During the Winter 2026 quarter, all of our meetings will be held in-person in Skye Hall 268.
Talks will run from 11a-12p PT, but feel free to show up early for socializing with the speaker.
Current organizers: Brian Collier, Filippo Mazzoli
WINTER AND SPRING 2026 SCHEDULE
January 9th, 2026 NO TALK THIS WEEK
January 16th, 2026
Brian Collier (UCR)
Title: Counting connected components of character varieties.
Abstract: In this talk I will present the classification of the connected component count of character varieties of surface groups into real semisimple Lie groups. In particular, I will discuss how for compact and complex groups, the components are classified by topological invariants. while for real groups, something more interesting can occur.
January 23rd, 2026
Fernando Al Assal (University of Wisconsin Madison)
Title: Asymptotic properties of essential surfaces
Abstract: Let M be a real hyperbolic 3-manifold. A sequence of distinct (non-commensurable) essential closed surfaces in M is asymptotically geodesic if their principal curvatures go uniformly to zero. When M is closed, these sequences exist abundantly by the Kahn-Markovic surface subgroup theorem, and we will discuss the fact that such surfaces are always asymptotically dense, even though they do not always equidistribute. We will also talk about the fact that such sequences do not exist when M is geometrically finite of infinite volume. This is joint work with Ben Lowe.
Finally, time permitting, we will describe an ongoing project with Mitul Islam and Filippo Mazzoli aiming to build essential surfaces in a 2-complex dimensional complex hyperbolic manifold that have a prescribed ratio of their Toledo number by their Euler characteristic.
January 30th, 2026
Sarah Yeakel (UCR)
Title: Isovariant Homotopy Theory
Abstract: Given a finite group G and two G-spaces, an isovariant map between them is a continuous function that preserves both the G-action and isotropy subgroups. The category of G-spaces with isovariant maps has a nice notion of homotopy theory where homotopy equivalences can capture interesting structure on manifolds. In this talk, we'll discuss some homotopical results in this category and hopefully an interesting application in progress with Inbar Klang.
February 13th, 2026
Fred Wilhelm (UCR)
Title: PL-Stability, finiteness and dimension 4
Abstract: See PDF attached.
February 20th, 2026
Title: A geometric correspondence for reparameterizations of geodesic flows of hyperbolic groups
Abstract: Given a closed hyperbolic surface, its Teichmüller space is a classical construction that parameterizes the geometric actions of its fundamental group on the hyperbolic plane. This space can be enlarged to a metric space that encodes all its geometric actions on Gromov hyperbolic spaces. This enlarged space is infinite dimensional, as it contains all its Hitchin components, as well as other geometric/probabilistic spaces defined in terms of the fundamental group. In this talk I will present a joint work with Stephen Cantrell and Dídac Martínez-Granado, in which we describe an explicit correspondence between this space and the space of reparameterizations of the geodesic flow of the surface. Our argument relies on Green metrics, which encode the behavior of random walks on the fundamental group.
February 27th, 2026
TBA
Title: TBA
Abstract: TBA
March 13th, 2026
Rodrigo Pereira (University of Porto)
Title:
Abstract:
March 20th, 2026 NO TALK THIS WEEK
March 27th, 2026 NO TALK THIS WEEK (Spring break)
April 24th , 2026
TBA
Title: TBA
Abstract: TBA
May 1st, 2026
Mason Hart (UVA)
Title:
Abstract:
May 8th , 2026
Sara Maloni (UVA)
Title: TBA
Abstract: TBA