Agnese Barbensi

The 3D index and Dehn filling We provide a rigorous proof of the Gang-Yonekura formula describing the transformation of the 3D index under Dehn filling a cusp in an orientable 3-manifold. The 3D index, originally introduced by Dim...

arxiv.org/abs/2509.09886
/The 3D index and Dehn filling/
Daniele Celoria, Craig D. Hodgson, J. Hyam Rubinstein

6/ All of this is backed by extensive certified computations, a beautiful blend of theory and code. If you're into geometric topology, or the interface of maths and physics, this is worth a read!!

A figure from the paper showing a path on the Farey graph.

5/ As an application, they compute indices for large surgeries, confirming conjectures and revealing new structural patterns.The results suggest a well-defined extension of the index to closed manifolds.

A figure from the paper showing a schematic for the effect of replacing a standard cusp C with a layered solid torus L along the filling curve α.

4/ Building on a reinterpretation of the index as a generating function over Q-normal surfaces, the authors develop a gluing formula for relative indices.

3/ The 3D index is a q-series inspired by physics, associated to ideal triangulations of cusped 3-manifolds. It encodes rich geometric and physical information, and it is conjecturally a topological invariant.

A figure from the paper, showing the two ways of completing a boundary curve to a spun annulus in the standard cusp. The two possibilities spin in opposite directions, and are related by an involution.

2/ The paper proves the Gang–Yonekura formula, describing how the 3D index transforms under Dehn filling a cusp in a 3-manifold.

The 3D index and Dehn filling We provide a rigorous proof of the Gang-Yonekura formula describing the transformation of the 3D index under Dehn filling a cusp in an orientable 3-manifold. The 3D index, originally introduced by Dim...

1/ Husband's paper out on arXiv! He's not one to post about his work, but this one is a big and kind of a breakthrough!!
arxiv.org/abs/2509.09886

Embedding Sustainability in Undergraduate Mathematics with Actionable Case Studies There is a growing need to integrate sustainability into tertiary mathematics education given the urgency of addressing global environmental challenges. This paper presents four case studies from Aust...

Ooh arXiv paper from @matthholden.bsky.social @katehelmstedt.bsky.social about embedding sustainability in undergraduate maths with case studies 👀 Looks very actionable!

arxiv.org/abs/2508.07594

Job alert: 2.75 -3 yr postdoc in Mathematical ecology/epidemiology or Decision Sci at the University of Queensland on the value of information for decisions with @hugepossum.bsky.social @katehelmstedt.bsky.social Katriona Shea & myself #MathSky 🌍 uq.wd3.myworkdayjobs.com/uqcareers/jo... please share

Congrats!!! @monsoon0.bsky.social

Discrete signature tensors for persistence landscapes Signature tensors of paths are a versatile tool for data analysis and machine learning. Recently, they have been applied to persistent homology, by embedding barcodes into spaces of paths. Among the d...

Very excited that my paper "Discrete signature tensors for persistence landscapes" with @haharrington.bsky.social and Daniel Tolosa is now on arXiv! We use discrete signature tensors to vectorise barcodes, and we showcase such approach on a knotted protein dataset.

arxiv.org/abs/2505.02800

Exciting to see this one out!!

Topologically Directed Simulations Reveal the Impact of Geometric Constraints on Knotted Proteins Simulations of knotting and unknotting in polymers or other filaments rely on random processes to facilitate topological changes. Here we introduce a method of \textit{topological steering} to determi...

Very happy that my work with @agnesebarbensi.bsky.social is finally preprinted. We developed a very cool technique to see how the topology of open curves evolves, and applied it to learn some cool things about knotted proteins.

arxiv.org/abs/2504.12659

A screenshot from the website linked, showing my picture and title and abstract from my talk

Excited about this one: seminargeotop-a.com/next-talks
Speaking in a few hours (7am Los Angeles/10am NY/3pm Paris and midnight QLD) about a joint work with @aklotz.bsky.social and Dimos Goundaroulis!

New preprint with @finnthompson.bsky.social and former student Maria Maalouf looking at how the space writhe of knots is correlated with their signature, using molecular dynamics simulations.

arxiv.org/html/2501.02...

My fault!!! Hopefully out soon

Picture of a talk title slide

@agnesebarbensi.bsky.social is presenting our research three hours ago tomorrow right now in New Zealand

Thanks!!

We hope that the topological information we generated here will aid and inspire new functional and evolutionary analysis of proteins!

We think that this only scratches the surfaces of what topology can teach us on proteins. We mapped the topology of the currently known protein universe and made it available online.

On the top, 2-dimensional topological features shown superimposed on two different protein structures. These proteins are the same enzyme on different organisms, and they are homologous. On the bottom, the result of statistical analysis of 2-dim top features on enzymes across different organisms, showing that thermophiles organisms have proteins with more compact features.

Topological features also identify locations of mutations that are disease-causing and structurally damaging, and capture differences between homologous enzymes in thermophile and mesophile organisms.

Cartoon representation of a protein with colours indicating CATH domains (on the left) and topological clusters (on the right)

We analyze topologically the whole of AlphaFold2, and show how topological features capture global features of the protein universe, such as domain architecture, binding sites and thermodynamics.

Image showing a schematic for the output of topological analysis of the protein universe

New preprint "The Topological Properties of the Protein Universe". Work carried on by PhD student Christian Madsen, with @syz.bsky.social, M. Stumpf, D. Pires and others www.biorxiv.org/content/10.1...