You are free to:
Share — copy and redistribute the material in any medium or format
Adapt — remix, transform, and build upon the material
for any purpose, even commercially.
The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
More information (license deed): https://creativecommons.org/licenses/by-sa/4.0/
Submitted by IMAGINARY on
Die Steuerung einer Last an einem Kran ist ein technisch und mathematisch schwieriges Problem, da die Bewegung der Last nur indirekt beeinflusst werden kann. Anhand eines Masse-Feder-Systems illustrieren wir diese Schwierigkeiten und zeigen wie man mit einem zum konventionellen Lösungsweg alternativen Optimierungsansatz die auftretenden Komplikationen teilweise umgehen kann.
Submitted by IMAGINARY on
In this snapshot, we give a survey of some problems in the study of rational points on higher genus curves, discussing questions ranging from the era of the ancient Greeks to a few posed by mathematicians of the 20th century. To answer these questions, we describe a selection of techniques in modern number theory that can be used to determine the set of rational points on a curve.
Submitted by IMAGINARY on
Pattern is ubiquitous and seems totally familiar. Yet if we ask what it is, we find a bewildering collection of answers. Here we suggest that there is a common thread, and it revolves around dynamics.
Submitted by IMAGINARY on
The advances in biomedical imaging techniques have enabled us to access the 3D shapes of a variety of structures: organs, cells, proteins. Since biological shapes are related to physiological functions, shape data may hold the key to unlocking outstanding mysteries in biomedicine. This snapshot introduces the mathematical framework of geometric statistics and learning and its applications to biomedicine.
Submitted by IMAGINARY on
In this snapshot, we explain two important mathematical concepts (representation and degeneration) in elementary terms. We will focus on the simplest meaningful examples, and motivate both concepts by study of symmetry.
Submitted by IMAGINARY on
The goal of inverse problems is to find an unknown parameter based on noisy data. Such problems appear in a wide range of applications including geophysics, medicine, and chemistry. One method of solving them is known as the Bayesian approach. In this approach, the unknown parameter is modelled as a random variable to reflect its uncertain value. Bayes’ theorem is applied to update our knowledge given new information from noisy data.
Submitted by IMAGINARY on
In this snapshot, we will first give an introduction to hyperbolic geometry and we will then show how certain matrix groups of a number-theoretic origin give rise to a large variety of interesting tessellations of 3-dimensional hyperbolic space. Many of the building blocks of these tessellations exhibit beautiful symmetry and have inspired the design of 3D printed jewellery.
Submitted by IMAGINARY on
Geophysicists and mathematicians work together to detect geological structures located deep within the earth by measuring and interpreting echoes from manmade earthquakes. This inverse problem naturally involves the mathematics of wave propagation, but we will see that a different mathematical theory – optimal transport – also turns out to be very useful.
Submitted by IMAGINARY on
The Monster finite simple group is almost unimaginably large, with about 8×1053 elements in it. Trying to understand such an immense object requires both theory and computer programs. In this snapshot, we discuss finite groups, representations, and finally Brauer trees, which offer some new understanding of this vast and intricate structure.
Submitted by IMAGINARY on
I am going to describe the Robinson–Schensted algorithm which transforms a permutation of the numbers from 1 to n into a pair of combinatorial objects called “standard Young tableaux”. I will then say a little bit about a few of the fascinating properties of this transformation, and how it connects to current research.