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math.AG2025
Conformal blocks are quasi-geometric
Pierre Godfard
We prove that the bundles with flat connections on configuration spaces associated to braided fusion categories, as well as the bundles with flat connections on moduli spaces of cu…
math.AG2025
Semisimplicity of conformal blocks
Pierre Godfard
We prove that braid group representations associated to braided fusion categories and mapping class group representations associated to modular fusion categories are always semisim…
math.AG2024
Hodge structures on conformal blocks
Pierre Godfard
We prove existence and uniqueness of complex Hodge structures on modular functors. The proof is based on the non-Abelian Hodge correspondence and Ocneanu rigidity. Given a modular…