What does ">" really mean?
Submitted by IMAGINARY on
This Snapshot is about the generalization of “>” from ordinary numbers to so-called fields. At the end, I will touch on some ideas in recent research.
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Billiards and flat surfaces
Submitted by IMAGINARY on
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.
Friezes and tilings
Submitted by IMAGINARY on
Friezes have occured as architectural ornaments for many centuries. In this snapshot, we consider the mathematical analogue of friezes as introduced in the 1970s by Conway and Coxeter. Recently, infinite versions of such friezes have appeared in current research. We are going to describe them and explain how they can be classified using some nice geometric pictures.
Chaos and chaotic fluid mixing
Submitted by IMAGINARY on
Very simple mathematical equations can give rise to surprisingly complicated, chaotic dynamics, with behavior that is sensitive to small deviations in the initial conditions. We illustrate this with a single recurrence equation that can be easily simulated, and with mixing in simple fluid flows.
Stochastic Art - Animation
Submitted by Jean Constant on
Random processes and visual perception.
After Dr. E Porteus demonstration: “The shortest route problem in optimisation models” - Fondations of stochastic inventory theory - Stanford University Press. 2002.
Modelling communication and movement: from cells to animals and humans
Submitted by IMAGINARY on
Communication forms the basis of biological interactions. While the use of a single communication mechanism (for example visual communication) by a species is quite well understood, in nature the majority of species communicate via multiple mechanisms. Here, I review some mathematical results on the unexpected behaviors that can be observed in biological aggregations where individuals interact with each other via multiple communication mechanisms.
El Cubo de Roli
Submitted by Aubin Arroyo on
Un paseo por un politopo quiral de dimensión pequeña.
The ternary Goldbach Problem
Submitted by IMAGINARY on
Leonhard Euler (1707–1783) – one of the greatest mathematicians of the eighteenth century and of all times – often corresponded with a friend of his, Christian Goldbach (1690–1764), an amateur and polymath who lived and worked in Russia, just like Euler himself. In a letter written in June 1742, Goldbach made a conjecture – that is, an educated guess – on prime numbers:
“Es scheinet wenigstens, dass eine jede Zahl, die größer ist als 2, ein aggregatum trium numerorum primorum sey.”
Matrixfaktorisierungen
Submitted by IMAGINARY on
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.
Dirichlet Series
Submitted by IMAGINARY on
Mathematicians are very interested in prime numbers. In this snapshot, we will discuss some problems concerning the distribution of primes and introduce some special infinite series in order to study them.