Szegő. From a modern perspective, the local behavior of zeros is studied via scaling limits of the Christoffel--Darboux kernel. One says that orthogonal polynomials exhibit bulk universality at a point if the scaling limit is given by the sine kernel. In this case, the zeros display local asymptotic equal spacing. In this talk, we present the first necessary and sufficient conditions for bulk universality limits. We will also discuss other universality classes, corresponding to convergence to different limit kernels and analogous results for eigenvalues of Schrödinger operators.
This talk is based on joint works with Lukić, Simanek and Woracek.
-
Véronique Fischer (Bath): High-frequency analysis for subelliptic operators
In this talk, I will describe recent progress on the analysis of high frequencies for subelliptic operators, highlighting how techniques from Lie group analysis and harmonic analysis can be adapted to this non-elliptic context. I will present some representative results and explain how they connect with microlocal and semiclassical approaches, pointing to several open problems.
-
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).
-
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.
-
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.
-
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.
-
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).
-
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.
-
Lauritz Streck (Edinburgh): A geometric approach to counting rationals near curves
In this talk, we present a novel, geometric approach to estimating the number of rationals in the neighborhood of planar and other curves. We discuss the underlying principles and possible connections to other open problems. Work in progress.
-
Christiane Tretter (Bern): High-frequency analysis for subelliptic operators
In this talk various essential numerical range concepts will be presented and compared. Their potential to capture spectral pollution and spectral invisibility makes them a valuable tool, in particular, for applications to partial differential operators. This is a joint work with Sabine Bögli and Marco Marletta.
-
Ian Wood (Kent): Spectrum of the Maxwell equations for a flat interface between non-homogeneous dispersive media
This talk concerns the time-harmonic Maxwell equation in three-dimensional space, divided into two half-spaces by a flat interface. The two half-spaces are filled with media whose electric permittivity is frequency-dependent and varies as a function of the distance from the interface only; this dependence is assumed to satisfy a regularity condition in each half-space but may be discontinuous at the interface. No specific model for the frequency dependence is assumed. For the associated operator pencil, we characterise subsets of the resolvent set and separate subsets of the Weyl spectrum corresponding to radiation away from the interface and along the interface, respectively. If the media are periodic in the direction orthogonal to the interface, a more explicit description of these sets can be given in terms of Floquet theory of related Sturm-Liouville equations.
This is joint work with Malcolm Brown (Cardiff), Tomas Dohnal (Halle), Karl Michael Schmidt (Cardiff) and Michael Plum (Karlsruhe).
Contact:
All further questions and inquiries can be addressed to Marco Marletta at:
- MarlettaM at cardiff dot ac dot uk