arXiv subjects

Florian Dorsch

Publications and source records attributed to Florian Dorsch.

7 recordsLinked to original sources

arXiv2026

The shifted symplectic geometry of derived higher groupoids

The main goal of this work is to introduce derived Lie n-groupoids and their shifted symplectic structures. We further define shifted lagrangian structures and prove that their composition is well defined under suitable conditions. As an application, we show that our framework incorporates several reduction procedures at critical values, including: classical Hamiltonian reduction, group valued moment maps, Poisson Lie group valued moment maps and Mikami-Weinstein for proper symplectic groupoids.

math.SG↗

arXiv2024

On the local Kan structure and differentiation of simplicial manifolds

We prove that arbitrary simplicial manifolds satisfy Kan conditions in a suitable local sense. This allows us to expand a technique for differentiating higher Lie groupoids worked out in current research to the setting of general simplicial manifolds. Consequently, we derive a method to differentiate simplicial manifolds into higher Lie algebroids.

math.DG↗

arXiv2022

Partially hyperbolic random dynamics on Grassmannians

A sequence of invertible matrices given by a small random perturbation around a fixed diagonal partially hyperbolic matrix induces a random dynamics on the Grassmann manifolds. Under suitable weak conditions it is known to have a unique invariant (Furstenberg) measure. The main result gives concentration bounds on this measure showing that with high probability the random dynamics stays in the vicinity of stable fixed points of the unperturbed matrix, in a regime where the strength of the random perturbation dominates the local hyperbolicity of the diagonal matrix. As an application, bounds on sums of Lyapunov exponents are obtained.

math-ph↗

arXiv2021

Random Möbius dynamics on the unit disc and perturbation theory for Lyapunov exponents

Randomly drawn $2\times 2$ matrices induce a random dynamics on the Riemann sphere via the Möbius transformation. Considering a situation where this dynamics is restricted to the unit disc and given by a random rotation perturbed by further random terms depending on two competing small parameters, the invariant (Furstenberg) measure of the random dynamical system is determined. The results have applications to the perturbation theory of Lyapunov exponents which are of relevance for one-dimensional discrete random Schrödinger operators.

math-ph↗

arXiv2020

Pseudo-gaps for random hopping models

For one-dimensional random Schrödinger operators, the integrated density of states is known to be given in terms of the (averaged) rotation number of the Prüfer phase dynamics. This paper develops a controlled perturbation theory for the rotation number around an energy, at which all the transfer matrices commute and are hyperbolic. Such a hyperbolic critical energy appears in random hopping models. The main result is a Hölder continuity of the rotation number at the critical energy that, under certain conditions on the randomness, implies the existence of a pseudo-gap. The proof uses renewal theory. The result is illustrated by numerics.

math-ph↗

arXiv2019

Random perturbations of hyperbolic dynamics

A sequence of large invertible matrices given by a small random perturbation around a fixed diagonal and positive matrix induces a random dynamics on a high-dimensional sphere. For a certain class of rotationally invariant random perturbations it is shown that the dynamics approaches the stable fixed points of the unperturbed matrix up to errors even if the strength of the perturbation is large compared to the relative increase of nearby diagonal entries of the unperturbed matrix specifying the local hyperbolicity.

math-ph↗

arXiv2016

Accumulation Rate of Bound States of Dipoles Generated by Point Charges in Strained Graphene

We consider strained graphene, modelled by the two-dimensional massive Dirac operator, with potentials corresponding to charge distributions with vanishing total charge, non-vanishing dipole moment and finitely many point charges of subcritical coupling constants located in the graphene sheet. We show that the bound state energies accumulate exponentially fast at the edges of the spectral gap by determining the leading order of the accumulation rate.

math-ph↗