In 1795, French mathematician Gaspard de Prony invented an ingenious trick to solve a recovery problem, aiming at reconstructing functions from their values at given points, which arose from a specific application in ...

Algebraic Statistics builds on the idea that statistical models can be understood via polynomials. Many statistical models are parameterized by polynomials in the model parameters; others are described implicitly by ...

In this snapshot we present the concept of topological recursion – a new, surprisingly powerful formalism at the border of mathematics and physics, which has been actively developed within the last decade. After introducing ...

Sometimes the volume of a convex body needs to be estimated, if we cannot calculate it analytically. We explain how statistics can be used not only to approximate the volume of the convex body, but also its shape.

In recent years, mathematicians have developed new approaches to study convex sets: instead of considering convex sets themselves, they explore certain functions or measures that are related to them. Problems from ...

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 ...

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 ...

Topological complexity is a number that measures how hard it is to plan motions (for robots, say) in terms of a particular space associated to the kind of motion to be planned. This is a burgeoning subject within the ...

When you describe a physical process, for example, the weather on Earth, or an engineered system, such as a self-driving car, you typically have two sources of information. The first is a mathematical model, and the ...

What kind of strange spaces hide behind the enigmatic name of tropical geometry? In the tropics, just as in other geometries, one of the simplest objects is a line. Therefore, we begin our exploration by considering tropical ...