2 papers
math.CO2025
Full Resolution to Papikian's Conjecture
Paul Vollrath
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…
math.GR2024
Bounds on Systoles and Homotopy Complexity
Tsachik Gelander, Paul Vollrath
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 i…