[Dottorcomp] Seminari di Matematica Applicata, 18/11/2025, Astrid Herremans, Yannick Sire

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 18 Novembre 2025, alle ore 15 precise, presso l'aula Beltrami del
Dipartimento di Matematica dell'Università di Pavia,

Astrid Herremans (KU Leuven, Belgio)

terrà un seminario dal titolo

Sampling for approximation in non-orthogonal bases

e alle ore 16,00 precise

Yannick Sire (Johns Hopkins University)
terrà un seminario dal titolo:

Geometric measure of nodal, critical and singular sets for solutions of
degenerate equations.

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Abstract (Herremans): Non-orthogonal bases arise naturally in many areas of
computational mathematics, including Trefftz methods, approximation on
irregular domains and data-driven or learned representations. While these
building blocks efficiently capture the behaviour of the target function,
they also introduce numerical challenges. In particular, the influence of
numerical rounding errors on the approximation error can be non-negligible.
In this talk, we investigate the stability and accuracy of least squares
approximation in non-orthogonal bases from a sampling-theoretic
perspective. We show how the interplay between floating-point arithmetic
and sampling strategies affects the quality of approximation. Building on
connections with row subsampling problems in numerical linear algebra, we
develop an efficient and robust algorithm for discretizing such problems.
The results provide both theoretical insights and practical tools for
working with non-orthogonal systems. This is joint work with Daan Huybrechs
and Ben Adcock.

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Abstract (Sire): I will describe recent results on the “size” of various
sets associated to solutions of some elliptic PDEs whose coefficients are
degenerate or singular. In the case of eigenfunctions of the associated
second order operators, these estimates are related to some famous
conjectures by Yau (formulated in a more classical setting). Degenerate
PDEs appear in a lot of different contexts like conical spaces,
realizations of Dirichlet-to-Neumann maps, Poincare-Einstein manifolds in
conformal geometry, etc… I will describe several strategies to get these
estimates, leading for some of them to sharp bounds. Along the way, I will
also describe some eigenfunction and cluster estimates, which are very much
related to this topic.
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Pagina web Seminari di Matematica Applicata
https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/