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 ...

Throughout the history of dynamical systems, instruments have been used to calculate and visualize (approximate) solutions of differential equations. Here we describe the approach of a group of physicists and engineers ...

If we want to express the size of a two-dimensional shape with a number, then we usually think about its area or circumference. But what makes these quantities so special? We give an answer to this question in terms of ...

We consider surfaces of three types: the sphere, the torus, and many-holed tori. These surfaces naturally admit geometries of positive, zero, and negative curvature, respectively. It is interesting to study straight line ...

This snapshot compares two techniques of shuffling a deck of cards, asking how long it will take to shuffle the cards until a “well-mixed deck” is obtained. Surprisingly, the number of shuffles can be very different for ...

Diophantine equations are polynomial equations whose solutions are required to be integer numbers. They have captured the attention of mathematicians during millennia and are at the center of much of contemporary research. ...

Las métricas riemannianas dan a las variedades suaves, como las superficies, propiedades geométricas intrínsecas, por ejemplo la curvatura. También permiten medir cantidades como distancias, ángulos y volúmenes. Estas son ...

The research field of finite geometries investigates structures with a finite number of objects. Classical examples include vector spaces, projective spaces, and affine spaces over finite fields. Although many of these ...

How can we fairly divide a necklace with various types of beads? We use this problem as a motivating example to explain how geometry naturally appears in solutions of non-geometric problems. The strategy we develop to solve ...

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 ...