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 ...

We provide a leisurely introduction to ℓ²-Betti numbers, which are topological invariants, by relating them to their much older cousins, Betti numbers. In the end we present an open research problem about ℓ²-Betti numbers.

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 ...

Nowadays 3D computer animation is increasingly realistic as the models used for the characters become more and more complex. These models are typically represented by meshes of hundreds of thousands or even millions ...

We give a brief survey of the connection between seemingly unrelated problems such as sets in the plane containing lines pointing in many directions, vibrating strings and drum heads, and a classical problem from Fourier analysis.

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 ...

The symmetry of objects plays a crucial role in many branches of mathematics and physics. It allowed, for example, the early prediction of the existence of new small particles. “Quantum symmetry” concerns a generalized ...

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 ...

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 ...

Les fibrés de Higgs sont apparus il y a quelques décennies comme solutions de certaines équations en physique, et ils ont attiré beaucoup d’attention en géométrie comme dans d’autres domaines des mathématiques et de la ...