Let $C$ be a smooth, projective, geometrically integral hyperelliptic curve of genus $g \ge 2$ over a number field $k$. We investigate the structure of the $\mathbb{P}^1$-parameterized density degree set $\delta_{\mathbb{P}^1}(C/k)$ (equivalently, the Lüroth semigroup) for such curves, consisting of degrees arising from morphisms to $\mathbb{P}^1$. Building on foundational frameworks for parameterized points, we provide […]

This will be a sequel of my last ANTC talk on bundles of probability schemes. We introduce entropy for fiber bundles of probability schemes and higher-order entropy for hypercubes of […]