Jan 30, 2026 Speaker :  Chloé Postel-Vinay

Affiliation:-  U  Chicago 

Title:-  k-shuffle braid groups

Abstract:- Braid groups are known to arise as from many places, two of which are as the Garside group obtained from the poset of non-crossing partitions, and as the fundamental group of the space of square-free complex polynomials of degree n. The latter is a K(B_n,1) while the former can be used to build a CW-complex with nice combinatorial properties, which is also a K(B_n,1). In 2024, McCammond and Dougherty described explicitly the homotopy allowing to go from one to the other.

In this talk, we introduce a new family of groups called the k-shuffle braid groups. We will see how they arise in two similar contexts: first, we will look at certain families of non-crossing partitions and obtain a (metric) CW-complex following classical arguments from Garside theory for Artin groups. Second, from spaces of complex monic polynomials with a certain set of prescribed regular values. Both spaces also happen to be classifying spaces.

No prior knowledge about braid groups will be assumed.

Feb. 13, 2026 Speaker :   Miri Son

Affiliation:-  Rice University

Title:-  Classification of SL(n,R)-actions on closed manifolds 

Abstract:-  Recently, Fisher and Melnick classified SL(n,R)-actions on n-dimensional manifolds for n≥3. In this talk, we generalize this result by classifying smooth or real-analytic SL(n,R)-actions on m-dimensional manifolds for 3≤n≤m≤2n-3. This work is motivated by the Zimmer program and is central to it, as Lie group actions restrict to their lattice actions. 

This classification relies on the linearization of SL(n,R)-actions when there is a global fixed point. The analytic case was proved by Guillemin—Sternberg and Kushinirenko. We discuss the smooth case which is ongoing joint work with Insung Park.

Feb. 20, 2026 Speaker :   Junzhi Huang 

Affiliation:-  Yale University 

Title:-  Pseudo-Anosov flows and geometry of transverse surfaces

Abstract:-  Pseudo-Anosov homeomorphisms are a class of interesting homeomorphisms of surfaces. Suspending a pseudo-Anosov homeomorphism in a 3-dimensional pseudo-Anosov mapping tori gives a pseudo-Anosov flow. Such flows turn out to be extremely useful in understanding the topological structure and organizing classes of surfaces in a 3-manifold. I will introduce some basics of pseudo-Anosov homeomorphisms and flows, and then talk about a beautiful result by Cooper-Long-Reid, generalized by Fenley, which shows that the geometry type of a transverse surface can be determined by combinatorial information encoded by the flow.

March 6, 2026 Speaker :- Ellis Buckminster

Affiliation:-  University of Pennsylvania 

Title:-  Flows, foliations, and actions on circles 

Abstract:- When a closed hyperbolic three-manifold M can be expressed as a surface bundle over the circle, Thurston showed the monodromy is a pseudo-Anosov map — the type of surface homeomorphisms with the most interesting dynamics. The universal cover of the surface can be naturally compactified with a circle, and this circle captures all the information about M and the pseudo-Anosov map. By work of Fenley and Barbot, considering this picture from a more flow-theoretic perspective allows us to recover much of this structure in a broader setting. In particular, one can still define an action of the fundamental group on a circle, and this circle recovers the original pseudo-Anosov flow by work of Barthelme--Frankel--Mann. 

March 20, 2026 Speaker :-  Junmo Ryang 

Affiliation:-  Rice University  

Title:- Pseudo-Anosov subgroups of surface bundles over tori  

Abstract:-  In 2002, Farb and Mosher introduced the notion of convex cocompactness in the mapping class group to capture coarse geometric information of the associated surface group extensions. Convex cocompact subgroups are necessarily finitely generated and purely pseudo-Anosov, but it is an open question whether the converse is true. Several partial results are known in certain settings, however. For example, work of Dowdall, Kent, Leininger, Russell, and Schleimer give a positive answer for subgroups of fibered 3-manifold groups (aka surface-by-cyclic extensions) naturally embedded in punctured mapping class groups via the Birman exact sequence. We present a generalization of this in the setting of surface-by-abelian extensions.