Calendar

Posted January 28, 2026

Geometry and Topology Seminar Seminar website

Konrad Wrobel, University of Texas at Austin
Measure equivalence classification of Baumslag-Solitar groups

We complete the classification of Baumslag-Solitar groups up to measure equivalence by showing all Baumslag-Solitar groups with nonunimodular Bass-Serre tree are measure equivalent (i.e., BS(r,s) with r between 1 and s). The proof makes critical use of combinatorial descriptive set theory tools in the measure class preserving setting and passes through the world of measure equivalence of nonunimodular locally compact groups. In particular, as an intermediate step we obtain measure equivalence couplings between all groups of the form Aut(T_{r,s}) for r between 1 and s where T_{r,s} is the directed tree with r incoming edges and s outgoing edges at each vertex. This is joint work with Damien Gaboriau, Antoine Poulin, Anush Tserunyan, and Robin Tucker-Drob.

Posted January 28, 2026
Last modified February 3, 2026

Geometry and Topology Seminar Seminar website

Joshua Sabloff, Haverford College
On the Non-Orientable Genera of a Knot: Connections and Comparisons

We define a new quantity, the Euler-normalized non-orientable genus, to connect a variety of ideas in the theory of non-orientable surfaces bounded by knots.  We use this quantity to explore the geography of non-orientable surfaces bounded by a fixed knot in 3 and 4 dimensions.  In particular, we will use the Euler-normalized non-orientable genus to reframe non-orientable slice-torus bounds on the (ordinary) non-orientable 4-genus and to bound below the Turaev genus as a measure of distance to an alternating knot.  This is joint work with Julia Knihs, Jeanette Patel, and Thea Rugg.

Posted January 28, 2026
Last modified February 17, 2026

Geometry and Topology Seminar Seminar website

Nilangshu Bhattacharyya, Louisiana State University
Steenrod Square on Khovanov Homology

Khovanov homology assigns a knot or a link to a bigraded homology theory that categorifies the Jones polynomial. It has concrete applications, for instance Rasmussen’s $s$-invariant, extracted from Lee’s deformation, which gives a lower bound on the smooth slice genus. At the same time, while the theory is very combinatorial and closely tied to the representation theory of $U_q(\mathfrak{sl}_2)$, it can be hard to see the underlying geometric picture directly from the homology groups. The stable homotopy refinement, introduced by Lipshitz and Sarkar, upgrades Khovanov homology to a space-level invariant: a spectrum whose cohomology recovers Khovanov homology while supporting additional structure that is invisible at the level of homology. This refinement induces stable cohomology operations, such as Steenrod squares, on Khovanov homology. In this talk, I will explain how to compute $Sq^1$ and $Sq^2$ on Khovanov homology.

Posted January 28, 2026
Last modified February 17, 2026

Geometry and Topology Seminar Seminar website

Nir Gadish, University of Pennsylvania
Letter braiding invariants of words in groups

How can we tell if a group element can be written as k-fold nested commutator? One way is to find a collection of computable function that vanish only on nested commutators. This talk will introduce letter-braiding invariants - these are elementarily defined functions on words, inspired by the homotopy theory of loop-spaces and carrying deep geometric content. They give a universal finite-type invariant for arbitrary groups, extending the influential Magnus expansion of free groups that already had countless applications in low dimensional topology. As a consequence we get new geometric formulas for braid and link invariants, and a way to linearize automorphisms of general groups that specializes to the Johnson homomorphism of mapping class groups.

Posted January 19, 2026
Last modified March 3, 2026

Geometry and Topology Seminar Seminar website

Ettore Marmo, Università degli Studi di Milano-Bicocca
Toric arrangements and Bloch-Kato pro-p groups

For every field K we can define a distinguished extension K^{sep} called its separable closure. The maximal pro-p quotient G_K(p) of the Galois group $G_K = Gal(K^{sep}/K)$ is called the maximal pro-p Galois group of K, many arithmetical properties of the field are encoded in the structure of this group. It is interesting to ask which pro-p groups can be realized as the maximal pro-p Galois group of some field. It is known that any such group must also satisfy a cohomological property called the Bloch-Kato property. In this talk we will discuss some families of pro-p groups arising as from toric arrangements and some techniques to study the Bloch-Kato property in this context. This talk is based on joint work with Th. Weigel and E. Delucchi.

Posted March 17, 2026

Geometry and Topology Seminar Seminar website

Jonathan Fruchter, University of Bonn
Virtual homological torsion in low dimensions

A long-standing conjecture of Bergeron and Venkatesh predicts that in closed hyperbolic 3-manifolds, the amount of torsion in the first homology of finite-sheeted normal covers should grow exponentially with the degree of the cover as the covers become larger, at a rate reflecting the volume of the manifold. Yet no finitely presented residually finite group is known to exhibit such behaviour, and meaningful lower bounds on torsion growth are rare. In this talk I will explain how a particular two-dimensional lens offers a clearer view of some of the underlying mechanisms that create homological torsion in finite covers, and how they might relate to its growth. If time allows, I will also discuss how these ideas connect to the question of profinite rigidity: how much information about a group is encoded in its finite quotients.