@article{51204,
  abstract     = {{Given a real semisimple connected Lie group $G$ and a discrete torsion-free
subgroup $\Gamma < G$ we prove a precise connection between growth rates of the
group $\Gamma$, polyhedral bounds on the joint spectrum of the ring of
invariant differential operators, and the decay of matrix coefficients. In
particular, this allows us to completely characterize temperedness of
$L^2(\Gamma\backslash G)$ in this general setting.}},
  author       = {{Lutsko, Christopher and Weich, Tobias and Wolf, Lasse Lennart}},
  journal      = {{Duke Math. Journal }},
  title        = {{{Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces}}},
  volume       = {{(to appear)}},
  year         = {{2026}},
}

@article{51207,
  abstract     = {{Let $X=X_1\times X_2$ be a product of two rank one symmetric spaces of
non-compact type and $\Gamma$ a torsion-free discrete subgroup in $G_1\times
G_2$. We show that the spectrum of $\Gamma \backslash X$ is related to the
asymptotic growth of $\Gamma$ in the two direction defined by the two factors.
We obtain that $L^2(\Gamma \backslash G)$ is tempered for large class of
$\Gamma$.}},
  author       = {{Weich, Tobias and Wolf, Lasse Lennart}},
  journal      = {{Geom Dedicata}},
  title        = {{{Temperedness of locally symmetric spaces: The product case}}},
  doi          = {{https://doi.org/10.1007/s10711-024-00904-4}},
  volume       = {{218}},
  year         = {{2024}},
}

@article{52876,
  author       = {{Arends, Christian and Wolf, Lasse Lennart and Meinecke, Jasmin and Barkhofen, Sonja and Weich, Tobias and Bartley, Tim}},
  issn         = {{2643-1564}},
  journal      = {{Physical Review Research}},
  keywords     = {{General Physics and Astronomy}},
  number       = {{1}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Decomposing large unitaries into multimode devices of arbitrary size}}},
  doi          = {{10.1103/physrevresearch.6.l012043}},
  volume       = {{6}},
  year         = {{2024}},
}

@article{31189,
  abstract     = {{Given a geometrically finite hyperbolic surface of infinite volume it is a
classical result of Patterson that the positive Laplace-Beltrami operator has
no $L^2$-eigenvalues $\geq 1/4$. In this article we prove a generalization of
this result for the joint $L^2$-eigenvalues of the algebra of commuting
differential operators on Riemannian locally symmetric spaces $\Gamma\backslash
G/K$ of higher rank. We derive dynamical assumptions on the $\Gamma$-action on
the geodesic and the Satake compactifications which imply the absence of the
corresponding principal eigenvalues. A large class of examples fulfilling these
assumptions are the non-compact quotients by Anosov subgroups.}},
  author       = {{Weich, Tobias and Wolf, Lasse Lennart}},
  journal      = {{Communications in Mathematical Physics}},
  title        = {{{Absence of principal eigenvalues for higher rank locally symmetric  spaces}}},
  doi          = {{https://doi.org/10.1007/s00220-023-04819-1}},
  volume       = {{403}},
  year         = {{2023}},
}

@article{31190,
  abstract     = {{For a compact Riemannian locally symmetric space $\Gamma\backslash G/K$ of
arbitrary rank we determine the location of certain Ruelle-Taylor resonances
for the Weyl chamber action. We provide a Weyl-lower bound on an appropriate
counting function for the Ruelle-Taylor resonances and establish a spectral gap
which is uniform in $\Gamma$ if $G/K$ is irreducible of higher rank. This is
achieved by proving a quantum-classical correspondence, i.e. a
1:1-correspondence between horocyclically invariant Ruelle-Taylor resonant
states and joint eigenfunctions of the algebra of invariant differential
operators on $G/K$.}},
  author       = {{Hilgert, Joachim and Weich, Tobias and Wolf, Lasse Lennart}},
  journal      = {{Analysis & PDE}},
  number       = {{10}},
  pages        = {{2241–2265}},
  publisher    = {{MSP}},
  title        = {{{Higher rank quantum-classical correspondence}}},
  doi          = {{https://doi.org/10.2140/apde.2023.16.2241}},
  volume       = {{16}},
  year         = {{2023}},
}

@unpublished{31191,
  abstract     = {{The kinetic Brownian motion on the sphere bundle of a Riemannian manifold $M$
is a stochastic process that models a random perturbation of the geodesic flow.
If $M$ is a orientable compact constant negatively curved surface, we show that
in the limit of infinitely large perturbation the $L^2$-spectrum of the
infinitesimal generator of a time rescaled version of the process converges to
the Laplace spectrum of the base manifold. In addition, we give explicit error
estimates for the convergence to equilibrium. The proofs are based on
noncommutative harmonic analysis of $SL_2(\mathbb{R})$.}},
  author       = {{Kolb, Martin and Weich, Tobias and Wolf, Lasse Lennart}},
  booktitle    = {{arXiv:1909.06183}},
  title        = {{{Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces}}},
  year         = {{2019}},
}