4 papers
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, for a few thousand dollars of tokens, solving long-open problems (OpenAI, August 2026). The introspection t…
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…
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. St…
Symmetries of spaces and numbers -- anabelian geometry
Benjamin Collas, Takahiro Murotani, Naganori Yamaguchi
``Can number and geometric spaces be reconstructed from their symmetries?'' This question, which is at the heart of anabelian geometry, a theory built on the collaborative efforts…