http://publications.mfo.de/handle/mfo/3695 Tue, 07 Apr 2026 14:48:20 GMT 2026-04-07T14:48:20Z http://publications.mfo.de/handle/mfo/3820 Dynamics of Gravitational Collapse in the Axisymmetric Einstein-Vlasov System Ames, Ellery; Andréasson, Håkan; Rinne, Oliver We numerically investigate the dynamcis near black hole formation of solutions to the Einstein-Vlasov system in axisymmetry. Our results are obtained using a particle-in-cell and finite difference code based on the (2+1)+1 formulation of the Einstein field equations in axisymmetry. Solutions are launched from generic type initial data and exhibit type I critical behaviour. In particular we find lifetime scaling in solutions containing black holes, and support that the critical solutions are stationary. Our results contain examples of solutions that form black holes, perform damped oscillations, and appear to disperse. We prove that complete dispersal of the solution implies that it has nonpositive binding energy. Tue, 15 Dec 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3820 2020-12-15T00:00:00Z Ames, Ellery Andréasson, Håkan Rinne, Oliver We numerically investigate the dynamcis near black hole formation of solutions to the Einstein-Vlasov system in axisymmetry. Our results are obtained using a particle-in-cell and finite difference code based on the (2+1)+1 formulation of the Einstein field equations in axisymmetry. Solutions are launched from generic type initial data and exhibit type I critical behaviour. In particular we find lifetime scaling in solutions containing black holes, and support that the critical solutions are stationary. Our results contain examples of solutions that form black holes, perform damped oscillations, and appear to disperse. We prove that complete dispersal of the solution implies that it has nonpositive binding energy. http://publications.mfo.de/handle/mfo/3802 Octonion Polynomials with Values in a Subalgebra Chapman, Adam In this paper, we prove that given an octonion algebra $A$ over a field $F$, a subring $E \subseteq F$ and an octonion $E$-algebra $R$ inside $A$, the set $S$ of polynomials $f(x) \in A[x]$ satisfying $f(R) \subseteq R$ is an octonion $(S\cap F[x])$-algebra, under the assumption that either $\frac{1}{2} \in R$ or $\operatorname{char}(F) \neq 0$, and $R$ contains the standard generators of $A$ and their inverses. The project was inspired by a question raised by Werner on whether integer-valued octonion polynomials over the reals form a nonassociative ring. We also prove that the polynomials $\frac{1}{p}(x^{p^2}-x)(x^p-x)$ for prime $p$ are integer-valued in the ring of polynomials $A[x]$ over any real nonsplit Cayley-Dickson algebra $A$. Thu, 22 Oct 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3802 2020-10-22T00:00:00Z Chapman, Adam In this paper, we prove that given an octonion algebra $A$ over a field $F$, a subring $E \subseteq F$ and an octonion $E$-algebra $R$ inside $A$, the set $S$ of polynomials $f(x) \in A[x]$ satisfying $f(R) \subseteq R$ is an octonion $(S\cap F[x])$-algebra, under the assumption that either $\frac{1}{2} \in R$ or $\operatorname{char}(F) \neq 0$, and $R$ contains the standard generators of $A$ and their inverses. The project was inspired by a question raised by Werner on whether integer-valued octonion polynomials over the reals form a nonassociative ring. We also prove that the polynomials $\frac{1}{p}(x^{p^2}-x)(x^p-x)$ for prime $p$ are integer-valued in the ring of polynomials $A[x]$ over any real nonsplit Cayley-Dickson algebra $A$. http://publications.mfo.de/handle/mfo/3800 Homology and $K$-Theory of Torsion-Free Ample Groupoids and Smale Spaces Proietti, Valerio; Yamashita, Makoto Given an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to the $K$-groups of the groupoid C*-algebra when the groupoid has torsion-free stabilizers and satisfies the strong Baum–Connes conjecture. The construction is based on the triangulated category approach to the Baum–Connes conjecture by Meyer and Nest. For the unstable equivalence relation of a Smale space with totally disconnected stable sets, this spectral sequence shows Putnam’s homology groups on the second sheet. Fri, 09 Oct 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3800 2020-10-09T00:00:00Z Proietti, Valerio Yamashita, Makoto Given an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to the $K$-groups of the groupoid C*-algebra when the groupoid has torsion-free stabilizers and satisfies the strong Baum–Connes conjecture. The construction is based on the triangulated category approach to the Baum–Connes conjecture by Meyer and Nest. For the unstable equivalence relation of a Smale space with totally disconnected stable sets, this spectral sequence shows Putnam’s homology groups on the second sheet. http://publications.mfo.de/handle/mfo/3799 Unexpected Properties of the Klein Configuration of 60 Points in $\mathbb{P}^3$ Pokora, Piotr; Szemberg, Tomasz; Szpond, Justyna Felix Klein in course of his study of the regular and its symmetries encountered a highly symmetric configuration of 60 points in $\mathbb{P}^3$. This configuration has appeared in various guises, perhaps post notably as the configuration of points dual to the 60 reflection planes in the group $G_{31}$ in the Shephard-Todd list. In the present note we show that the 60 points exhibit interesting properties relevant from the point of view of two paths of research initiated recently. Firstly, they give rise to two completely different unexpected surfaces of degree 6. Unexpected hypersurfaces have been introduced by Cook II, Harbourne, Migliore, Nagel in 2018. One of unexpected surfaces associated to the configuration of 60 points is a cone with a single singularity of multiplicity 6 and the other has three singular points of multiplicities 4; 2 and 2. Secondly, Chiantini and Migliore observed in 2020 that there are non-trivial sets of points in $\mathbb{P}^3$ with the surprising property that their general projection to $\mathbb{P}^2$ is a complete intersection. They found a family of such sets, which they called grids. An appendix to their paper describes an exotic configuration of 24 points in $\mathbb{P}^3$ which is not a grid but has the remarkable property that its general projection is a complete intersection. We show that the Klein configuration is also not a grid and it projects to a complete intersections. We identify also its proper subsets, which enjoy the same property. Wed, 07 Oct 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3799 2020-10-07T00:00:00Z Pokora, Piotr Szemberg, Tomasz Szpond, Justyna Felix Klein in course of his study of the regular and its symmetries encountered a highly symmetric configuration of 60 points in $\mathbb{P}^3$. This configuration has appeared in various guises, perhaps post notably as the configuration of points dual to the 60 reflection planes in the group $G_{31}$ in the Shephard-Todd list. In the present note we show that the 60 points exhibit interesting properties relevant from the point of view of two paths of research initiated recently. Firstly, they give rise to two completely different unexpected surfaces of degree 6. Unexpected hypersurfaces have been introduced by Cook II, Harbourne, Migliore, Nagel in 2018. One of unexpected surfaces associated to the configuration of 60 points is a cone with a single singularity of multiplicity 6 and the other has three singular points of multiplicities 4; 2 and 2. Secondly, Chiantini and Migliore observed in 2020 that there are non-trivial sets of points in $\mathbb{P}^3$ with the surprising property that their general projection to $\mathbb{P}^2$ is a complete intersection. They found a family of such sets, which they called grids. An appendix to their paper describes an exotic configuration of 24 points in $\mathbb{P}^3$ which is not a grid but has the remarkable property that its general projection is a complete intersection. We show that the Klein configuration is also not a grid and it projects to a complete intersections. We identify also its proper subsets, which enjoy the same property. http://publications.mfo.de/handle/mfo/3773 The Pelletier-Ressayre Hidden Symmetry for Littlewood-Richardson Coefficients Grinberg, Darij We prove an identity for Littlewood–Richardson coefficients conjectured by Pelletier and Ressayre. The proof relies on a novel birational involution defined over any semifield. Tue, 08 Sep 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3773 2020-09-08T00:00:00Z Grinberg, Darij We prove an identity for Littlewood–Richardson coefficients conjectured by Pelletier and Ressayre. The proof relies on a novel birational involution defined over any semifield. http://publications.mfo.de/handle/mfo/3771 Braidoids Gügümcü, Neslihan; Lambropoulou, Sofia Braidoids generalize the classical braids and form a counterpart theory to the theory of planar knotoids, just as the theory of braids does for the theory of knots. In this paper, we introduce the notion of braidoids in $\mathbb{R}^2$, a closure operation for braidoids, we prove an analogue of the Alexander theorem, namely an algorithm that turns a knotoid into a braidoid, and we formulate and prove a geometric analogue of the Markov theorem for braidoids using the $L$-moves. Thu, 03 Sep 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3771 2020-09-03T00:00:00Z Gügümcü, Neslihan Lambropoulou, Sofia Braidoids generalize the classical braids and form a counterpart theory to the theory of planar knotoids, just as the theory of braids does for the theory of knots. In this paper, we introduce the notion of braidoids in $\mathbb{R}^2$, a closure operation for braidoids, we prove an analogue of the Alexander theorem, namely an algorithm that turns a knotoid into a braidoid, and we formulate and prove a geometric analogue of the Markov theorem for braidoids using the $L$-moves. http://publications.mfo.de/handle/mfo/3768 Maximal Quaternion Orders in Quadratic Extensions - in Hurwitz’s Diaries Oswald, Nicola; Steuding, Jörn We present and comment on some unpublished work of Adolf Hurwitz on quaternion arithmetic from his diaries. Mon, 03 Aug 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3768 2020-08-03T00:00:00Z Oswald, Nicola Steuding, Jörn We present and comment on some unpublished work of Adolf Hurwitz on quaternion arithmetic from his diaries. http://publications.mfo.de/handle/mfo/3767 Hopf Algebras in Combinatorics, Volume 2 Grinberg, Darij; Reiner, Victor Thu, 30 Jul 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3767 2020-07-30T00:00:00Z Grinberg, Darij Reiner, Victor http://publications.mfo.de/handle/mfo/3766 Hopf Algebras in Combinatorics, Volume 1 Grinberg, Darij; Reiner, Victor Wed, 29 Jul 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3766 2020-07-29T00:00:00Z Grinberg, Darij Reiner, Victor http://publications.mfo.de/handle/mfo/3765 How Quantum Information Can Improve Social Welfare Groisman, Berry; Mc Gettrick, Michael; Mhalla, Mehdi; Pawlowski, Marcin In [2, 18, 5, 19, 4] it has been shown that quantum resources can allow us to achieve a family of equilibria that can have sometimes a better social welfare, while guaranteeing privacy. We use graph games to propose a way to build non- cooperative games from graph states, and we show how to achieve an unlimited improvement with quantum advice compared to classical advice. Thu, 16 Jul 2020 00:00:00 GMT http://publications.mfo.de/handle/mfo/3765 2020-07-16T00:00:00Z Groisman, Berry Mc Gettrick, Michael Mhalla, Mehdi Pawlowski, Marcin In [2, 18, 5, 19, 4] it has been shown that quantum resources can allow us to achieve a family of equilibria that can have sometimes a better social welfare, while guaranteeing privacy. We use graph games to propose a way to build non- cooperative games from graph states, and we show how to achieve an unlimited improvement with quantum advice compared to classical advice.