5 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 solving long-open problems. The introspection this has prompted about the future of mathematical discovery i…
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. Sta…
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…
On Oda's problem and special loci
Benjamin Collas, Séverin Philip
Oda's problem, which deals with the fixed field of the universal monodromy representation of moduli spaces of curves and its independence with respect to the topological data, is a…