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How Quantum Information Can Improve Social Welfare
[OWP-2020-13] (Mathematisches Forschungsinstitut Oberwolfach, 2020-07-16)
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 ...
Splitting Necklaces, with Constraints
[OWP-2020-03] (Mathematisches Forschungsinstitut Oberwolfach, 2020-02-11)
We prove several versions of Alon's "necklace-splitting theorem", subject to additional constraints, as illustrated by the following results.
(1) The "almost equicardinal necklace-splitting theorem" claims that, without ...
Positive Line Bundles Over the Irreducible Quantum Flag Manifolds
[OWP-2020-01] (Mathematisches Forschungsinstitut Oberwolfach, 2020-02-03)
Noncommutative Kähler structures were recently introduced by the third author as a framework for studying noncommutative Kähler geometry on quantum homogeneous spaces. It was subsequently observed that the notion of a ...
Unexpected Properties of the Klein Configuration of 60 Points in $\mathbb{P}^3$
[OWP-2020-19] (Mathematisches Forschungsinstitut Oberwolfach, 2020-10-07)
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 ...
Singularities and Bifurcations of Pseudospherical Surfaces
[OWP-2020-08] (Mathematisches Forschungsinstitut Oberwolfach, 2020-03-17)
We study singularities and bifurcations of constant negative curvature surfaces in Euclidean 3-space via their association with Lorentzian harmonic maps. This preprint presents the basic results on this, the full proofs ...
Rational Functions with Small Value Set
[OWP-2020-05] (Mathematisches Forschungsinstitut Oberwolfach, 2020-03-14)
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 ...
Theoretical Analysis and Simulation Methods for Hawkes Processes and their Diffusion Approximation
[OWP-2020-09] (Mathematisches Forschungsinstitut Oberwolfach, 2020-03-30)
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 ...
Dynamics of Gravitational Collapse in the Axisymmetric Einstein-Vlasov System
[OWP-2020-22] (Mathematisches Forschungsinstitut Oberwolfach, 2020-12-15)
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 ...
Octonion Polynomials with Values in a Subalgebra
[OWP-2020-21] (Mathematisches Forschungsinstitut Oberwolfach, 2020-10-22)
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 $f(R) \subseteq R$ ...
Hopf Algebras in Combinatorics, Volume 2
[OWP-2020-15] (Mathematisches Forschungsinstitut Oberwolfach, 2020-07-30)