Browsing 1 - Oberwolfach Preprints (OWP) by MFO Scientific Program "Research in Pairs 2020"
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Boundary Conditions for Scalar Curvature
[OWP-2021-01] (Mathematisches Forschungsinstitut Oberwolfach, 2021-01-04)Based on the Atiyah-Patodi-Singer index formula, we construct an obstruction to positive scalar curvature metrics with mean convex boundaries on spin manifolds of infinite $K$-area. We also characterize the extremal case. ... -
Diophantine Approximation in Metric Space
[OWP-2021-07] (Mathematisches Forschungsinstitut Oberwolfach, 2021-06-14)Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the ... -
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 ... -
Generating Finite Coxeter Groups with Elements of the Same Order
[OWP-2020-07] (Mathematisches Forschungsinstitut Oberwolfach, 2020-03-16)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 ... -
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 $f(R) \subseteq R$ ... -
On the Computational Content of the Theory of Borel Equivalence Relations
[OWP-2021-06] (Mathematisches Forschungsinstitut Oberwolfach, 2021-03-17)This preprint offers computational insights into the theory of Borel equivalence relations. Specifically, we classify equivalence relations on the Cantor space up to computable reductions, i.e., reductions induced by Turing ... -
On Weakly Complete Universal Enveloping Algebras of pro-Lie Algebras
[OWP-2020-10] (Mathematisches Forschungsinstitut Oberwolfach, 2020-04-27) -
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 ... -
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 ...