Sesión número 126 del Seminario Iberoamericano de Matemáticas (SIM126)
Lugar: Excepcionalmente se celebrará en el Aula A125 de la Facultad de Ciencias de la Universidad de Valladolid.
Fecha: Viernes 19 de abril de 2024.
Para unirse via Teams:
PROGRAMA (GMT+2):
10:00-10:50 Alberto Fernández Boix (Universidad de Valladolid):
Approximation results of Artin-Tougeron-type for general filtrations and for rings of smooth functions
Various versions of Artin approximation are widely used in Algebraic/Analytic Geometry, Commutative Algebra and Singularity Theory; traditionally, the approximation statements were restricted to Noetherian rings and to filtrations by powers of ideals. The goal of this talk is to explain how to extend some of the classical approximation results both for general filtrations and for rings of smooth functions; for instance, our statements allow some immediate applications of Artin approximation to the study of non-isolated singularities of maps and schemes.
The content of this talk is based on joint work with Genrich Belitskii and Dmitry Kerner (Ben Gurion University of the Negev, Beer Sheva, Israel).
11:00-11:50 Gerhard Schindl (University of Vienna):
Interpolation of derivatives and ultradifferentiable regularity
Interpolation results are classical problems in Mathematics. In this talk we are concerned with the following basic question: When given an infinitely differentiable function let us assume that some derivatives admit a precise growth control; i.e. information is available on a prescribed subsequence of all integers. Can then this lacunary information be extended to all derivatives? We are interested in this problem within the so-called ultradifferentiable setting; i.e. when the given derivatives are bounded by a fixed weight sequence, weight function, or even weight matrix.
In order to proceed it is natural to study and understand the interplay of the weights and the lacunary sequence on which information is available and, finally, to involve suitable interpolation inequalities. The most prominent example is the classical "Gorny-Cartan-inequality".
We treat this problem by reviewing some more interpolation inequalities for derivatives and work within the general weight matrix setting to obtain results for weight sequences and functions automatically. We also deal with some non-standard cases; e.g. Gelfand-Shilov-type classes.
This is joint work with Armin Rainer (University of Vienna).