Finding the total number of species in a population based on a finite sample is a difficult but practically important problem. In this snapshot, we will attempt to shed light on how during World War II, two cryptanalysts, ...

In school, we learn that the interior angles of any triangle sum up to pi. However, there exist spaces different from the usual Euclidean space in which this is not true. One of these spaces is the ''hyperbolic space'', ...

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 ...

Given a set X, ultrafilters determine which subsets of X should be considered as large. We illustrate the use of ultrafilter methods in combinatorics by discussing two cornerstone results in Ramsey theory, namely ...

Current research in statistics has taken interesting new directions, as data collected from scientific studies has become increasingly complex. At first glance, the number of experiments conducted by a scientist must ...

Representation theory is an area of mathematics that deals with abstract algebraic structures and has numerous applications across disciplines. In this snapshot, we will talk about the representation theory of a class ...

The theory of $C^*$-algebras traces its origins back to the development of quantum mechanics and it has evolved into a large and highly active field of mathematics. Much of the progress over the last couple of decades ...

What is the dollar game? What can you do to win it? Can you always win it? In this snapshot you will find answers to these questions as well as several of the mathematical surprises that lurk in the background, including ...

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 ...

Lagrangian mean curvature flow is a powerful tool in modern mathematics with connections to topics in analysis, geometry, topology and mathematical physics. I will describe some of the key aspects of Lagrangian mean curvature ...