In this snapshot we discuss the notion of codimension, which is, in a sense, “dual” to the notion of dimension and is useful when studying the relative position of one object insider another one.

In this snapshot we introduce configuration spaces and explain how a mathematician studies their ‘shape’. This will lead us to consider paths of configurations and braid groups, and to explore how algebraic properties of ...

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.

Fluid-structure interaction is a rich and active field of mathematics that studies the interaction between fluids and solid objects. In this short article, we give a glimpse into this exciting field, as well as a ...

Many problems in mathematics have remained unsolved because of missing links between mathematical disciplines, such as algebra, geometry, analysis, or number theory. Here we introduce a recently discovered result concerning ...

Algorithms are mathematical procedures developed to solve a problem. When encoded on a computer, algorithms must be "translated" to a series of simple steps, each of which the computer knows how to do. This task is ...

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.

We present some examples of optimal transport problems and of applications to different sciences (logistics, economics, image processing, and a little bit of evolution equations) through the crazy story of an industrial ...