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Arrangements of lines
[SNAP-2014-005-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)
We discuss certain open problems in the context of arrangements of lines in the plane.
Fokus-Erkennung bei Epilepsiepatienten mithilfe moderner Verfahren der Zeitreihenanalyse
[SNAP-2016-008-DE] (Mathematisches Forschungsinstitut Oberwolfach, 2016)
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 ...
Is it possible to predict the far future before the near future is known accurately?
[SNAP-2019-021-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-12-18)
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 ...
The adaptive finite element method
[SNAP-2016-013-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)
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 ...
Prime tuples in function fields
[SNAP-2016-010-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)
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 ...
Vertex-to-self trajectories on the platonic solids
[SNAP-2020-003-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2020-04-15)
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 ...
Footballs and donuts in four dimensions
[SNAP-2016-012-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)
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 ...
Seeing through rock with help from optimal transport
[SNAP-2022-004-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-05-06)
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
[SNAP-2021-011-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2021-09-16)
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 ...
Finite geometries: pure mathematics close to applications
[SNAP-2021-010-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2021-09-22)
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 ...