activity
20232026
collaborators

7 papers

math.GT2026

On the density and surjectivity of -Witten-Reshetikhin-Turaev quantum representations

Renaud Detcherry, Pierre Godfard, Ramanujan Santharoubane

In this paper, we establish several new fundamental properties of -quantum representations $ρ_{p,g,\underlineλ}\colon\mathrm{PMod} (Σ_{g,n})\longrightarrow \mathrm{…

math.GT2025

Rigidity of and quantum representations of mapping class groups at prime levels

Pierre Godfard

We prove the rigidity of Witten-Reshetikhin-Turaev and quantum representations of mapping class groups at all prime levels for closed surfaces of…

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…

math.GT2024

Construction of Hodge structures on the modular functors

Pierre Godfard

We prove that modular functors in genus have geometric origin and support integral variations of Hodge structures for any odd level and -th root of unit…

math.GT2023

Rigidity of Fibonacci representations of mapping class groups

Pierre Godfard

We prove that level Witten-Reshetikhin-Turaev quantum representations, also known as the Fibonacci representations, of mapping class groups are locally rigid.…