Julian Wykowski
Julian Wykowski
I am a postdoctoral researcher at the Institute for Algebra and Geometry of the Karlsruhe Institute of Technology (KIT), working in the research group of Elia Fioravanti. My email is julian.wykowski@kit.edu.
Previously, I obtained a PhD in Mathematics at the University of Cambridge, with a thesis on the Profinite Rigidity of Groups Acting on Trees and Modules supervised by Gareth Wilkes. Before that, I completed an MSci in Mathematics at Imperial College London.
My research interests revolve around profinite rigidity and the residual properties of discrete groups. I aim to connect the discrete and profinite worlds of group theory using tools from geometry, representation theory, as well as commutative and homological algebra. My most recent research was the subject of my talk Profinite Rigidity, Noetherian Domains, and Solvable Groups at the Isaac Newton Institute, a recording of which is available here.
Publications and Preprints
Nikolov, N. & Wykowski, J. The Profinite Rigidity of Torsion-Free Lamplighter Groups. Mathematische Annalen 396, 17 (2026). ISSN: 0025-5831. DOI: 10.1007/s00208-026-03548-9. ArXiv: 2512.19295 [math.GR].
Wykowski, J. The Profinite Rigidity of Free Metabelian Groups. Preprint at ArXiv: 2503.10321 [math.GR] (Mar 2025).
Wykowski, J. Profinite Rigidity over Noetherian Domains. Preprint at ArXiv: 2502.10278 [math.GR] (Feb 2025).
Cohen, W. & Wykowski, J. Cohomological Separability of Baumslag–Solitar Groups and Their Generalisations. Journal of Algebra 668, 660–693 (2026). ISSN: 0021-8693. DOI: 10.1016/j.jalgebra.2025.08.044. ArXiv: 2406.03960 [math.GR].
Phan, L., …, Wykowski, J., …, et al. A benchmark of expert-level academic questions to assess AI capabilities. Nature 649, 1139–1146 (2026). DOI: 10.1038/s41586-025-09962-4. ArXiv: 2501.14249 [cs.LG]. See also the NY Times Article.
Wykowski, J. Profinite Subgroup Accessibility and Recognition of Amalgamated Factors. Groups, Geometry, and Dynamics (2025), published online first. ISSN: 1661-7215. DOI: 10.4171/ggd/851. ArXiv: 2308.12185 [math.GR].
Wykowski, J. & Schedler, T. An investigation into Lie algebra representations obtained from regular holonomic D-modules (2021). Preprint at ArXiv: 2111.14774 [math.AG].
Teaching
At Cambridge, I supervised Part II Algebraic Topology across six college, in the academic years 2022-2023 and 2025-2026.
I was also an academic tutor for the Downing College International Programme, where I designed and taught the first iteration of the Foundations of Algebra and Cryptography course.