http://publications.mfo.de/handle/mfo/3734 Tue, 07 Apr 2026 06:23:20 GMT 2026-04-07T06:23:20Z http://publications.mfo.de/handle/mfo/4119 Fibrés de Higgs sans géométrie Rayan, Steven; Schaposnik, Laura P. Les fibrés de Higgs sont apparus il y a quelques décennies comme solutions de certaines équations en physique, et ils ont attiré beaucoup d’attention en géométrie comme dans d’autres domaines des mathématiques et de la physique. Ici, nous donnons un aperçu très informel de quelques aspects d’algèbre linéaire qui anticipent la structure profonde de l’espace de modules des fibrés de Higgs. Tue, 05 Mar 2024 00:00:00 GMT http://publications.mfo.de/handle/mfo/4119 2024-03-05T00:00:00Z Rayan, Steven Schaposnik, Laura P. Les fibrés de Higgs sont apparus il y a quelques décennies comme solutions de certaines équations en physique, et ils ont attiré beaucoup d’attention en géométrie comme dans d’autres domaines des mathématiques et de la physique. Ici, nous donnons un aperçu très informel de quelques aspects d’algèbre linéaire qui anticipent la structure profonde de l’espace de modules des fibrés de Higgs. http://publications.mfo.de/handle/mfo/3831 Quantum symmetry Caspers, Martijn 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 notion of symmetry. It is an abstract way of characterizing the symmetry of a much richer class of mathematical and physical objects. In this snapshot we explain how quantum symmetry emerges as matrix symmetries using a famous example: Mermin’s magic square. It shows that quantum symmetries can solve problems that lie beyond the reach of classical symmetries, showing that quantum symmetries play a central role in modern mathematics. Thu, 31 Dec 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3831 2020-12-31T00:00:00Z Caspers, Martijn 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 notion of symmetry. It is an abstract way of characterizing the symmetry of a much richer class of mathematical and physical objects. In this snapshot we explain how quantum symmetry emerges as matrix symmetries using a famous example: Mermin’s magic square. It shows that quantum symmetries can solve problems that lie beyond the reach of classical symmetries, showing that quantum symmetries play a central role in modern mathematics. http://publications.mfo.de/handle/mfo/3798 Shape space – a paradigm for character animation in computer graphics Heeren, Behrend; Rumpf, Martin 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 of triangles. The mathematical notion of a shape space allows us to effectively model, manipulate, and animate such meshes. Once an appropriate notion of dissimilarity measure between different triangular meshes is defined, various useful tools in character modeling and animation turn out to coincide with basic geometric operations derived from this definition. Wed, 07 Oct 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3798 2020-10-07T00:00:00Z Heeren, Behrend Rumpf, Martin 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 of triangles. The mathematical notion of a shape space allows us to effectively model, manipulate, and animate such meshes. Once an appropriate notion of dissimilarity measure between different triangular meshes is defined, various useful tools in character modeling and animation turn out to coincide with basic geometric operations derived from this definition. http://publications.mfo.de/handle/mfo/3793 Higgs bundles without geometry Rayan, Steven; Schaposnik, Laura P. 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 stroll through some aspects of linear algebra that anticipate the deeper structure in the moduli space of Higgs bundles.; [Also available in French] Tue, 29 Sep 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3793 2020-09-29T00:00:00Z Rayan, Steven Schaposnik, Laura P. 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 stroll through some aspects of linear algebra that anticipate the deeper structure in the moduli space of Higgs bundles. [Also available in French] http://publications.mfo.de/handle/mfo/3777 Rotating needles, vibrating strings, and Fourier summation Zahl, Joshua 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. Mon, 21 Sep 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3777 2020-09-21T00:00:00Z Zahl, Joshua 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. http://publications.mfo.de/handle/mfo/3747 Quantum symmetry Weber, Moritz 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 spaces to quantum spaces, from groups to quantum groups, and from symmetry to quantum symmetry, following an analytical approach. Thu, 04 Jun 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3747 2020-06-04T00:00:00Z Weber, Moritz 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 spaces to quantum spaces, from groups to quantum groups, and from symmetry to quantum symmetry, following an analytical approach. http://publications.mfo.de/handle/mfo/3739 Determinacy versus indeterminacy Berg, Christian 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 if the interval is finite, and no if the interval is infinite. Wed, 22 Apr 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3739 2020-04-22T00:00:00Z Berg, Christian 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 if the interval is finite, and no if the interval is infinite. http://publications.mfo.de/handle/mfo/3737 Vertex-to-self trajectories on the platonic solids Athreya, Jayadev S.; Aulicino, David 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 dodecahedron. Wed, 15 Apr 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3737 2020-04-15T00:00:00Z Athreya, Jayadev S. Aulicino, David 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 dodecahedron. http://publications.mfo.de/handle/mfo/3736 Random matrix theory: Dyson Brownian motion Finocchio, Gianluca 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 Dyson, who were both concerned with the statistical description of heavy atoms and their electromagnetic properties. In this snapshot, we show how mathematical properties can have unexpected links to physical phenomenena. In particular, we show that the eigenvalues of some particular random matrices can mimic the electrostatic repulsion of the particles in a gas. Wed, 15 Apr 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3736 2020-04-15T00:00:00Z Finocchio, Gianluca 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 Dyson, who were both concerned with the statistical description of heavy atoms and their electromagnetic properties. In this snapshot, we show how mathematical properties can have unexpected links to physical phenomenena. In particular, we show that the eigenvalues of some particular random matrices can mimic the electrostatic repulsion of the particles in a gas. http://publications.mfo.de/handle/mfo/3735 From Betti numbers to ℓ²-Betti numbers Kammeyer, Holger; Sauer, Roman We provide a leisurely introduction to ℓ²-Betti 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 ℓ²-Betti numbers. Wed, 15 Apr 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3735 2020-04-15T00:00:00Z Kammeyer, Holger Sauer, Roman We provide a leisurely introduction to ℓ²-Betti 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 ℓ²-Betti numbers.