Submitted by IMAGINARY on
We consider surfaces of three types: the sphere, the torus, and many-holed tori. These surfaces naturally admit geometries of positive, zero, and negative cur- vature, respectively. It is interesting to study straight line paths, known as geodesics, in these geometries. We discuss the issue of counting closed geodesics; this is particularly rich for hyperbolic (negatively curved) surfaces.
Submitted by IMAGINARY on
Die Yang–Baxter-Gleichung ist eine faszinierende Gleichung, die in vielen Gebieten der Physik und der Mathematik auftritt und die am besten diagrammatisch dargestellt wird. Dieser Snapshot schlägt einen weiten Bogen vom Zöpfeflechten über die Yang–Baxter-Gleichung bis hin zur aktuellen Forschung zu Systemen von unendlichdimensionalen Algebren, die wir „Unterfaktoren“ nennen.
Submitted by IMAGINARY on
Submitted by IMAGINARY on
Submitted by IMAGINARY on
Can a continuous function on an interval be uniquely determined if we know all the integrals of the function against the natural powers of the variable? Following Weierstrass and Stieltjes, we show that the answer is yes if the interval is finite, and no if the interval is infinite.
Submitted by IMAGINARY on
Higgs bundles appeared a few decades ago as solutions to certain equations from physics and have attracted much attention in geometry as well as other areas of mathematics and physics. Here, we take a very informal stroll through some aspects of linear algebra that anticipate the deeper structure in the moduli space of Higgs bundles.
Submitted by IMAGINARY on
In mathematics, symmetry is usually captured using the formalism of groups. However, the developments of the past few decades revealed the need to go beyond groups: to “quantum groups”. We explain the passage from spaces to quantum spaces, from groups to quantum groups, and from symmetry to quantum symmetry, following an analytical appr
Submitted by Bianca Violet on
We describe a journey through our exhibition La La Lab - the Mathematics of Music, which mixes a laboratory format with interactive exhibits to present visitors with the historical, conceptual, and artistic connections between mathematics and music, pushing forward musical creativity, mathematical knowledge and any blending of the two.
Submitted by IMAGINARY on
We consider the problem of walking in a straight line on the surface of a Platonic solid. While the tetrahedron, octahedron, cube, and icosahedron all exhibit the same behavior, we find a remarkable difference with the dodecahedron.
Submitted by IMAGINARY on
The theory of random matrices was introduced by John Wishart (1898–1956) in 1928. The theory was then developed within the field of nuclear physics from 1955 by Eugene Paul Wigner (1902–1995) and later by Freeman John Dyson, who were both concerned with the statistical description of heavy atoms and their electromagnetic properties. In this snap- shot, we show how mathematical properties can have unexpected links to physical phenomenena. In particular, we show that the eigenvalues of some particular random matrices can mimic the electrostatic repul- sion of the particles in a gas.