Talks

The original problem of counting domino towers was first studied by G. Viennot in 1985, see also D. Zeilberger (The Amazing 3^n Theorem). We analyse a generalisation of domino towers that was proposed by T. M. Brown (J. Integer Seq. 20.3 (2017), Art. 17.3.1), which we call S-omino towers. After establishing an equation that the generating function must satisfy and applying the Lagrange Inversion Formula, we find a closed formula for the number of towers.

The talk should hopefully also be accessible to people not used to this kind of mathematics.

This talk is divided into two parts. The first part will be given on Thursday 08.11.18 by Dennis Gallaun.
In this talk we study sufficient conditions for obserability of systems in Banach spaces. In an abstract Banach space setting we show that an uncertainty relation together with a dissipation estimate implies an obserbability estimate with explicite dependence on the model parameters. Our approach unifies and generalizes the respective advantages from earlier results obtained in the context of Hilbert spaces. As an application we consider elliptic operators on Lp(Rd) and on Lp(Td) for 1 < p < ∞. Combined with the well-known relation between observability and controllability we derive sufficient conditions for null-controllability and bounds on the control cost.

This talk is divided into two parts. The second part will be given on Thursday 15.11.18 by Christian Seifert.
In this talk we study sufficient conditions for obserability of systems in Banach spaces. In an abstract Banach space setting we show that an uncertainty relation together with a dissipation estimate implies an obserbability estimate with explicite dependence on the model parameters. Our approach unifies and generalizes the respective advantages from earlier results obtained in the context of Hilbert spaces. As an application we consider elliptic operators on Lp(Rd) and on Lp(Td) for 1 < p < ∞. Combined with the well-known relation between observability and controllability we derive sufficient conditions for null-controllability and bounds on the control cost.

My talk will consist of three short, independent parts, the first one being a quick introduction of myself. In the second and the third part, I will give an ''easy-to-digest'' survey of my graduate theses [1,2].

References:

[1] Implementation and Performance Analyses of a Highly Efficient Algorithm for Pressure-Velocity Coupling. Master Thesis Computational Engineering, Darmstadt, 2015

[2] On the L^p Theory of the Stokes Operator in Lipschitz Domains. Master Thesis Mathematics, Darmstadt, 2018

Talk (PDF, 2.1MB)

It is a classical result that every $\mathbb{C}$-valued holomorphic function has a local power series representation.
This even remains true for holomorphic functions with values in a locally complete locally convex Hausdorff space $E$ over
$\mathbb{C}$. Motivated by this example we try to answer the following question. Let $E$ be a locally convex Hausdorff space
over a field $\mathbb{K}$, $\mathcal{FV}(\Omega)$ be a locally convex Hausdorff space of $\mathbb{K}$-valued functions on a set $\Omega$ and $\mathcal{FV}(\Omega,E)$ be an $E$-valued counterpart of $\mathcal{FV}(\Omega)$
(where the term $E$-valued counterpart needs clarification itself).
For which spaces is it possible to lift series representations of elements of $\mathcal{FV}(\Omega)$ to elements of $\mathcal{FV}(\Omega,E)$?
We derive sufficient conditions for the answer to be affirmative which are applicable for many classical spaces of functions
$\mathcal{FV}(\Omega)$ having a Schauder basis.

BA-Vortrag

This talk will be an extended version of the talk I gave on the SOTA 2018 in Poland.
I will discuss existence and uniqueness of the so-called Harmonic extension approach to fractional powers of linear operators.