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: Gluing Resolutions of Singularities
Abstract: In algebraic geometry, a singular variety can be understood through its resolution of singularities. If the variety has additional structure (i.e., a Poisson structure) then one can ask for the resolution to preserve this structure (i.e., be a Poisson map). This gives rise to Beauville’s notion of a symplectic resolution of a symplectic singularity.
In joint work with Travis Schedler, we describe obstructions to gluing local symplectic resolution to a global symplectic resolution. We provide new examples of symplectic resolutions when these obstructions vanish. In this talk, I will survey these results focusing on low-dimensional examples.
April 30, 2026
Jeremy Taylor (UCLA)
Title: Coherent sheaves on the Grothendieck-Springer stack
Abstract: In characteristic zero, Arkhipov and Bezrukavnikov famously constructed a functor from coherent sheaves on the Grothendieck-Springer stack to the affine Hecke category. Their argument does not extend directly to positive characteristic, because a certain multi-graded ring does not seem to admit a costandard filtration. However Achar and Riche extended it to positive characteristic in the case of GL(n). I will recall how to view the Grothendieck-Springer scheme as the proj scheme of a multi-graded ring. Then I will explain how to extend Arkhipov and Bezrukavnikov's construction for arbitrary reductive groups by passing to very dominant weights. This is part of a joint project with Gurbir Dhillon on Bezrukavnikov's equivalence over the integers.
May 7, 2026
Trung Vu (Yale)
Title: Quantum Harish-Chandra bimodules at roots of unity
Abstract: Harish-Chandra bimodules were firstly studied by Harish-Chandra in his works about infinite dimensional representations of complex groups as real groups. They are related to many other objects in representation theory and related areas such as category O, character sheaves, knot homology and such. The notation of Harish-Chandra bimodules has been generalized to the context of filtered quantizations, affine Lie algebras, Deligne categories. In this talk, I will introduce the category of Harish-Chandra bimodules for quantum groups. When the parameter $q$ of quantum group is an odd order roots of unity, I will relate the category of quantum Harish-Chandra bimodules to the category of affine Soergel bimodules and Non-commutative Springer resolutions.
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
Lucas Buzaglo (UCSD)
Title: The boundary Carrollian conformal algebra
Abstract: I will talk about the boundary Carrollian conformal algebra (BCCA), an infinite-dimensional Lie algebra recently discovered in the context of Carrollian physics. The BCCA is an intriguing object from both physical and mathematical perspectives, since it is a filtered but not graded Lie algebra. In this talk, I will briefly introduce the physical context in which this Lie algebra appeared, and then mention some of my recent work on the representation theory of this Lie algebra. This is joint work with Xiao He, Tuan Pham, Haijun Tan, Girish Vishwa, and Kaiming Zhao.
June 4, 2026
Helen Wong (Claremont McKenna)
Title: TBD
Abstract: TBD