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Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties
Yohsuke Matsuzawa
https://arxiv.org/abs/2507.05027

Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties
Consider a dominant rational self-map $f$ on a smooth projective variety $X$ defined over $\overline{\mathbb{Q}}$. We prove that \begin{align} \lim_{n \to \infty} \frac{h_{Y}(f^{n}(x))}{h_{H}(f^{n}(x)) } = 0, \end{align} where $h_{Y}$ is a height associated with a closed subscheme $Y \subset X$ of codimension $c$, $h_{H}$ is any ample height on $X$, and $x \in X(\overline{\mathbb{Q}})$ is a point with well-defined orbit, under the following assumptions: (1) either $f$ is a morphism, or $Y$ is p…

Optimal Transport on Lie Group Orbits
Bahar Taskesen
https://arxiv.org/abs/2508.09377 https://arxiv.org/pdf/2508.09377

Optimal Transport on Lie Group Orbits
In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as symmetry and formalize it using Lie group theory. Fixing a Lie group action on the outcome space and a reference distribution, we study optimal transport between measures lying on the same Lie group orbit of the reference distribution. In this setting, the Monge problem admits an …