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:
Australian Geometric Topology Webinar, ‘From Lando graphs to extreme Khovanov homology for certain link families‘
Seung Yeop Yang, Kyungpook National University
Wednesday 15th April 2026 at 12 pm, Zoom with a screening in the SMRI Seminar Room (A12 Macleay Room 301)
Abstract: Khovanov homology is a categorification of the Jones polynomial and provides a powerful invariant of knots and links. One of the fundamental questions in the subject is the existence of geometric realizations of Khovanov homology. A notable answer was given by Lipshitz and Sarkar, who associated to each link a family of spectra whose reduced singular cohomology recovers its Khovanov homology. In a different direction, González-Meneses, Manchón, and Silvero identified the extreme Khovanov homology of a link diagram with the reduced (co)homology of the independence simplicial complex of the corresponding Lando graph.
In this talk, we present explicit realizations of the real-extreme Khovanov homology for certain families of links using Lando graphs. This establishes an explicit connection between combinatorial structures arising from link diagrams and topological realizations of their homological invariants. In particular, we describe such realizations for several families of links, including pretzel links and 2-bridge links. This is joint work with Mark H. Siggers, Jinseok Oh, and Hongdae Yun.
Geometric & Topology Seminar, ‘Topology in quantum systems’
Adam Rennie, University of Wollongong
Wednesday 22nd April 2026 at 12 pm, SMRI Seminar Room (A12 Macleay Room 301)
Abstract: The machinery underpinning the Atiyah-Singer index theorem applies in much more general situations. I will give some examples from geometry and dynamics before describing two applications in quantum physics: topological insulators and scattering systems. I will not get into the technical weeds in this talk, focussing on how stable homotopy invariants arise. As an overview talk, this relies on many prior works and many coauthors. I will try to indicate these as I go along.
Past:
Australian Geometric Topology Webinar, ‘On the mapping class group of the universal smoothing of R^4’
Arunima Ray, University of Melbourne
Wednesday 1 April, 2026
Abstract: I’ll begin with an overview of exotic smoothings of R^4 and their mapping class groups. In the rest of the talk I will give a high-level sketch a proof showing that compactly supported diffeomorphisms of the Freedman-Taylor universal smoothing of R^4 are trivial in its smooth mapping class group. The proof involves an adaptation to the non-compact setting of a pseudo-isotopy-implies-isotopy argument of Quinn, and its recent correction by Gabai-Gay-Hartman-Krushkal-Powell. This is based on joint work in progress with Gompf and Orson.
Geometric & Topology Seminar, ‘Divergence in Coxeter groups‘
Anne Thomas, University of Sydney
Wednesday 25th March 2026
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.
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.