During the Spring 2026 quarter, all of our meetings will be held in-person in 268 Skye Hall, primarily on Thursdays.
Talks will run from 12:30-1:30pm unless otherwise indicated, but feel free to show up early for socializing with the speaker.
Current organizers: Tom Gannon, Jacob Greenstein
Spring 2026 schedule
April 2, 2026
Jacob Greenstein (UC Riverside)
Title: Monomial bialgebras
Abstract: Starting from a single solution of QYBE (or CYBE) we produce an infinite family of solutions of QYBE (or CYBE) parametrized by transitive arrays and, in particular, by signed permutations. We are especially interested in cases when such solutions yield quasi-triangular structures on direct powers of Lie bialgebras and tensor powers of Hopf algebras (joint work with A. Berenstein and J.-R. Li)
April 9, 2026
Cris Negron (USC)
Title: TQFTs from derived categories of quantum group representations
Abstract: The usual Reshetikhin-Turaev TQFT uses the representation theory of the quantum group at a root of 1, in conjunction with a semisimple truncation procedure, to produce a 3-dimensional topological field theory. I will discuss a means of producing a 'derived' variant of the Reshetikhin-Turaev theory which employs quantum group representations directly, i.e. without semisimple truncation. Just as usual RT provides a mathematical formalization of Chern-Simons theory, our derived TQFTs formalize certain exotic field theories which appear in physics. I will discuss these physical motivations, contextualize our study within the more general framework/philosophy of 'nonsemisimple' TQFT, and give some details for our construction. Parts of this are joint work with Agustina Czenky.
April 16, 2026
Tonie Scroggin (UCSB)
Title: Splicing braid varieties
Abstract: Braid varieties are a rich class of smooth affine algebraic varieties that generalize open Richardson and positroid varieties. They appear naturally in several contexts, including the study of Legendrian links. In this talk, we introduce the "splicing map," a geometric and algebraic construction inspired by braid composition. We show that the splicing map is a quasi-cluster isomorphism that preserves the natural cluster structure on these varieties. This construction provides a geometric "factorization" of complex braid varieties into elementary components, revealing how the cluster structures of torus links and the relations between Plücker coordinates behave under braid concatenation.
April 23, 2026
Dan Kaplan (CSULB)
Title: TBD
Abstract: TBD
April 30, 2026
Jeremy Taylor (UCLA)
Title: TBD
Abstract: TBD
May 7, 2026
Trung Vu (Yale)
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 21, 2026
Nikolay Grantcharov (UGA)
Title: TBD
Abstract: TBD
May 28, 2026
Vyjayanthi Chari (UCR)
Title: TBD
Abstract: TBD
June 4, 2026
Peter Crooks (Utah State)
Title: TBD
Abstract: TBD