Talks

This will be an introductory talk on how the fundamental assumptions of quantum mechanics are modeled and how this relies on the spectral theory of unbounded self-adjoint operators on separable Hilbert spaces.

I will introduce myself and present the topic of my master thesis.

In my thesis, I derived a method for model order reduction of parametric linear time-invariant systems. With this method we can compute parametric reduced-order models that are optimal with respect to the $\mathcal{H}_2 \otimes \mathcal{L}_\infty$-error. The method combines interpolatory methods with numerical optimization. We furthermore discuss the computation of the $\mathcal{H}_2 \otimes \mathcal{L}_\infty$-error and have a look at some numerical results.

Deformable image registration is a key technology in medical imaging; there the goal is to compute a meaningful spatial correspondence between two or more images of the same scene. One approach is to use an optimal control formulation to compute a stationary velocity field that parameterize the deformation map. The same methods can be used to estimate the motion of contrast agents from 3d ultrasound images.

This is work-in-progress; in the talk I’ll introduce the application problem and discuss computational techniques for its solution, with a focus on using parallelization in time to reduce the time-to-solution. It should be accessible for a broad audience.

An overview talk about interesting topics in mathematical physics I used over the last years. It should be accessible for a broader audience.

This will be an overview talk on Evolution Equations (and a bit on Evolutionary Equations).

We consider the Caffarelli-Silvestre problem in a Banach space $X$ which is finding a solution $u$ to the problem
\[
u''(t) + \frac{1-2\alpha}{t} u'(t) = Au(t), \quad u(0)=x
\]
where $\alpha \in (0,1)$ is a given parameter and $A \in \mathcal{S}_{\omega}$ is a sectorial operator. Goal of the presentation will be to sketch of a proof that a solution got to be unique (we will not deal with existence but this is a much easier anyway).
The proof is simpler and independent of what can be found in

J. Meichsner and C. Seifert. On the Harmonic Extension Aproach to Fractional Powers in Banach Spaces. arxiv preprint https://arxiv.org/abs/1905.06779

All existing QR decompositions for hierarchical matrices suffer from numerical drawbacks that limit their use in many applications. In this talk, I will present a new method based on the recursive WY-based QR decomposition by Elmroth and Gustavson. It is an extension of an already existing method for a subclass of hierarchical methods developed by Kressner and Susnjara.

I will try to keep things as simple as possible and give a short introduction to hierarchical matrices as well. Previous knowledge of hierarchical matrices is not necessary to understand the basic ideas and main obstacles of the new algorithm. Although this talk is similar to my last one in November I will try to focus on some aspects we have only touched upon and present some new results as well.