We discuss certain open problems in the context of arrangements of lines in the plane.

Viele epileptische Anfälle entstehen in einer begrenzten Region im Gehirn, dem sogenannten Anfallsursprung. Eine chirurgische Entfernung dieser Region kann in vielen Fällen zu Anfallsfreiheit führen. Aus diesem Grund ist ...

It has always been the dream of mankind to predict the future. If the future is governed by laws of physics, like in the case of the weather, one can try to make a model, solve the associated equations, and thus predict ...

Computer simulations of many physical phenomena rely on approximations by models with a finite number of unknowns. The number of these parameters determines the computational effort needed for the simulation. On the other ...

How many prime numbers are there? How are they distributed among other numbers? These are questions that have intrigued mathematicians since ancient times. However, many questions in this area have remained unsolved, and ...

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 ...

In this snapshot, we explore connections between the mathematical areas of counting and geometry by studying objects called simplicial complexes. We begin by exploring many familiar objects in our three dimensional world ...

Geophysicists and mathematicians work together to detect geological structures located deep within the earth by measuring and interpreting echoes from manmade earthquakes. This inverse problem naturally involves the ...

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 ...

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 ...