Julian Wykowski
Julian Wykowski
I am a final-year PhD candidate in Mathematics at the University of Cambridge, working on geometric group theory under the supervision of Gareth Wilkes. My email address is jw2006@cam.ac.uk.
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.
Previously, I completed an MSci in Mathematics at Imperial College London. My MSci thesis was on Galois correspondence in Model Theory (PDF) under the supervision of Charlotte Kestner.
Publications and Preprints
Nikolov, N. & Wykowski, J. The Profinite Rigidity of Torsion-Free Lamplighter Groups. Preprint at ArXiv: 2512.19295 [math.GR] (Dec 2025).
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].
Seminars
I co-organise the Junior Geometry Seminar in Cambridge. Please get in touch if you have any suggestions for speakers or would like to be added to the mailing list.
I also co-organise the GGT journal club. Please get in touch if you'd like to be added to the mailing list.
Teaching
I am supervising for the Part II Algebraic Topology course this Michealmas. The example sheets will be released here.