Lehrerfortbildung Mathematik: Mathematik + Informatik= Digitale Schlüsseltechnologien

Am Mittwoch, dem 19. März 2025, findet im Institut für Mathematik der TU Clausthal, Erzstraße 1, in der Zeit von 9.30 Uhr bis 16.30 Uhr, eine Lehrerfortbildung zum Thema: Mathematik + Informatik = Digitale Schlüsseltechnologien statt.

Oberseminar AG Mathematische Modellierung

Mittwoch, den 29.01.2025 um 11.00 Uhr in B7 - 210

Vortrag von Anatole Gaudin (Clausthal) zum Thema: „Besov Spaces as Spaces of Traces“.

Abstract: In this presentation, we continue the study of Besov spaces, now considering them as spaces of traces of Sobolev functions. Indeed, while Sobolev (or Besov) functions on $\mathbb{R}^n$ might not have a continuous representative, one can make sense of their restriction (\textit{i.e.}, taking a trace) with respect to one or several variables, and such a restriction yields a function that lies in an appropriate Besov space with a non-integer amount of regularity. First, we show some basic trace results. We will then exhibit that such a procedure is possible for $\L^p$-based Sobolev and Besov spaces at the cost of a $1/p$ derivative, and that the optimal range of the trace operator in the said Besov space is actually sharp. Since this procedure can be extended to the half-space, by a localization argument, a rotation, and a flattening procedure…

Oberseminar AG Mathematische Modellierung

Montag, den 20.01.2025 um 17.00 Uhr in B7 - 210

Vortrag von Adrian Martini (Oxford) zum Thema „Additive-Noise Approximation to Keller–Segel–Dean–Kawasaki Dynamics“.

Abstract:

The theory of fluctuating hydrodynamics aims to describe density fluctuations of interacting particle systems as so-called Dean–Kawasaki stochastic partial differential equations. However, those Dean–Kawasaki equations are ill-posed and recent focus has shifted towards finding well-posed approximations that retain the statistical properties of the particle system. In this talk, we consider the fluctuating hydrodynamics of a system in which particles are attracted to one another through a Coulomb force (Keller–Segel dynamics). We propose an additive-noise approximation and show that it retains the same law of large numbers and central limit theorem as (conjectured for) the particle system. We further deduce a large deviation principle and show that the approximation error lies in the skeleton equation that…

Oberseminar AG Mathematische Modellierung

Montag, den 13.01.2025 um 17.00 Uhr in B7 - 210

Vortrag von Prof. Dr. Dominic Breit (Clausthal) zum Thema: „Constrained differential operators, Sobolev inequalities,  and Riesz potentials“.

Abstract:

Inequalities for Riesz potentials are well-known to be equivalent to Sobolev inequalities of the same order for domain norms "far" from L^1, but to be weaker otherwise. Recent contributions by Van Schaftingen,  by Hernandez, Raita and Spector, and by Stolyarov proved that this gap can be filled in Riesz potential inequalities for vector-valued functions in  L^1 fulfilling a co-canceling differential condition. This work demonstrates that such a property is not just peculiar to the space L^1. Indeed, under the same differential constraint, a Riesz potential inequality is shown to hold for any domain and target rearrangement-invariant norms that render a Sobolev inequality of the same order true. This is based on a new interpolation inequality, which, via a kind of duality argument,…