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math.HO2026
Fundamental Mathematics in the Age of AI -- The Residue, the Journey, and the Ecology
Benjamin Collas
Large language models have begun refuting long-standing conjectures and solving long-open problems. The introspection this has prompted about the future of mathematical discovery i…
math.AG2026
Anabelian geometry for Deligne-Mumford curves
Benjamin Collas, Séverin Philip, Naganori Yamaguchi
We develop an anabelian framework for general Deligne-Mumford curves, showing that their stack and orbifold structures are encoded in the group-theoretic properties of their étale…
math.AG2026
Anabelian perspectives in Galois-Teichmüller theory
Benjamin Collas
By exploiting the arithmetic homotopy of the moduli spaces of curves, Galois-Teichmüller theory stands at the interface of braid-mapping class groups and of anabelian geometry. Sta…