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Classical Algebraic Geometry and Discrete Integrable Systems
Gessica Alecci, Michele Graffeo, Alexander Stokes
https://arxiv.org/abs/2510.12647 https://arx…

Classical Algebraic Geometry and Discrete Integrable Systems
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry side, which is applied to differential and discrete Painlevé equations on the integrable systems side. Along the way we also discuss the theory of resolution of indeterminacies, which is applied to the cohomological computation of algebraic entropy of biration…

Oh good! Someone from the @… community can weigh in on the benefits.
Oh wait…
Anyway, sooner or later the time for computable reals will come. I'm still HODLing stock in continued fractions (and teaching them every year to my first-year students).

Low-Discrepancy Set Post-Processing via Gradient Descent
Fran\c{c}ois Cl\'ement, Linhang Huang, Woorim Lee, Cole Smidt, Braeden Sodt, Xuan Zhang
https://arxiv.org/abs/2511.10496 https://arxiv.org/pdf/2511.10496 https://arxiv.org/html/2511.10496
arXiv:2511.10496v1 Announce Type: new
Abstract: The construction of low-discrepancy sets, used for uniform sampling and numerical integration, has recently seen great improvements based on optimization and machine learning techniques. However, these methods are computationally expensive, often requiring days of computation or access to GPU clusters. We show that simple gradient descent-based techniques allow for comparable results when starting with a reasonably uniform point set. Not only is this method much more efficient and accessible, but it can be applied as post-processing to any low-discrepancy set generation method for a variety of standard discrepancy measures.
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