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Datum Zeit Ort Vortrag
20.07.20 15:30 Zoom Noncommutative geometry, K-theory and other interesting stuff
Julian Großmann

An overview talk about interesting topics in mathematical physics I used over the last years. It should be accessible for a broader audience.
13.07.20 15:30 Zoom Evolution Equations
Christian Seifert

This will be an overview talk on Evolution Equations (and a bit on Evolutionary Equations).
06.07.20 15:30 Zoom Uniqueness of solutions to the Caffarelli-Silvestre Problem
Jan Meichsner

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
29.06.20 15:00 Zoom A new approach to the QR decomposition of hierarchical matrices
Vincent Griem

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.
22.06.20 15:30 Zoom Analysis of the discretization error in the RBF-FD method
Willi Leinen

Partial differential equations can be solved numerically by the radial basis function-generated finite difference (RBF-FD) method, which can be viewed as a generalization of the finite difference method to unstructured point sets.
A so-called stencil is computed for each interior node and radial basis functions are used for the computation of the stencil weights. The discretization error depends on the type of the point set (i.e. on the number of interior and boundary nodes and their distribution), the stencil size, the RBF type and the shape parameter of the RBF.
In this talk, I present an introduction of the RBF-FD method and a numerical analysis of the influence of the various parameters on the discretization error. I focus on Poisson's equation and on the convection-diffusion equation in three-dimensions.
15.06.20 15:30 Zoom Approximate null-controllability of heat-like equations in $L_1(\mathbb{R}^d)$
Dennis Gallaun
25.05.20 15:30 Zoom On periodic Finite Sections
Riko Ukena, E-10

I will introduce myself and talk about my master thesis.

The topic of my thesis was "On periodic finite sections", which are an approximation method based on the regular finite section method. The methods are used to approximate (the inverses of) infite matrices by finite matrices.
18.05.20 15:30 Zoom Many-Body Localization: A Spectral Theoretic Investigation of Spin Chains
Katharina Klioba, E-10

Since most of you couldn't attend my master thesis defense due to the university closure, I would like to use this talk to present you some results of my master thesis "Many-body localization: A spectral theoretic investigation of spin chains". Spin chains are a class of quantum-mechanical models well-suited to study many-body localization (MBL) phenomena due to their one-dimensional structure. After a brief introduction to one-particle (Anderson) localization and spectral properties of infinite-dimensional operators, we will see possible definitions and manifestations of MBL. The proofs of MBL for two specific spin chains will be sketched, illustrating how one-particle and many-body techniques can be combined. Furthermore, I would like to use this talk to properly present myself in case you wondered who that person in the guest office was.
11.05.20 15:30 Zoom $\mathcal{H}$-Matrix Approximation of Finite Element Problems
Jonas Grams

Since I am new to the institute, I want to use this talk to introduce myself to you, and talk a little bit about my master thesis.

For the thesis I studied the approximability of the inverse of finite element matrices, i.e. matrices which are gained from the discretization of elliptic PDE's with the finite element method, by hierarchical matrices. So, after introducing myself, i will give an overview about the construction of the approximation and the error analysis.
06.05.20 10:00 Online Development of Solid-State LIDAR Configuration Tool and Optimization of SPAD Detection Performance [Master thesis]
Puja Dutta, student of Microelectronics and Microsystems Engineering

supervision by Prof. Ernst Brinkmeyer (retired 2013, hence not hosted by him)

no maths topic