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Mirco Richter

Publications and source records attributed to Mirco Richter.

5 recordsLinked to original sources
arXiv2019

Crisis: Probabilistically Self Organizing Total Order in Unstructured P2P Networks

A framework for asynchronous, signature free, fully local and probabilistically converging total order algorithms is developed, that may survive in high entropy, unstructured Peer-to-Peer networks with near optimal communication efficiency. Regarding the natural boundaries of the CAP-theorem, Crisis chooses different compromises for consistency and availability, depending on the severity of the attack. The family is parameterized by a few constants and external functions called voting-weight, incentivation \& punishement, difficulty oracle and quorum-selector. These functions are necessary to fine tune the dynamics and very different long term behavior might appear, depending on any actual choice.

cs.DC↗
arXiv2018

Towards Homotopy Poisson-n Algebras from N-plectic Structures

We associate a homotopy Poisson-n algebra to any higher symplectic structure, which generalizes the common symplectic Poisson algebra of smooth functions. This provides robust n-plectic prequantum data for most approaches to quantization. UPDATE: It has been brought to my attention that the exterior product does not close on the exterior cotensors called Poisson cotensors in the present paper. Therefore the set of Poisson cotensors as presented, is not quite yet a homotopy Poisson-n algebra. However for those Poisson cotensor that do multiply into Poisson cotensors under the exterior prodoct, the computation remains valid and interesting, nonetheless. Therefor this paper might better be seen as a hint towards homotopy Poisson-n algebras in higher symplectic geometry, rather then a finished theory.

math.DG↗
arXiv2014

Higher symplectic structure on torsionless Lie-Rinehart pairs

We define an n-plectic structure as a commutative and torsionless Lie Rinehart pair, together with a distinguished cocycle from its Chevalley-Eilenberg complex. This 'n-plectic cocycle' gives rise to an extension of the Chevalley-Eilenberg complex by so called symplectic tensors. The cohomology of this extension generalizes Hamiltonian functions and vector fields to tensors and cotensors in a range of degrees, up to certain coboundaries and has the structure of a Lie oo-algebra. Finally we show, that momentum maps appear in this context just as weak Lie oo-morphisms from an arbitrary Lie oo-algebra into the Lie oo-algebra of Hamiltonian (co)tensors.

math.DG↗