2014, Lerche, Wolfgang

Im Folgenden soll ein kurzer Abriss des Themas Matrixfaktorisierungen gegeben werden. Wir werden darlegen, warum dieses recht simple Konzept zu erstaunlich tiefen mathematischen Gedankengängen führt und auch in der modernen theoretischen Physik wichtige Anwendungen hat.

2015, Sangwin, Christopher J.

This snapshot looks at educational aspects of the design of curricula in mathematics. In particular, we examine choices textbook authors have made when introducing the concept of the completness of the real numbers. Can significant choices really be made? Do these choices have an effect on how people learn, and, if so, can we understand what they are?

2015, Hoenig, Volker, Bodendiek, Nils

Hauptziel dieses Forschungsvorhabens war es, die Auswirkungen der Sauerstoffanreicherung von Drehofenflammen in Zementklinkerproduktionsanlagen auf das Produkt Klinker, den Ofenbetrieb und den Alternativbrennstoffeinsatz sowie auf die Abgaszusammensetzung zu evaluieren.

2014, Buchweitz, Ragnar-Olaf, Faber, Eleonore

Platonic solids, Felix Klein, H.S.M. Coxeter and a flap of a swallowtail: The five Platonic solids tetrahedron, cube, octahedron, icosahedron and dodecahedron have always attracted much curiosity from mathematicians, not only for their sheer beauty but also because of their many symmetry properties. In this snapshot we will start from these symmetries, move on to groups, singularities, and finally find the connection between a tetrahedron and a “swallowtail”. Our running example is the tetrahedron, but every construction can be carried out with any other of the Platonic solids.

2015, Davis, Diana

Billiards, the study of a ball bouncing around on a table, is a rich area of current mathematical research. We discuss questions and results on billiards, and on the related topic of flat surfaces.

2014, Valette, Alain

In quantum mechanics, unlike in classical mechanics, one cannot make precise predictions about how a system will behave. Instead, one is concerned with mere probabilities. Consequently, it is a very important task to determine the basic probabilities associated with a given system. In this snapshot we will present a recent uniqueness result concerning these probabilities.

2014, Harbourne, Brian, Szemberg, Tomasz

We discuss certain open problems in the context of arrangements of lines in the plane.

2015, Breiner, Christine

What is the most efficient way to fence land when you’ve only got so many metres of fence? Or, to put it differently, what is the largest area bounded by a simple closed planar curve of fixed length? We consider the answer to this question and others like it, making note of recent results in the same spirit.

2015, Rué, Juanjo

Imagine you have a cutout from a piece of squared paper and a pile of dominoes, each of which can cover exactly two squares of the squared paper. How many different ways are there to cover the entire paper cutout with dominoes? One specific paper cutout can be mathematically described as the so-called Aztec Diamond, and a way to cover it with dominoes is a domino tiling. In this snapshot we revisit some of the seminal combinatorial ideas used to enumerate the number of domino tilings of the Aztec Diamond. The existing connection with the study of the so-called alternating-sign matrices is also explored.

2015, Kiritchenko, Valentina, Timorin, Vladlen, Smirnov, Evgeny

In this snapshot, we will consider the problem of finding the number of solutions to a given system of polynomial equations. This question leads to the theory of Newton polytopes and Newton-Okounkov bodies of which we will give a basic notion.