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Cohomological nonvanishing for algebraic fundamental groups of ball quotients
Matthew Stover
https://arxiv.org/abs/2508.20847 https://arxiv.org/pdf/2508.20…

Cohomological nonvanishing for algebraic fundamental groups of ball quotients
Suppose $Γ< \mathrm{PU}(n,1)$ is a cocompact arithmetic lattice of simplest type with profinite completion $\widehatΓ$. This paper proves there is an open subgroup $\widehatΓ_0 \le \widehatΓ$ such that $H^j(\widehatΔ, \mathbb{F}_p)$ is nontrivial for every open subgroup ${\widehatΔ \le \widehatΓ_0}$, $j \le 2n$, and sufficiently large prime $p$. If $n \ge 2$, nonvanishing is new for all $j \ge 2$. Consequently, the virtual cohomological dimension of $\widehatΓ$ is at least $2n$, improvi…

What Do Bouncing Balls Tell Us About the Universe? A Journey into Billiard Systems
Weiqi Chu, Matthew Dobson
https://arxiv.org/abs/2508.18519 https://arxiv…

What Do Bouncing Balls Tell Us About the Universe? A Journey into Billiard Systems
Have you ever played or watched a game of pool? If so, you have already seen a billiard system in action. In mathematics and physics, a billiard system describes a ball that moves in straight lines and bounces off walls. Despite these simple rules, billiard systems can produce remarkably rich behaviors: some table shapes generate regular, periodic patterns, while others give rise to complete chaos. Scientists also study what happens when we shrink the ball down to the size of an electron to a w…

Methods for Estimating Neutron Star Parameters using Multiple Mechanisms for Gravitational Wave Emission Associated with Pulsar Glitches
Matthew Ball, Raymond Frey
https://arxiv.org/abs/2508.15965

Methods for Estimating Neutron Star Parameters using Multiple Mechanisms for Gravitational Wave Emission Associated with Pulsar Glitches
Several mechanisms for gravitational wave (GW) emission are believed to be associated with pulsar glitches. This emission may be split between long duration continuous waves and short duration bursts. In the Advanced LIGO era, searches for GWs associated with pulsar glitches have only considered continuous wave emission. The increasing sensitivity of the detectors and the prospects for future detectors suggest that astrophysically motivated analyses involving multiple mechanisms may be possible…

A Bound on the Symplectic Systolic Ratio of Polytopes in Even-Dimensional Euclidean Space
Matthew Zediker
https://arxiv.org/abs/2509.19083 https://arxiv.or…