Ein Mekka für Mathematiker – Oberwolfach

Mathematisches Forschungsinstitut Oberwolfach

“Tübingen, in der Nähe von Oberwolfach”, was für viele Menschen wie eine absurde Ortsbeschreibung klingt, ist unter Mathematikern absolut verständlich. Denn im beschaulichen Oberwolfach im Schwarzwald befindet sich das Mathematische Forschungsinstitut Oberwolfach (MFO). Es bietet Platz für Workshops, Sommerschulen und Forschungsaufenthalte und beherbergt eine der größten mathematischen Bibliotheken der Welt, ein Mekka für Mathematiker. Ende März nahmen sechs von uns am Workshop “Geometric Numerical Integration” teil: neben mir die beiden Organisatoren Marlis Hochbruck und Christian Lubich sowie Volker Grimm, Tobias Jahnke und Katharina Schratz.

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Travel Report: GRK 1838 Workshop – Quantum Dynamics and Functional Inequalities

Blaubeuren Workshop 2016 Poster (with kind permission of RTG 1838)

Blaubeuren Workshop 2016 Poster (with kind permission of RTG 1838)

In March 2016, we, that is a small delegation of the applied analysis workgroup at KIT (Ioannis Anapolitanos, Leonid Chaichenets, Michael Hott, Johanna Richter, and Tobias Ried), had the opportunity to participate in a workshop on Quantum Dynamics and Functional Inequalities, organised by the Stuttgart/Tübingen RTG 1838 “Spectral Theory and Dynamics of Quantum Systems”. It covered a very diverse range of topics from mathematical physics:

Benjamin Schlein (University of Zurich) gave an introduction to the derivation of effective equations for quantum systems with a large number of particles. In the case of bosons this leads to a description of the dynamics of Bose-Einstein condensates.

The connection between functional inequalities and geometric problems, as well as their application in kinetic theory, were discussed by Michael Loss (Georgia Institute of Technology).

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Graphene – From a dG workshop to Berlin and back

Everyone knows graphite. We find it in pencils, it is used in electrical motors and generators…

pencil2

A line of a pencil is made of graphite. photo by Patrick Krämer

But did you know that we can make way more out of this material, or more precisely out of the extracted layers of this material, called graphene?
In the future it could be used for designing a new generation of smartphone displays, transistors, electrodes, biomicrorobotics and many more.

In November 2015 we invited the physics group of Kurt Busch from Humboldt Universität zu Berlin to a „Discontinuous Galerkin SFB Workshop” at our institute. The aim of the workshop was to find a common starting point for the combination of theory and practice in the efficient simulation of problems arising from physics under realistic conditions. For this purpose the idea was to combine the expertise of Kurt Busch’s group in the parallel implementation of a specific class of methods for the spatial discretization of PDEs, so called discontinuous Galerkin (dG)  methods,  on large clusters with efficient time integration methods developed in our SFB.

My specific field of research within the SFB is the efficient time integration of the MaxwellDirac (MD) system in a highly oscillatory regime. This system describes the interaction of e.g. an electron with its self-generated electromagnetic field.  During this very interesting workshop Julia Werra, a PHD student of Kurt Busch’s group, told me that in particular the MD system is used to model electrons in the material graphene.

Since Julia’s research is on the analysis of the physical properties of graphene and we wanted to learn more about the physical point of view of the MD system, we planned to discuss the connection of the physical with the mathematical aspects of this material together with her a little bit more. So I went for 4 days to Berlin in March 2016.  This exchange of knowledge proved very valuable. Now Kurt Busch’s group and I think about how we can combine physics and mathematics in the efficient simulation of graphene.

At this point I also want to put some light also on what graphene actually is:

Graphene-graphite_relation

Graphene can be seen as an extracted layer of graphite. Click for source.

Graphene is a 2D crystal of carbon atoms which are structured in a hexagonal honeycomb lattice. It can be seen as an extracted layer of graphite. Each carbon atom in graphene only has 3 partners, so by the missing fourth partner at each atom there are free electrons that make the material a good electrical conductor. Here its electronic band structure plays an important role. The band structure of a solid helps to understand its electrical, thermal and optical properties. The band structure of graphene shows a peculiarity, the so called Dirac cone, at the so called Dirac points, where two energy bands cross each other. On Youtube you can find a pretty nice and informative video on graphene, its band structure and Dirac cones.

Physicists all over the world see graphene as the material of the future as it has very nice properties due to its atomic structure: It is transparent, impermeable for many molecules, much stronger than for example steel even though it is much lighter, and it has an exceptionally good electrical and thermal conductivity. Furthermore, it is one of the most frequent materials on earth.

If you are interested in a related work on the so-called Maxwell-Klein-Gordon equation you can listen to the modellansatz podcast on numerical time integration which we recorded together with Gudrun Thäter in the context of the Cooking Math project of KIT together with the Hochschule für Gestaltung Karlsruhe.

What actually is cat content?

Welcome to the seminar - poster

photo by Tobias Maier

We, thirteen fearless mathematicians, started our journey into the world of online science communication. The goal was always in our minds: inspiration of the public and representation of our research center. We had to plan our routes, get to know fabulous lookouts and dangerous cliffs and were thrown into the deep to learn to fly.

T.Maier

Our guide Tobias Maier, photo by Gudrun Thäter

Like every journey, we began with packing our bags by participating at a kick-off workshop with the NaWik. Our guide Dr. Tobias Maier, biochemist and writer of the blog WeiterGen, was always at our side. He helped us though the difficult starting process. First we worked out aims and target groups for our online presentation. We want to be visible for you, our reader. We want to fascinate you about our research, the beauty of mathematics and to report from our activities like workshops, conferences and summer schools. A particular challenge is to deal with different target audiences. Naturally, we want to be visible for other scientists and students to inform them and to find new collaborations. In addition we want to address a general public, journalists, school kids or our families and friends. Mathematics is everywhere in our everyday life, but it often hides itself like a shy animal. We want to help changing the peoples attitude towards mathematics and explain to them why our research can make a difference.

 

Blogteam

photo by Tobias Maier

To reach the different target audiences, Tobias Meier gave us a walk-through to various kinds of online media. In a lively debate we discussed advantages and disadvantages of Twitter, Facebook and others, and learned how to analyze our impact in such media. We are a heterogeneous group with professors, post doctoral researchers and also PhD students, thus, the students used their chance to turn the tables and to bring their expertise to bear. We discussed question like: Why do we need a facebook account if we already have a blog? How do mentions on twitter work? Or how can we find pictures to illustrate our blog articles without infringing copyright laws?

We had also had two sessions with external guests. Dr. Gudrun Thäter, a mathematician from our department and producer of the podcast Modellansatz, talked about math podcasts. A cooperation between this podcast and the CRC just started, since the current episodes (Modell080 f.) discuss the project ´Cooking Math’, a cooperation between students of Hochschule fuer Gestaltung and PhD-students of the CRC. On the other hand, Denis Elbl provided an insight into the KIT online team consisting of a facebook and a twitter account. He gave us useful tips how to manage accounts in social networks and shared his experience on feedback and comments with us.

In the last session we started our journey, hoisted our sails. The blog team set up this blog with a first blog entry. The social media team created a facebook and a twitter account. The video team started an youtube channel. Every team has milestones on their first route, which they want to achieve. So, come back soon to visit us again. It will be worth while!

And for those who expected to find some cat content here: I’m sorry, we decided to just have dog content here.

dog Gonzo

Gonzo, dog of the CRC-speaker Marlis Hochbruck, photo by: Dana Geithner