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Dynamics of Gravitational Collapse in the Axisymmetric EinsteinVlasov System
[OWP202022] (Mathematisches Forschungsinstitut Oberwolfach, 20201215)We numerically investigate the dynamcis near black hole formation of solutions to the EinsteinVlasov system in axisymmetry. Our results are obtained using a particleincell and finite difference code based on the (2+1)+1 ... 
Octonion Polynomials with Values in a Subalgebra
[OWP202021] (Mathematisches Forschungsinstitut Oberwolfach, 20201022)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 $f(R) \subseteq R$ ... 
Homology and $K$Theory of TorsionFree Ample Groupoids and Smale Spaces
[OWP202020] (Mathematisches Forschungsinstitut Oberwolfach, 20201009)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 torsionfree ... 
Unexpected Properties of the Klein Configuration of 60 Points in $\mathbb{P}^3$
[OWP202019] (Mathematisches Forschungsinstitut Oberwolfach, 20201007)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 PelletierRessayre Hidden Symmetry for LittlewoodRichardson Coefficients
[OWP202018] (Mathematisches Forschungsinstitut Oberwolfach, 20200908)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. 
Braidoids
[OWP202017] (Mathematisches Forschungsinstitut Oberwolfach, 20200903)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 ... 
Maximal Quaternion Orders in Quadratic Extensions  in Hurwitz’s Diaries
[OWP202016] (Mathematisches Forschungsinstitut Oberwolfach, 20200803)We present and comment on some unpublished work of Adolf Hurwitz on quaternion arithmetic from his diaries. 
Hopf Algebras in Combinatorics, Volume 2
[OWP202015] (Mathematisches Forschungsinstitut Oberwolfach, 20200730) 
Hopf Algebras in Combinatorics, Volume 1
[OWP202014] (Mathematisches Forschungsinstitut Oberwolfach, 20200729) 
How Quantum Information Can Improve Social Welfare
[OWP202013] (Mathematisches Forschungsinstitut Oberwolfach, 20200716)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 ... 
SpaceTime Euler Discretization Schemes for the Stochastic 2D NavierStokes Equations
[OWP202012] (Mathematisches Forschungsinstitut Oberwolfach, 20200506)We prove that the implicit time Euler scheme coupled with finite elements space discretization for the 2D NavierStokes equations on the torus subject to a random perturbation converges in $L^2(\Omega)$, and describe the ... 
lTorsion Bounds for the Class Group of Number Fields with an l Group as Galois Group
[OWP202011] (Mathematisches Forschungsinstitut Oberwolfach, 20200504)We describe the relations among the $\ell$torsion conjecture for $\ell$extensions, the discriminant multiplicity conjecture for nilpotent extensions and a conjecture of Malle giving an upper bound for the number of ... 
On Weakly Complete Universal Enveloping Algebras of proLie Algebras
[OWP202010] (Mathematisches Forschungsinstitut Oberwolfach, 20200427) 
Theoretical Analysis and Simulation Methods for Hawkes Processes and their Diffusion Approximation
[OWP202009] (Mathematisches Forschungsinstitut Oberwolfach, 20200330)Oscillatory systems of interacting Hawkes processes with Erlang memory kernels were introduced in Ditlevsen and Löcherbach (2017). They are piecewise deterministic Markov processes (PDMP) and can be approximated by a ... 
Singularities and Bifurcations of Pseudospherical Surfaces
[OWP202008] (Mathematisches Forschungsinstitut Oberwolfach, 20200317)We study singularities and bifurcations of constant negative curvature surfaces in Euclidean 3space via their association with Lorentzian harmonic maps. This preprint presents the basic results on this, the full proofs ... 
Generating Finite Coxeter Groups with Elements of the Same Order
[OWP202007] (Mathematisches Forschungsinstitut Oberwolfach, 20200316)Supposing $G$ is a group and $k$ a natural number, $d_k(G)$ is defined to be the minimal number of elements of $G$ of order $k$ which generate $G$ (setting $d_k(G) = 0$ if $G$ has no such generating sets). This paper ... 
Nonexistence of Subcritical Solitary Waves
[OWP202006] (Mathematisches Forschungsinstitut Oberwolfach, 20200315)We prove the nonexistence of twodimensional solitary gravity water waves with subcritical wave speeds and an arbitrary distribution of vorticity. This is a longstanding open problem, and even in the irrotational case there ... 
Rational Functions with Small Value Set
[OWP202005] (Mathematisches Forschungsinstitut Oberwolfach, 20200314)In connection with Galois Theory and Algebraic Curves, this paper investigates rational functions $h(x) = f(x)/g(x) \in \mathbb{F}_q(x)$ for which the value set $V_h = {\{h(α)  α \in \mathbb{F}_q \cup\{\infty\}}\}$ is ... 
Multivariate Hybrid Orthogonal Functions
[OWP202004] (Mathematisches Forschungsinstitut Oberwolfach, 20200312)We consider multivariate orthogonal functions satisfying hybrid orthogonality conditions with respect to a moment functional. This kind of orthogonality means that the product of functions of different parity order ... 
Splitting Necklaces, with Constraints
[OWP202003] (Mathematisches Forschungsinstitut Oberwolfach, 20200211)We prove several versions of Alon's "necklacesplitting theorem", subject to additional constraints, as illustrated by the following results. (1) The "almost equicardinal necklacesplitting theorem" claims that, without ...