Asymptotics, Operators, and Functionals

Leading the discussion in 2019:

16 January Conference "Operators, Operator Families and Asymptotics II"

21 January Rafael del Río (IIMAS-UNAM) (Topic: Resonances under rank-one perturbations) Abstract: I shall discuss resonances generated by rank-one perturbations of self-adjoint operators with eigenvalues embedded in the continuous spectrum. I shall demonstrate the instability of these eigenvalues and an "almost-exponential" decay for the associated resonant states. I shall then show how these results can be applied to Sturm-Liouville operators.

28 January Josué Cangas (IIMAS-UNAM) (Topic: Dissipative linear relations on orthogonal polynomials)

4 February Kirill Cherednichenko (Topic: Electromagnetic time-dispersive media ("metamaterials") by homogenisation I)

11 February Kirill Cherednichenko (Topic: Electromagnetic time-dispersive media ("metamaterials") by homogenisation II)

18 February Elaine Crooks (Swansea) (Topic: Compensated convexity and its applications)

Away: [25 February, 4 March INI Programme "The Mathematical Design of New Materials", University of Cambridge]

11 March Kirill Cherednichenko (Topic: Electromagnetic time-dispersive media ("metamaterials") by homogenisation III)

18 March Serena D'Onofrio (Topic: Helmholtz decomposition for the system of Maxwell equations)

25 March William Graham (Topic: Singular photonic fibres)

1 April Aaron Pim (Topic: Article "Theory of light-matter interaction in nematic liquid crystals and the second Painlevé equation" by M. G. Clerc et al.)

8 April Anja Schlömerkemper (Würzburg) (Topic: Passages from discrete to continuous systems allowing for fracture, external forces and heterogeneities) Abstract

Away: [15, 22 April Department of Mathematics, IIT Bombay, Mumbai]

29 April Kirill Cherednichenko (Topic: Interlacing property for the Dirichlet and Neumann eigenvalues of the Laplacian)

13 May Yulia Karpeshina (Alabama at Birmingham) (Topic: Solutions of the Gross-Pitaevskii equation with a periodic potential in two dimensions) Abstract

              Günter Stolz (Alabama at Birmingham) (Topic: Anderson localization vs many-body localization: some examples) Abstract: The mathematical reasons for Anderson localization, i.e., that the introduction of disorder into a one-particle (non-interacting) quantum system can suppress quantum transport, are reasonably well understood. Much less is known, however, about many-body localization, asking if this phenomenon persists if interactions are considered. We will use examples from quantum spin systems to try to describe some of the similarities as well as differences between the one-body and many-body case.

20 May Sabine Bögli (Imperial College London) (Topic: Essential numerical ranges for linear operator pencils) Abstract: We study concepts of numerical ranges and essential numerical ranges for linear operators pencils A–zB (with A, B linear operators and z the spectral parameter). In contrast to the operator case (where B is the identity operator), these concepts are in general neither convex nor even connected. We use the essential numerical range to describe the set of spectral pollution when approximating an operator pencil by projection and truncation methods and apply the results to various differential operator pencils. This talk is based on joint work with Marco Marletta.

3 June Mat Hunt (Warwick) (Topic: A continuum model for lithium-ion batteries via homogenisation.) Abstract: Electric vehicles are becoming more widely used and are powered by the use of lithium-ion batteries. As such, the equivalent of a "fuel gauge" is required, which requires an accurate description of the operation of the battery during the charge and discharge process. In this talk, we will discuss the microphysics involved in this context and a high-contrast homogenisation approach to deriving the related model. I will then compare the derived model with the well-known P2D model.

17 June Graeme Milton (Utah) (Topic: Exact relations for Green's functions in linear PDE and boundary field equalities: a generalization of conservation laws) Abstract

Away: [24 June "Small Scales and Homogenisation", Cardiff School of Mathematics]

1 July Marco Marletta (Cardiff) (Topic: Part I: The recovery of coefficients of the system of Maxwell equations on a bounded domain with partial data. Part II: The essential spectra of Maxwell problems on unbounded domains.)

8 July Matteo Icardi (Nottingham) (Topic: Upscaling challenges in advection-diffusion-reaction in porous media) Abstract

Away: [2 September BUC-XVI: "Resonant" media: wave scattering phenomena under strong length-scale interactions, IIMAS-UNAM, México City]

Away: [9 September Pontificia Universidad Católica Santiago, Chile]

23 September Igor Velčić (Zagreb)