arXiv subjects

Paul Vollrath

Publications and source records attributed to Paul Vollrath.

2 recordsLinked to original sources

arXiv2025

Full Resolution to Papikian's Conjecture

We prove Papikian's conjecture on the spectrum of the signed up-down walk on the spherical building. Namely, we show that in the spherical building of dimension n-2 and thickness q + 1, the number of distinct eigenvalues is independent of q and for q going to infinity the positive eigenvalues converge to n-1, ... , n-i.

math.CO↗

arXiv2024

Bounds on Systoles and Homotopy Complexity

We give an elementary proof of a weak variant of the homotopy type conjecture from [Gel04]. The proof relies on Belolipetskys estimate on the systole in terms of the volume which is a consequence of Prasads volume formula. In particular we extend the estimate established in [B20] for hyperbolic manifolds to general arithmetic manifolds.

math.GR↗