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Intersection cohomology of Vinberg-Popov varieties
Andrew Dancer, Johan Martens, Nicholas Proudfoot
https://arxiv.org/abs/2507.16492 https://

Intersection cohomology of Vinberg-Popov varieties
The Vinberg-Popov variety of a simply connected reductive algebraic group $G$ is a singular affine variety that contains the basic affine space $G/U$ as a Zariski open subset. It is defined as the spectrum of the ring of functions on $G/U$, and can also be identified with the universal symplectic implosion for the maximal compact subgroup of $G$. We provide a recursive procedure for computing the intersection cohomology of this variety, with an emphasis on the case where $G = \operatorname{SL}_…

Been playing this game I dig on the Android tablet called Dungeon Raid. It's a card flipping dungeon crawler (the dev calls it an 'adventure card roguelike') that's fairly easy to figure out-- lots of strategy and replayability. At first, you can start out playing as either a knight or a vampire, delving down, trying not to die of hunger.
If a relic in a game you can choose is a fried egg, you can probably assume it's a game for me.
There's also Linux, M…

Families of curves in Vinberg representations
Jef Laga, Beth Romano
https://arxiv.org/abs/2508.09607 https://arxiv.org/pdf/2508.09607

Families of curves in Vinberg representations
Inspired by orbit parametrizations in arithmetic statistics, we explain how to construct families of curves associated to certain nilpotent elements in $\mathbb{Z}/m\mathbb{Z}$-graded Lie algebras, generalizing work of Thorne to the $m\geq 3$ case and the non-simply laced case. We classify such families arising from subregular nilpotents in stable gradings and interpret almost all orbit parametrizations associated with algebraic curves appearing in the literature in this framework. As an extend…

Street design and driving behavior: evidence from a large-scale study in Milan, Amsterdam, and Dubai
Giacomo Orsi, Titus Venverloo, Andrea La Grotteria, Umberto Fugiglando, F\'abio Duarte, Paolo Santi, Carlo Ratti
https://arxiv.org/abs/2507.04434

Street design and driving behavior: evidence from a large-scale study in Milan, Amsterdam, and Dubai
In recent years, cities have increasingly reduced speed limits from 50 km/h to 30 km/h to enhance road safety, reduce noise pollution, and promote sustainable modes of transportation. However, achieving compliance with these new limits remains a key challenge for urban planners. This study investigates drivers' compliance with the 30 km/h speed limit in Milan and examines how street characteristics influence driving behavior. Our findings suggest that the mere introduction of lower speed limits…