Jonathan Fruchter

📧 j🅾︎nathan.fr🆄chter 🐌 icmat.es Office 101, Instituto de Ciencias Matemáticas, Madrid

_{📃 Papers 🔸 🎓 Teaching 🔸 🎇 Beyond}

I am a Severo Ochoa postdoctoral research associate at the Instituto de Ciencias Matemáticas (ICMAT), Madrid.

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 am also interested in model theory and the first-order theory of groups.

Previously, I was a postdoctoral research associate at the University of Bonn, working in Giles Gardam’s team. I completed my DPhil at the University of Oxford under the supervision of Martin Bridson, and 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, to appear in the Proceedings of the AMS.

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)