Forrest Glebe

So far, my research has centered around "stability problems" for groups. That is when an "almost" multiplicative map from a group to complex unitary groups is "close" to a genuinely multiplicative map, for various formal definitions of "almost" and "close."  My research so far has been concerned with making explicit almost-representations that are far from genuine representations. Lately, I've been thinking about vector bundles of associated to almost-representations and topological invariants associated to them.

Non math hobbies of mine include, hiking, table-top roleplaying games, and reading fantasy and science fiction.  Some of my favorite series/novels at the moment are A Song of Ice and Fire by George R.R. Martin, the Earthseed novels by Octavia Butler, the Farseer trilogy by Robin Hobb, the Imperial Radch trilogy by Ann Leckie, The Space Between Worlds by Micaiah Jonson, the Broken Earth trilogy by N.K. Jemisin, and Slaughterhouse-Five by Kurt Vonnegut.

Publications and preprints:

5) Dadarlat, M. Glebe, F. Central extensions and almost representations. arXiv, 2024

https://arxiv.org/abs/2502.04590

4) Glebe, F A cup product obstruction to Frobenius stability, To appear in Münster Journal of Mathematics 2024

https://arxiv.org/abs/2312.01533

3) Glebe, F. Frobenius Non-Stability of Nilpotent Groups. To appear in Advances in Mathematics 428:Paper No. 109129 (2023)

 https://arxiv.org/abs/2209.05425 

2) Glebe, F. A constructive proof that many groups with non-torsion 2-cohomology are not matricially stable. Groups, Geometry, and Dynamics, 19:195-226 2025 

https://arxiv.org/abs/2204.10354 

1) Brauner, S., Glebe, F. & Perkinson, D. Enumerating linear systems on graphs. Mathematische Zeitschrift 296, 1101–1134 (2020) 

https://arxiv.org/abs/1906.04768