Jonathan Fruchter

📧 fruchter [at] math.uni-bonn.de 1.27, Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115

_{📃 Papers 🔸 🎓 Teaching 🔸 🎇 Beyond}

Postdoctoral research associate at the University of Bonn, working in Giles Gardam’s team.

My research is in geometric group theory and low-dimensional topology. I study negatively curved groups and spaces by looking at the asymptotic behaviour of their finite-sheeted covers, often with applications to profinite rigidity. I also work with group rings of infinite groups, focusing on the Kaplansly conjectures, and I am interested in model theory and the first-order theory of groups.

I completed my DPhil at the University of Oxford, under the supervision of Martin Bridson. Before that, I obtained my Master’s degree at the Hebrew University of Jerusalem under the supervision of Zlil Sela.

Research papers: ⬆️

Virtual homological torsion: abundance versus growth in books of $I$-bundles.
🔗arXiv:2509.22052.

Homological torsion growth in non-normal chains of graphs of free groups, with Dario Ascari.
🔗arXiv:2509.15075.

Virtual homological torsion in graphs of free groups with cyclic edge groups, with Dario Ascari.
🔗arXiv:2505.20960.
_{Extras: Recorded talk. Poster and its accompanying casual extended abstract (presented at Martin Bridson’s 60th birthday conference).}

Virtual homology of limit groups and profinite rigidity of direct products, with Ismael Morales.
🔗arXiv:2209.14925, to appear in the Israel Journal of Mathematics.

Limit groups over coherent right-angled Artin groups are cyclic subgroup separable.
Michigan Mathematical Journal 73-5 (2023): 909-923 🔗(journal version) 🔗(arXiv:2101.10458).

Formal solutions and the first-order theory of acylindrically hyperbolic groups, with Simon André.
Journal of the London Mathematical Society 105-2 (2022), 1012-1072 🔗(open access).

Teaching:⬆️

In Winter Semester 2024-2025 I gave a lecture course titled ``Groups, Geometry and Logic’‘ (Module V5D4 - Selected Topics in Geometry). The course revolved mostly around the first-order theory of non-abelian free groups. Lecture notes are available.
In summer 2024 I gave a mini-course on profinite rigidity (with an emphasis on low-dimensional topology) as part of the Workshop on Profinite Rigidity at the Karlsruher Institut für Technologie (KIT). Lecture notes are available.
In 2022-2023 I was a Stipendiary Lecturer in Pure Mathematics at Exeter College (University of Oxford), teaching A2: Metric Spaces and Complex Analysis in Michaelmas ‘22-23 and A4: Integration in Hilary ‘23.
Before that I was a tutor and a TA at the University of Oxford, the Hebrew University of Jerusalem and Reichman University (IDC Herzliya). I taught linear algebra, discrete mathematics, general topology, set theory, mathematical logic, infinite groups, geometry of surfaces, group theory and integration.

Mathematics beyond research:⬆️

I really enjoy it when mathematics and visual arts come together.

In ‘20-21 I volunteered with Multaka and co-produced the Precious and Rare: Islamic Metalwork from The Courtauld exhibition at the History of Science in Oxford.
I made a short animated video explaining symmetry for the exhibition, and you can see me talking about the exhibition here. I also made a computer programme which allowed exhibition visitors to generate their own symmetric patterns inspired by Islamic art (feel free to email me if you made a cool design and want to share):

(compatible with mobile devices - drag the point on the big triangle)