During semester, this seminar is usually on Wednesdays from 12 pm — 1 pm, in the SMRI Seminar Room (A12 Macleay Room 301). To receive notifications of upcoming seminars, please subscribe to the weekly seminar email update.
Upcoming:
Geometric & Topology Seminar, ‘Divergence in Coxeter groups‘
Anne Thomas, University of Sydney
Wednesday 25th March 2026 at 12 pm, SMRI Seminar Room (A12 Macleay Room 301)
Abstract: The divergence of a pair of geodesic rays measures how fast they move away from each other. In the 1990s, Gersten used this idea to define a quasi-isometry invariant for finitely generated groups, also called divergence, and divergence has since been investigated for many families of groups of importance in geometric group theory. In this talk, we discuss progress on understanding divergence in (infinite) Coxeter groups. The right-angled case is now well-understood, and we have a partly conjectural picture for general Coxeter groups. This includes joint work and work-in-progress with Pallavi Dani, Max Mikkelsen, Yusra Naqvi and Ignat Soroko.
Past:
Geometric & Topology Seminar, ‘Non-additivity of the unknotting number‘
Hans Boden, McMaster University
Wednesday 11th March 2026
Abstract: Every knot diagram can be converted into an unknot diagram by applying crossing changes. For a given knot, the minimum number of crossing changes needed, taken over all representative diagrams, is the unknotting number of that knot. In 1937 Wendt studied the unknotting number of composite knots, namely those of the form K # J. He posited that the unknotting number of K # J should be equal to the sum of the unknotting numbers of K and and that of J. Early evidence in support of the conjecture came from Marty Scharlemann, who in 1985 proved it for knots K, J with unknotting number one. The goal of the talk is to survey two recent preprints disproving the conjecture. The preprints are due to Mark Brittenham and Susan Hermiller, and their discovery has been a major breakthrough and suggests that knot theorists really do not understand unknotting at all well!
Australian Geometric Topology Webinar, ‘Embedding in Three Dimensions: Topology, Algorithms, and Complexity‘
Eric Sedgwick, DePaul University, Chicago
Wednesday 4th March, 2026
Abstract: Given a finite simplicial complex, does it embed in three-dimensional space without self-intersections? More generally, for integers k and d, one can ask whether a k-dimensional complex embeds in d-dimensional space; the answer depends dramatically on the relationship between k and d. I will focus on the case of 2– and 3–complexes in dimension three. These embeddability problems are decidable, and their solution relies on tools from 3-manifold topology, including normal surface theory and Dehn surgery. I will sketch the structure of the decision procedure and briefly indicate how the same ideas also reveal unexpected computational hardness.
Geometry & Topology Seminar, ‘The symplectic geometry of branched hyperbolic structures‘
Arnaud Maret, Université de Strasbourg
Wednesday 25th February, 2026
Abstract: Hyperbolic geometry is one of the most iconic geometries studied on surfaces. When conical singularities at certain points are allowed, whose angles are integer multiples of 2π, one obtains branched hyperbolic structures. An important problem, proposed by Goldman, is to determine which surface group representations arise as holonomies of branched hyperbolic structures. In this talk, I will focus on the case of genus-2 surfaces and explain how to construct Fenchel–Nielsen (i.e. Darboux) coordinates on the space of holonomies of these branched hyperbolic structures. This is joint work with Gianluca Faraco.