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Quantum symmetry
[SNAP2020009EN] (Mathematisches Forschungsinstitut Oberwolfach, 20201231)The symmetry of objects plays a crucial role in many branches of mathematics and physics. It allowed, for example, the early prediction of the existence of new small particles. “Quantum symmetry” concerns a generalized ... 
Shape space – a paradigm for character animation in computer graphics
[SNAP2020007EN] (Mathematisches Forschungsinstitut Oberwolfach, 20201007)Nowadays 3D computer animation is increasingly realistic as the models used for the characters become more and more complex. These models are typically represented by meshes of hundreds of thousands or even millions ... 
Higgs bundles without geometry
[SNAP2020008EN] (Mathematisches Forschungsinstitut Oberwolfach, 20200929)Higgs bundles appeared a few decades ago as solutions to certain equations from physics and have attracted much attention in geometry as well as other areas of mathematics and physics. Here, we take a very informal ... 
Rotating needles, vibrating strings, and Fourier summation
[SNAP2020006EN] (Mathematisches Forschungsinstitut Oberwolfach, 20200921)We give a brief survey of the connection between seemingly unrelated problems such as sets in the plane containing lines pointing in many directions, vibrating strings and drum heads, and a classical problem from Fourier analysis. 
Quantum symmetry
[SNAP2020005EN] (Mathematisches Forschungsinstitut Oberwolfach, 20200604)In mathematics, symmetry is usually captured using the formalism of groups. However, the developments of the past few decades revealed the need to go beyond groups: to “quantum groups”. We explain the passage from ... 
Determinacy versus indeterminacy
[SNAP2020004EN] (Mathematisches Forschungsinstitut Oberwolfach, 20200422)Can a continuous function on an interval be uniquely determined if we know all the integrals of the function against the natural powers of the variable? Following Weierstrass and Stieltjes, we show that the answer is yes ... 
Vertextoself trajectories on the platonic solids
[SNAP2020003EN] (Mathematisches Forschungsinstitut Oberwolfach, 20200415)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 ... 
Random matrix theory: Dyson Brownian motion
[SNAP2020002EN] (Mathematisches Forschungsinstitut Oberwolfach, 20200415)The theory of random matrices was introduced by John Wishart (1898–1956) in 1928. The theory was then developed within the field of nuclear physics from 1955 by Eugene Paul Wigner (1902–1995) and later by Freeman John ... 
From Betti numbers to ℓ²Betti numbers
[SNAP2020001EN] (Mathematisches Forschungsinstitut Oberwolfach, 20200415)We provide a leisurely introduction to ℓ²Betti numbers, which are topological invariants, by relating them to their much older cousins, Betti numbers. In the end we present an open research problem about ℓ²Betti numbers.