UCR Representation and Lie Theory Seminar

April 2, 2026

• Cris Negron (USC)

Title: TBD

Abstract: TBD

April 16, 2026

• Tonie Scroggin (UCSB)

Title: TBD

Abstract: TBD

April 30, 2026

• Jeremy Taylor (UCLA)

Title: TBD

Abstract: TBD

May 14, 2026

• Pierre Godfard (UNC Chapel Hill)

Title: Rigidity of some quantum representations of mapping class groups via Ocneanu rigidity

Abstract: The property (T) conjecture predicts that finite dimensional unitary representations of mapping class groups $Mod(S_g^n)$ for $g\geq 3$ are rigid (in the sense that they admit no infinitesimal deformations). While extensively studied for representations with finite image, a special case known as the Ivanov conjecture, much less is known when the image is infinite. We establish rigidity of quantum representations of mapping class groups of closed surfaces arising from SU(2) and SO(3) modular categories, for $g\geq 7$ and at conformal levels $\ell$ such that $\ell+2$ is prime and at least $5$. These are natural infinite image examples arising in quantum topology via the Witten-Reshetikhin-Turaev construction or alternatively in algebraic geometry via non-abelian theta functions. The core of our argument is a proof that any infinitesimal deformation of such a quantum representation, within the space of all flat unitary representations, necessarily remains a quantum representation. This then implies triviality, since quantum representations admit no such internal deformations by a result known as Ocneanu rigidity. The proof combines the factorization property of quantum representations with elementary Hodge theory on twisted moduli spaces of curves, certain Kähler compact orbifolds whose fundamental groups are quotients of mapping class groups.

May 28, 2026

• Vyjayanthi Chari (UCR)

Title: TBD

Abstract: TBD